Dataset Viewer
configuration_id
int64 0
7
| load_position
float64 0
0.5
| parameters
stringclasses 4
values | x_coordinates
listlengths 100
200
| shear_force
listlengths 100
200
| bending_moment
listlengths 100
200
| slope
listlengths 100
200
| deflection
listlengths 100
200
| shear_force_info
stringclasses 4
values | bending_moment_info
stringclasses 6
values | slope_info
stringclasses 6
values | deflection_info
stringclasses 6
values | points
stringclasses 8
values | segments
stringclasses 4
values | reactions
stringclasses 8
values | internal_loads
stringclasses 6
values | deflections
stringclasses 6
values | query
listlengths 4
4
| answer
listlengths 2
2
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0
| 0
|
{"P": "-P", "q": 0, "L": "L", "M": 0, "E": "E", "I": "I"}
|
[
0,
0.010101010101010102,
0.020202020202020204,
0.030303030303030304,
0.04040404040404041,
0.05050505050505051,
0.06060606060606061,
0.07070707070707072,
0.08080808080808081,
0.09090909090909091,
0.10101010101010102,
0.11111111111111112,
0.12121212121212122,
0.13131313131313133,
0.14141414141414144,
0.15151515151515152,
0.16161616161616163,
0.17171717171717174,
0.18181818181818182,
0.19191919191919193,
0.20202020202020204,
0.21212121212121213,
0.22222222222222224,
0.23232323232323235,
0.24242424242424243,
0.25252525252525254,
0.26262626262626265,
0.27272727272727276,
0.2828282828282829,
0.29292929292929293,
0.30303030303030304,
0.31313131313131315,
0.32323232323232326,
0.33333333333333337,
0.3434343434343435,
0.3535353535353536,
0.36363636363636365,
0.37373737373737376,
0.38383838383838387,
0.393939393939394,
0.4040404040404041,
0.4141414141414142,
0.42424242424242425,
0.43434343434343436,
0.4444444444444445,
0.4545454545454546,
0.4646464646464647,
0.4747474747474748,
0.48484848484848486,
0.494949494949495,
0.5050505050505051,
0.5151515151515152,
0.5252525252525253,
0.5353535353535354,
0.5454545454545455,
0.5555555555555556,
0.5656565656565657,
0.5757575757575758,
0.5858585858585859,
0.595959595959596,
0.6060606060606061,
0.6161616161616162,
0.6262626262626263,
0.6363636363636365,
0.6464646464646465,
0.6565656565656566,
0.6666666666666667,
0.6767676767676768,
0.686868686868687,
0.696969696969697,
0.7070707070707072,
0.7171717171717172,
0.7272727272727273,
0.7373737373737375,
0.7474747474747475,
0.7575757575757577,
0.7676767676767677,
0.7777777777777778,
0.787878787878788,
0.797979797979798,
0.8080808080808082,
0.8181818181818182,
0.8282828282828284,
0.8383838383838385,
0.8484848484848485,
0.8585858585858587,
0.8686868686868687,
0.8787878787878789,
0.888888888888889,
0.8989898989898991,
0.9090909090909092,
0.9191919191919192,
0.9292929292929294,
0.9393939393939394,
0.9494949494949496,
0.9595959595959597,
0.9696969696969697,
0.9797979797979799,
0.98989898989899,
1
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
{"local_extrema": [], "null": [[0.0, 0], [0.010101010101010102, 0], [0.020202020202020204, 0], [0.030303030303030304, 0], [0.04040404040404041, 0], [0.05050505050505051, 0], [0.06060606060606061, 0], [0.07070707070707072, 0], [0.08080808080808081, 0], [0.09090909090909091, 0], [0.10101010101010102, 0], [0.11111111111111112, 0], [0.12121212121212122, 0], [0.13131313131313133, 0], [0.14141414141414144, 0], [0.15151515151515152, 0], [0.16161616161616163, 0], [0.17171717171717174, 0], [0.18181818181818182, 0], [0.19191919191919193, 0], [0.20202020202020204, 0], [0.21212121212121213, 0], [0.22222222222222224, 0], [0.23232323232323235, 0], [0.24242424242424243, 0], [0.25252525252525254, 0], [0.26262626262626265, 0], [0.27272727272727276, 0], [0.2828282828282829, 0], [0.29292929292929293, 0], [0.30303030303030304, 0], [0.31313131313131315, 0], [0.32323232323232326, 0], [0.33333333333333337, 0], [0.3434343434343435, 0], [0.3535353535353536, 0], [0.36363636363636365, 0], [0.37373737373737376, 0], [0.38383838383838387, 0], [0.393939393939394, 0], [0.4040404040404041, 0], [0.4141414141414142, 0], [0.42424242424242425, 0], [0.43434343434343436, 0], [0.4444444444444445, 0], [0.4545454545454546, 0], [0.4646464646464647, 0], [0.4747474747474748, 0], [0.48484848484848486, 0], [0.494949494949495, 0], [0.5050505050505051, 0], [0.5151515151515152, 0], [0.5252525252525253, 0], [0.5353535353535354, 0], [0.5454545454545455, 0], [0.5555555555555556, 0], [0.5656565656565657, 0], [0.5757575757575758, 0], [0.5858585858585859, 0], [0.595959595959596, 0], [0.6060606060606061, 0], [0.6161616161616162, 0], [0.6262626262626263, 0], [0.6363636363636365, 0], [0.6464646464646465, 0], [0.6565656565656566, 0], [0.6666666666666667, 0], [0.6767676767676768, 0], [0.686868686868687, 0], [0.696969696969697, 0], [0.7070707070707072, 0], [0.7171717171717172, 0], [0.7272727272727273, 0], [0.7373737373737375, 0], [0.7474747474747475, 0], [0.7575757575757577, 0], [0.7676767676767677, 0], [0.7777777777777778, 0], [0.787878787878788, 0], [0.797979797979798, 0], [0.8080808080808082, 0], [0.8181818181818182, 0], [0.8282828282828284, 0], [0.8383838383838385, 0], [0.8484848484848485, 0], [0.8585858585858587, 0], [0.8686868686868687, 0], [0.8787878787878789, 0], [0.888888888888889, 0], [0.8989898989898991, 0], [0.9090909090909092, 0], [0.9191919191919192, 0], [0.9292929292929294, 0], [0.9393939393939394, 0], [0.9494949494949496, 0], [0.9595959595959597, 0], [0.9696969696969697, 0], [0.9797979797979799, 0], [0.98989898989899, 0], [1.0, 0]]}
|
{"local_extrema": [], "null": [[0.0, 0], [0.010101010101010102, 0], [0.020202020202020204, 0], [0.030303030303030304, 0], [0.04040404040404041, 0], [0.05050505050505051, 0], [0.06060606060606061, 0], [0.07070707070707072, 0], [0.08080808080808081, 0], [0.09090909090909091, 0], [0.10101010101010102, 0], [0.11111111111111112, 0], [0.12121212121212122, 0], [0.13131313131313133, 0], [0.14141414141414144, 0], [0.15151515151515152, 0], [0.16161616161616163, 0], [0.17171717171717174, 0], [0.18181818181818182, 0], [0.19191919191919193, 0], [0.20202020202020204, 0], [0.21212121212121213, 0], [0.22222222222222224, 0], [0.23232323232323235, 0], [0.24242424242424243, 0], [0.25252525252525254, 0], [0.26262626262626265, 0], [0.27272727272727276, 0], [0.2828282828282829, 0], [0.29292929292929293, 0], [0.30303030303030304, 0], [0.31313131313131315, 0], [0.32323232323232326, 0], [0.33333333333333337, 0], [0.3434343434343435, 0], [0.3535353535353536, 0], [0.36363636363636365, 0], [0.37373737373737376, 0], [0.38383838383838387, 0], [0.393939393939394, 0], [0.4040404040404041, 0], [0.4141414141414142, 0], [0.42424242424242425, 0], [0.43434343434343436, 0], [0.4444444444444445, 0], [0.4545454545454546, 0], [0.4646464646464647, 0], [0.4747474747474748, 0], [0.48484848484848486, 0], [0.494949494949495, 0], [0.5050505050505051, 0], [0.5151515151515152, 0], [0.5252525252525253, 0], [0.5353535353535354, 0], [0.5454545454545455, 0], [0.5555555555555556, 0], [0.5656565656565657, 0], [0.5757575757575758, 0], [0.5858585858585859, 0], [0.595959595959596, 0], [0.6060606060606061, 0], [0.6161616161616162, 0], [0.6262626262626263, 0], [0.6363636363636365, 0], [0.6464646464646465, 0], [0.6565656565656566, 0], [0.6666666666666667, 0], [0.6767676767676768, 0], [0.686868686868687, 0], [0.696969696969697, 0], [0.7070707070707072, 0], [0.7171717171717172, 0], [0.7272727272727273, 0], [0.7373737373737375, 0], [0.7474747474747475, 0], [0.7575757575757577, 0], [0.7676767676767677, 0], [0.7777777777777778, 0], [0.787878787878788, 0], [0.797979797979798, 0], [0.8080808080808082, 0], [0.8181818181818182, 0], [0.8282828282828284, 0], [0.8383838383838385, 0], [0.8484848484848485, 0], [0.8585858585858587, 0], [0.8686868686868687, 0], [0.8787878787878789, 0], [0.888888888888889, 0], [0.8989898989898991, 0], [0.9090909090909092, 0], [0.9191919191919192, 0], [0.9292929292929294, 0], [0.9393939393939394, 0], [0.9494949494949496, 0], [0.9595959595959597, 0], [0.9696969696969697, 0], [0.9797979797979799, 0], [0.98989898989899, 0], [1.0, 0]]}
|
{"local_extrema": [], "null": [[0.0, 0], [0.010101010101010102, 0], [0.020202020202020204, 0], [0.030303030303030304, 0], [0.04040404040404041, 0], [0.05050505050505051, 0], [0.06060606060606061, 0], [0.07070707070707072, 0], [0.08080808080808081, 0], [0.09090909090909091, 0], [0.10101010101010102, 0], [0.11111111111111112, 0], [0.12121212121212122, 0], [0.13131313131313133, 0], [0.14141414141414144, 0], [0.15151515151515152, 0], [0.16161616161616163, 0], [0.17171717171717174, 0], [0.18181818181818182, 0], [0.19191919191919193, 0], [0.20202020202020204, 0], [0.21212121212121213, 0], [0.22222222222222224, 0], [0.23232323232323235, 0], [0.24242424242424243, 0], [0.25252525252525254, 0], [0.26262626262626265, 0], [0.27272727272727276, 0], [0.2828282828282829, 0], [0.29292929292929293, 0], [0.30303030303030304, 0], [0.31313131313131315, 0], [0.32323232323232326, 0], [0.33333333333333337, 0], [0.3434343434343435, 0], [0.3535353535353536, 0], [0.36363636363636365, 0], [0.37373737373737376, 0], [0.38383838383838387, 0], [0.393939393939394, 0], [0.4040404040404041, 0], [0.4141414141414142, 0], [0.42424242424242425, 0], [0.43434343434343436, 0], [0.4444444444444445, 0], [0.4545454545454546, 0], [0.4646464646464647, 0], [0.4747474747474748, 0], [0.48484848484848486, 0], [0.494949494949495, 0], [0.5050505050505051, 0], [0.5151515151515152, 0], [0.5252525252525253, 0], [0.5353535353535354, 0], [0.5454545454545455, 0], [0.5555555555555556, 0], [0.5656565656565657, 0], [0.5757575757575758, 0], [0.5858585858585859, 0], [0.595959595959596, 0], [0.6060606060606061, 0], [0.6161616161616162, 0], [0.6262626262626263, 0], [0.6363636363636365, 0], [0.6464646464646465, 0], [0.6565656565656566, 0], [0.6666666666666667, 0], [0.6767676767676768, 0], [0.686868686868687, 0], [0.696969696969697, 0], [0.7070707070707072, 0], [0.7171717171717172, 0], [0.7272727272727273, 0], [0.7373737373737375, 0], [0.7474747474747475, 0], [0.7575757575757577, 0], [0.7676767676767677, 0], [0.7777777777777778, 0], [0.787878787878788, 0], [0.797979797979798, 0], [0.8080808080808082, 0], [0.8181818181818182, 0], [0.8282828282828284, 0], [0.8383838383838385, 0], [0.8484848484848485, 0], [0.8585858585858587, 0], [0.8686868686868687, 0], [0.8787878787878789, 0], [0.888888888888889, 0], [0.8989898989898991, 0], [0.9090909090909092, 0], [0.9191919191919192, 0], [0.9292929292929294, 0], [0.9393939393939394, 0], [0.9494949494949496, 0], [0.9595959595959597, 0], [0.9696969696969697, 0], [0.9797979797979799, 0], [0.98989898989899, 0], [1.0, 0]]}
|
{"local_extrema": [], "null": [[0.0, 0], [0.010101010101010102, 0], [0.020202020202020204, 0], [0.030303030303030304, 0], [0.04040404040404041, 0], [0.05050505050505051, 0], [0.06060606060606061, 0], [0.07070707070707072, 0], [0.08080808080808081, 0], [0.09090909090909091, 0], [0.10101010101010102, 0], [0.11111111111111112, 0], [0.12121212121212122, 0], [0.13131313131313133, 0], [0.14141414141414144, 0], [0.15151515151515152, 0], [0.16161616161616163, 0], [0.17171717171717174, 0], [0.18181818181818182, 0], [0.19191919191919193, 0], [0.20202020202020204, 0], [0.21212121212121213, 0], [0.22222222222222224, 0], [0.23232323232323235, 0], [0.24242424242424243, 0], [0.25252525252525254, 0], [0.26262626262626265, 0], [0.27272727272727276, 0], [0.2828282828282829, 0], [0.29292929292929293, 0], [0.30303030303030304, 0], [0.31313131313131315, 0], [0.32323232323232326, 0], [0.33333333333333337, 0], [0.3434343434343435, 0], [0.3535353535353536, 0], [0.36363636363636365, 0], [0.37373737373737376, 0], [0.38383838383838387, 0], [0.393939393939394, 0], [0.4040404040404041, 0], [0.4141414141414142, 0], [0.42424242424242425, 0], [0.43434343434343436, 0], [0.4444444444444445, 0], [0.4545454545454546, 0], [0.4646464646464647, 0], [0.4747474747474748, 0], [0.48484848484848486, 0], [0.494949494949495, 0], [0.5050505050505051, 0], [0.5151515151515152, 0], [0.5252525252525253, 0], [0.5353535353535354, 0], [0.5454545454545455, 0], [0.5555555555555556, 0], [0.5656565656565657, 0], [0.5757575757575758, 0], [0.5858585858585859, 0], [0.595959595959596, 0], [0.6060606060606061, 0], [0.6161616161616162, 0], [0.6262626262626263, 0], [0.6363636363636365, 0], [0.6464646464646465, 0], [0.6565656565656566, 0], [0.6666666666666667, 0], [0.6767676767676768, 0], [0.686868686868687, 0], [0.696969696969697, 0], [0.7070707070707072, 0], [0.7171717171717172, 0], [0.7272727272727273, 0], [0.7373737373737375, 0], [0.7474747474747475, 0], [0.7575757575757577, 0], [0.7676767676767677, 0], [0.7777777777777778, 0], [0.787878787878788, 0], [0.797979797979798, 0], [0.8080808080808082, 0], [0.8181818181818182, 0], [0.8282828282828284, 0], [0.8383838383838385, 0], [0.8484848484848485, 0], [0.8585858585858587, 0], [0.8686868686868687, 0], [0.8787878787878789, 0], [0.888888888888889, 0], [0.8989898989898991, 0], [0.9090909090909092, 0], [0.9191919191919192, 0], [0.9292929292929294, 0], [0.9393939393939394, 0], [0.9494949494949496, 0], [0.9595959595959597, 0], [0.9696969696969697, 0], [0.9797979797979799, 0], [0.98989898989899, 0], [1.0, 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "-P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "P"}, {"point": "L", "type": "Force", "value": "0"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "L"], "shear_force": "0", "bending_moment": "0"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "L"], "deflection": "0", "rotation": "0"}]}
|
[
"Question: \nDetermine the reaction forces at the pin support (x=0) and the roller support (x=L) for a beam of length L with a downward point load of -P at x=0.0*L.",
"Given a beam of length L with a pin support at one end and a roller support at the other, and a downward-point load of -P at the loaded end, calculate the reaction forces at the supports.",
"What are the reaction forces at the pin and roller supports of a beam with length L, a downward point load of -P at one end, and supported by a pin at x=0 and a roller at x=L?",
"What are the reaction forces at the pin support (x=0) and the roller support (x=L) of a beam with length L, given a downward point load of -P at the pin support end?"
] |
[
"P",
"0"
] |
1
| 0.5
|
{"P": "-P", "q": 0, "L": "L", "M": 0, "E": "E", "I": "I"}
|
[
0,
0.005050505050505051,
0.010101010101010102,
0.015151515151515152,
0.020202020202020204,
0.025252525252525256,
0.030303030303030304,
0.03535353535353536,
0.04040404040404041,
0.045454545454545456,
0.05050505050505051,
0.05555555555555556,
0.06060606060606061,
0.06565656565656566,
0.07070707070707072,
0.07575757575757576,
0.08080808080808081,
0.08585858585858587,
0.09090909090909091,
0.09595959595959597,
0.10101010101010102,
0.10606060606060606,
0.11111111111111112,
0.11616161616161617,
0.12121212121212122,
0.12626262626262627,
0.13131313131313133,
0.13636363636363638,
0.14141414141414144,
0.14646464646464646,
0.15151515151515152,
0.15656565656565657,
0.16161616161616163,
0.16666666666666669,
0.17171717171717174,
0.1767676767676768,
0.18181818181818182,
0.18686868686868688,
0.19191919191919193,
0.196969696969697,
0.20202020202020204,
0.2070707070707071,
0.21212121212121213,
0.21717171717171718,
0.22222222222222224,
0.2272727272727273,
0.23232323232323235,
0.2373737373737374,
0.24242424242424243,
0.2474747474747475,
0.25252525252525254,
0.2575757575757576,
0.26262626262626265,
0.2676767676767677,
0.27272727272727276,
0.2777777777777778,
0.2828282828282829,
0.2878787878787879,
0.29292929292929293,
0.297979797979798,
0.30303030303030304,
0.3080808080808081,
0.31313131313131315,
0.31818181818181823,
0.32323232323232326,
0.3282828282828283,
0.33333333333333337,
0.3383838383838384,
0.3434343434343435,
0.3484848484848485,
0.3535353535353536,
0.3585858585858586,
0.36363636363636365,
0.36868686868686873,
0.37373737373737376,
0.37878787878787884,
0.38383838383838387,
0.3888888888888889,
0.393939393939394,
0.398989898989899,
0.4040404040404041,
0.4090909090909091,
0.4141414141414142,
0.4191919191919192,
0.42424242424242425,
0.42929292929292934,
0.43434343434343436,
0.43939393939393945,
0.4444444444444445,
0.44949494949494956,
0.4545454545454546,
0.4595959595959596,
0.4646464646464647,
0.4696969696969697,
0.4747474747474748,
0.47979797979797983,
0.48484848484848486,
0.48989898989898994,
0.494949494949495,
0.5,
0.5,
0.5050505050505051,
0.51010101010101,
0.5151515151515151,
0.5202020202020202,
0.5252525252525253,
0.5303030303030303,
0.5353535353535354,
0.5404040404040404,
0.5454545454545454,
0.5505050505050505,
0.5555555555555556,
0.5606060606060606,
0.5656565656565656,
0.5707070707070707,
0.5757575757575758,
0.5808080808080808,
0.5858585858585859,
0.5909090909090909,
0.595959595959596,
0.601010101010101,
0.6060606060606061,
0.6111111111111112,
0.6161616161616161,
0.6212121212121212,
0.6262626262626263,
0.6313131313131313,
0.6363636363636364,
0.6414141414141414,
0.6464646464646464,
0.6515151515151515,
0.6565656565656566,
0.6616161616161617,
0.6666666666666667,
0.6717171717171717,
0.6767676767676768,
0.6818181818181819,
0.6868686868686869,
0.6919191919191919,
0.696969696969697,
0.702020202020202,
0.7070707070707071,
0.7121212121212122,
0.7171717171717171,
0.7222222222222222,
0.7272727272727273,
0.7323232323232324,
0.7373737373737375,
0.7424242424242424,
0.7474747474747475,
0.7525252525252526,
0.7575757575757576,
0.7626262626262627,
0.7676767676767677,
0.7727272727272727,
0.7777777777777778,
0.7828282828282829,
0.7878787878787878,
0.7929292929292929,
0.797979797979798,
0.803030303030303,
0.8080808080808082,
0.8131313131313131,
0.8181818181818182,
0.8232323232323233,
0.8282828282828283,
0.8333333333333334,
0.8383838383838385,
0.8434343434343434,
0.8484848484848485,
0.8535353535353536,
0.8585858585858586,
0.8636363636363636,
0.8686868686868687,
0.8737373737373737,
0.8787878787878789,
0.8838383838383839,
0.8888888888888888,
0.893939393939394,
0.898989898989899,
0.9040404040404041,
0.9090909090909092,
0.9141414141414141,
0.9191919191919192,
0.9242424242424243,
0.9292929292929293,
0.9343434343434344,
0.9393939393939394,
0.9444444444444444,
0.9494949494949496,
0.9545454545454546,
0.9595959595959596,
0.9646464646464648,
0.9696969696969697,
0.9747474747474748,
0.9797979797979799,
0.9848484848484849,
0.98989898989899,
0.994949494949495,
1
] |
[
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5
] |
[
0,
-0.0025252525252525255,
-0.005050505050505051,
-0.007575757575757576,
-0.010101010101010102,
-0.012626262626262628,
-0.015151515151515152,
-0.01767676767676768,
-0.020202020202020204,
-0.022727272727272728,
-0.025252525252525256,
-0.02777777777777778,
-0.030303030303030304,
-0.03282828282828283,
-0.03535353535353536,
-0.03787878787878788,
-0.04040404040404041,
-0.042929292929292935,
-0.045454545454545456,
-0.04797979797979798,
-0.05050505050505051,
-0.05303030303030303,
-0.05555555555555556,
-0.05808080808080809,
-0.06060606060606061,
-0.06313131313131314,
-0.06565656565656566,
-0.06818181818181819,
-0.07070707070707072,
-0.07323232323232323,
-0.07575757575757576,
-0.07828282828282829,
-0.08080808080808081,
-0.08333333333333334,
-0.08585858585858587,
-0.0883838383838384,
-0.09090909090909091,
-0.09343434343434344,
-0.09595959595959597,
-0.0984848484848485,
-0.10101010101010102,
-0.10353535353535355,
-0.10606060606060606,
-0.10858585858585859,
-0.11111111111111112,
-0.11363636363636365,
-0.11616161616161617,
-0.1186868686868687,
-0.12121212121212122,
-0.12373737373737374,
-0.12626262626262627,
-0.1287878787878788,
-0.13131313131313133,
-0.13383838383838384,
-0.13636363636363638,
-0.1388888888888889,
-0.14141414141414144,
-0.14393939393939395,
-0.14646464646464646,
-0.148989898989899,
-0.15151515151515152,
-0.15404040404040406,
-0.15656565656565657,
-0.15909090909090912,
-0.16161616161616163,
-0.16414141414141414,
-0.16666666666666669,
-0.1691919191919192,
-0.17171717171717174,
-0.17424242424242425,
-0.1767676767676768,
-0.1792929292929293,
-0.18181818181818182,
-0.18434343434343436,
-0.18686868686868688,
-0.18939393939393942,
-0.19191919191919193,
-0.19444444444444445,
-0.196969696969697,
-0.1994949494949495,
-0.20202020202020204,
-0.20454545454545456,
-0.2070707070707071,
-0.2095959595959596,
-0.21212121212121213,
-0.21464646464646467,
-0.21717171717171718,
-0.21969696969696972,
-0.22222222222222224,
-0.22474747474747478,
-0.2272727272727273,
-0.2297979797979798,
-0.23232323232323235,
-0.23484848484848486,
-0.2373737373737374,
-0.23989898989898992,
-0.24242424242424243,
-0.24494949494949497,
-0.2474747474747475,
-0.25,
-0.25,
-0.24747474747474746,
-0.24494949494949497,
-0.24242424242424243,
-0.2398989898989899,
-0.23737373737373735,
-0.23484848484848486,
-0.23232323232323232,
-0.22979797979797978,
-0.2272727272727273,
-0.22474747474747475,
-0.2222222222222222,
-0.21969696969696972,
-0.21717171717171718,
-0.21464646464646464,
-0.2121212121212121,
-0.2095959595959596,
-0.20707070707070707,
-0.20454545454545453,
-0.202020202020202,
-0.1994949494949495,
-0.19696969696969696,
-0.19444444444444442,
-0.19191919191919193,
-0.1893939393939394,
-0.18686868686868685,
-0.18434343434343436,
-0.18181818181818182,
-0.17929292929292928,
-0.1767676767676768,
-0.17424242424242425,
-0.1717171717171717,
-0.16919191919191917,
-0.16666666666666663,
-0.16414141414141414,
-0.1616161616161616,
-0.15909090909090906,
-0.15656565656565657,
-0.15404040404040403,
-0.1515151515151515,
-0.148989898989899,
-0.14646464646464646,
-0.14393939393939392,
-0.14141414141414144,
-0.1388888888888889,
-0.13636363636363635,
-0.1338383838383838,
-0.13131313131313127,
-0.12878787878787878,
-0.12626262626262624,
-0.1237373737373737,
-0.12121212121212122,
-0.11868686868686867,
-0.11616161616161613,
-0.11363636363636365,
-0.1111111111111111,
-0.10858585858585856,
-0.10606060606060608,
-0.10353535353535354,
-0.101010101010101,
-0.09848484848484851,
-0.09595959595959591,
-0.09343434343434343,
-0.09090909090909088,
-0.08838383838383834,
-0.08585858585858586,
-0.08333333333333331,
-0.08080808080808077,
-0.07828282828282829,
-0.07575757575757575,
-0.0732323232323232,
-0.07070707070707072,
-0.06818181818181818,
-0.06565656565656564,
-0.06313131313131315,
-0.06060606060606055,
-0.058080808080808066,
-0.05555555555555558,
-0.05303030303030298,
-0.0505050505050505,
-0.047979797979797956,
-0.045454545454545414,
-0.04292929292929293,
-0.04040404040404039,
-0.037878787878787845,
-0.03535353535353536,
-0.03282828282828282,
-0.030303030303030276,
-0.02777777777777779,
-0.025252525252525193,
-0.022727272727272707,
-0.02020202020202022,
-0.017676767676767624,
-0.015151515151515138,
-0.012626262626262597,
-0.010101010101010055,
-0.007575757575757569,
-0.0050505050505050275,
-0.002525252525252486,
0
] |
[
0.0625,
0.062493623099683704,
0.06247449239873482,
0.06244260789715335,
0.06239796959493929,
0.062340577492092646,
0.06227043158861341,
0.06218753188450158,
0.062091878379757166,
0.06198347107438017,
0.061862309968370575,
0.06172839506172839,
0.06158172635445363,
0.06142230384654627,
0.06125012753800633,
0.06106519742883379,
0.06086751351902867,
0.06065707580859096,
0.06043388429752066,
0.060197938985817774,
0.059949239873482295,
0.05968778696051423,
0.05941358024691358,
0.05912661973268034,
0.05882690541781451,
0.05851443730231609,
0.05818921538618508,
0.05785123966942149,
0.0575005101520253,
0.05713702683399653,
0.05676078971533517,
0.05637179879604122,
0.05597005407611468,
0.05555555555555555,
0.05512830323436384,
0.05468829711253954,
0.054235537190082644,
0.053770023466993166,
0.053291755943271096,
0.052800734618916434,
0.052296959493929186,
0.05178043056830935,
0.051251147842056935,
0.05070911131517192,
0.05015432098765432,
0.049586776859504134,
0.04900647893072135,
0.04841342720130599,
0.04780762167125803,
0.04718906234057749,
0.04655774920926436,
0.04591368227731864,
0.04525686154474033,
0.04458728701152943,
0.04390495867768594,
0.043209876543209874,
0.042502040608101206,
0.04178145087235996,
0.04104810733598613,
0.04030200999897969,
0.039543158861340674,
0.038771553923069066,
0.03798719518416488,
0.037190082644628086,
0.03638021630445873,
0.035557596163656766,
0.03472222222222222,
0.03387409448015508,
0.03301321293745535,
0.032139577594123045,
0.031253188450158134,
0.030354045505560652,
0.029442148760330578,
0.028517498214467904,
0.027580093867972652,
0.0266299357208448,
0.02566702377308437,
0.024691358024691357,
0.023702938475665743,
0.02270176512600755,
0.021687837975716752,
0.020661157024793382,
0.019621722273237413,
0.018569533721048866,
0.017504591368227726,
0.016426895214773994,
0.015336445260687677,
0.014233241505968768,
0.01311728395061728,
0.011988572594633186,
0.01084710743801652,
0.009692888480767263,
0.008525915722885406,
0.007346189164370978,
0.006153708805223944,
0.004948474645444331,
0.0037304866850321333,
0.0024997449239873362,
0.0012562493623099608,
0,
0,
-0.0012562493623099746,
-0.002499744923987357,
-0.0037304866850321194,
-0.004948474645444345,
-0.0061537088052239786,
-0.007346189164370964,
-0.008525915722885413,
-0.00969288848076727,
-0.010847107438016534,
-0.011988572594633207,
-0.013117283950617287,
-0.014233241505968774,
-0.01533644526068767,
-0.016426895214774,
-0.01750459136822774,
-0.01856953372104886,
-0.01962172227323744,
-0.020661157024793375,
-0.021687837975716773,
-0.02270176512600755,
-0.023702938475665736,
-0.024691358024691357,
-0.025667023773084385,
-0.026629935720844822,
-0.027580093867972666,
-0.028517498214467918,
-0.029442148760330578,
-0.030354045505560645,
-0.03125318845015812,
-0.03213957759412306,
-0.03301321293745535,
-0.033874094480155104,
-0.03472222222222224,
-0.03555759616365678,
-0.03638021630445873,
-0.037190082644628114,
-0.03798719518416488,
-0.03877155392306908,
-0.03954315886134069,
-0.040302009998979704,
-0.04104810733598613,
-0.04178145087235996,
-0.0425020406081012,
-0.043209876543209874,
-0.04390495867768596,
-0.04458728701152945,
-0.045256861544740346,
-0.04591368227731865,
-0.046557749209264365,
-0.047189062340577514,
-0.047807621671258044,
-0.04841342720130598,
-0.04900647893072135,
-0.049586776859504134,
-0.05015432098765432,
-0.05070911131517192,
-0.05125114784205692,
-0.05178043056830936,
-0.05229695949392921,
-0.052800734618916434,
-0.053291755943271096,
-0.053770023466993166,
-0.054235537190082644,
-0.05468829711253956,
-0.05512830323436385,
-0.05555555555555555,
-0.05597005407611469,
-0.056371798796041206,
-0.05676078971533516,
-0.057137026833996546,
-0.057500510152025314,
-0.05785123966942149,
-0.05818921538618507,
-0.05851443730231609,
-0.05882690541781452,
-0.05912661973268035,
-0.05941358024691357,
-0.059687786960514244,
-0.0599492398734823,
-0.06019793898581777,
-0.06043388429752067,
-0.06065707580859095,
-0.060867513519028665,
-0.06106519742883379,
-0.06125012753800632,
-0.06142230384654626,
-0.061581726354453636,
-0.06172839506172839,
-0.06186230996837058,
-0.06198347107438015,
-0.06209187837975716,
-0.06218753188450157,
-0.062270431588613395,
-0.06234057749209265,
-0.06239796959493929,
-0.06244260789715336,
-0.062474492398734816,
-0.062493623099683704,
-0.0625
] |
[
0,
0.0003156458301341477,
0.0006312272471337873,
0.0009466798378644108,
0.0012619391891915104,
0.001576940887980578,
0.0018916205210971052,
0.0022059136754065847,
0.0025197559377745076,
0.0028330828950663663,
0.003145830134147653,
0.0034579332418838596,
0.0037693278051404776,
0.004079949410783,
0.004389733645676917,
0.004698616096687722,
0.005006532350680907,
0.005313417994521964,
0.005619208615076384,
0.00592383979920966,
0.006227247133787283,
0.0065293662056747455,
0.006830132601737541,
0.007129481908841159,
0.007427349713851092,
0.007723671603632833,
0.008018383165051874,
0.008311419984973705,
0.008602717650263821,
0.008892211747787709,
0.009179837864410867,
0.009465531586998786,
0.009749228502416954,
0.010030864197530865,
0.010310374259206013,
0.010587694274307887,
0.010862759829701979,
0.011135506512253784,
0.01140586990882879,
0.011673785606292494,
0.011939189191510385,
0.012202016251347954,
0.012462202372670693,
0.012719683142344096,
0.012974394147233654,
0.01322627097420486,
0.013475249210123203,
0.013721264441854179,
0.013964252256263276,
0.01420414824021599,
0.01444088798057781,
0.01467440706421423,
0.014904641077990739,
0.015131525608772829,
0.015354996243425997,
0.01557498856881573,
0.015791438171807524,
0.016004280639266868,
0.016213451558059252,
0.016418886515050173,
0.016620521097105122,
0.016818290891089587,
0.017012131483869063,
0.017201978462309045,
0.017387767413275017,
0.017569433923632475,
0.017746913580246916,
0.017920141969983823,
0.0180890546797087,
0.018253587296287024,
0.0184136754065843,
0.018569254597466008,
0.01872026045579765,
0.01886662856844471,
0.01900829452227269,
0.019145193904147075,
0.019277262300933358,
0.01940443529949703,
0.019526648486703588,
0.019643837449418514,
0.01975593777450731,
0.019862885048835464,
0.01996461485926847,
0.020061062792671815,
0.020152164435910995,
0.020237855375851502,
0.020318071199358828,
0.02039274749329846,
0.0204618198445359,
0.02052522383993663,
0.020582895066366146,
0.020634769110689937,
0.0206807815597735,
0.02072086800048233,
0.02075496401968191,
0.020783005204237738,
0.020804927141015297,
0.020820665416880095,
0.02083015561869761,
0.020833333333333336,
0.020833333333333363,
0.020830155618697624,
0.02082066541688013,
0.02080492714101532,
0.020783005204237752,
0.02075496401968193,
0.020720868000482354,
0.02068078155977353,
0.02063476911068997,
0.020582895066366166,
0.020525223839936636,
0.02046181984453592,
0.020392747493298474,
0.020318071199358842,
0.020237855375851516,
0.020152164435911016,
0.02006106279267182,
0.019964614859268495,
0.019862885048835488,
0.019755937774507334,
0.01964383744941854,
0.019526648486703616,
0.01940443529949705,
0.01927726230093338,
0.019145193904147095,
0.01900829452227272,
0.018866628568444732,
0.01872026045579768,
0.01856925459746603,
0.018413675406584312,
0.018253587296287052,
0.018089054679708713,
0.01792014196998383,
0.017746913580246923,
0.0175694339236325,
0.017387767413275024,
0.017201978462309073,
0.017012131483869083,
0.016818290891089605,
0.01662052109710513,
0.01641888651505019,
0.01621345155805927,
0.016004280639266885,
0.01579143817180753,
0.015574988568815742,
0.015354996243425997,
0.015131525608772858,
0.014904641077990763,
0.01467440706421426,
0.01444088798057784,
0.014204148240216027,
0.013964252256263285,
0.013721264441854189,
0.013475249210123205,
0.013226270974204896,
0.012974394147233684,
0.012719683142344104,
0.012462202372670692,
0.01220201625134798,
0.011939189191510421,
0.011673785606292522,
0.011405869908828817,
0.011135506512253798,
0.010862759829701987,
0.010587694274307904,
0.010310374259206043,
0.010030864197530867,
0.009749228502416982,
0.009465531586998796,
0.009179837864410859,
0.008892211747787718,
0.008602717650263839,
0.008311419984973714,
0.008018383165051893,
0.0077236716036328396,
0.007427349713851103,
0.007129481908841176,
0.006830132601737524,
0.00652936620567475,
0.00622724713378732,
0.005923839799209671,
0.005619208615076379,
0.005313417994521966,
0.005006532350680923,
0.004698616096687716,
0.0043897336456769215,
0.0040799494107829765,
0.003769327805140485,
0.0034579332418838288,
0.0031458301341476397,
0.002833082895066355,
0.0025197559377745232,
0.0022059136754065817,
0.0018916205210971065,
0.0015769408879805907,
0.0012619391891914994,
0.0009466798378644364,
0.0006312272471337838,
0.000315645830134173,
1.3877787807814457e-17
] |
{"local_extrema": [], "null": [[0.5, 0]]}
|
{"local_extrema": [[0.0, -0.0], [0.5, -0.25], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, 0.0625], [1.0, -0.0625]], "null": [[0.5, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.5, 0.020833333333333336], [1.0, 1.3877787807814457e-17]], "null": [[0.0, 0], [1.0, 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.5*L", "type": "Continuity point", "load": "-P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.5*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.5*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "0.5*P"}, {"point": "L", "type": "Force", "value": "0.5*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.5*L"], "shear_force": "-0.5*P", "bending_moment": "0.5*P*x"}, {"span": ["0.5*L", "L"], "shear_force": "0.5*P", "bending_moment": "0.5*L*P - 0.5*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.5*L"], "deflection": "-0.0625*L**2*P*x/(E*I) + 0.0833333333333333*P*x**3/(E*I)", "rotation": "-0.0625*L**2*P/(E*I) + 0.25*P*x**2/(E*I)"}, {"span": ["0.5*L", "L"], "deflection": "0.0208333333333333*L**3*P/(E*I) - 0.1875*L**2*P*x/(E*I) + 0.25*L*P*x**2/(E*I) - 0.0833333333333333*P*x**3/(E*I)", "rotation": "-0.1875*L**2*P/(E*I) + 0.5*L*P*x/(E*I) - 0.25*P*x**2/(E*I)"}]}
|
[
"Given a beam of length L with a pin support at x=0 and a roller support at x=L, and a downward point load of magnitude P at x=0.5L, calculate the reaction forces at the supports.",
"Given a beam of length \\( L \\) supported by a pin at \\( x = 0 \\) and a roller at \\( x = L \\), with a downward point load \\( -P \\) applied at \\( x = 0.5L \\), calculate the reaction forces at the supports.",
"Calculate the reaction forces at the pin support (x=0) and the roller support (x=L) for a beam of length L with a downward point load of -P at x=0.5L.",
"Calculate the reaction forces at the pin and roller supports of a beam with length L, where a downward point load of magnitude P is applied at the midpoint (x = 0.5L)."
] |
[
"0.5P",
"0.5P"
] |
2
| 0
|
{"P": "-2*P", "q": 0, "L": "L", "M": 0, "E": "E", "I": "I"}
|
[
0,
0.010101010101010102,
0.020202020202020204,
0.030303030303030304,
0.04040404040404041,
0.05050505050505051,
0.06060606060606061,
0.07070707070707072,
0.08080808080808081,
0.09090909090909091,
0.10101010101010102,
0.11111111111111112,
0.12121212121212122,
0.13131313131313133,
0.14141414141414144,
0.15151515151515152,
0.16161616161616163,
0.17171717171717174,
0.18181818181818182,
0.19191919191919193,
0.20202020202020204,
0.21212121212121213,
0.22222222222222224,
0.23232323232323235,
0.24242424242424243,
0.25252525252525254,
0.26262626262626265,
0.27272727272727276,
0.2828282828282829,
0.29292929292929293,
0.30303030303030304,
0.31313131313131315,
0.32323232323232326,
0.33333333333333337,
0.3434343434343435,
0.3535353535353536,
0.36363636363636365,
0.37373737373737376,
0.38383838383838387,
0.393939393939394,
0.4040404040404041,
0.4141414141414142,
0.42424242424242425,
0.43434343434343436,
0.4444444444444445,
0.4545454545454546,
0.4646464646464647,
0.4747474747474748,
0.48484848484848486,
0.494949494949495,
0.5050505050505051,
0.5151515151515152,
0.5252525252525253,
0.5353535353535354,
0.5454545454545455,
0.5555555555555556,
0.5656565656565657,
0.5757575757575758,
0.5858585858585859,
0.595959595959596,
0.6060606060606061,
0.6161616161616162,
0.6262626262626263,
0.6363636363636365,
0.6464646464646465,
0.6565656565656566,
0.6666666666666667,
0.6767676767676768,
0.686868686868687,
0.696969696969697,
0.7070707070707072,
0.7171717171717172,
0.7272727272727273,
0.7373737373737375,
0.7474747474747475,
0.7575757575757577,
0.7676767676767677,
0.7777777777777778,
0.787878787878788,
0.797979797979798,
0.8080808080808082,
0.8181818181818182,
0.8282828282828284,
0.8383838383838385,
0.8484848484848485,
0.8585858585858587,
0.8686868686868687,
0.8787878787878789,
0.888888888888889,
0.8989898989898991,
0.9090909090909092,
0.9191919191919192,
0.9292929292929294,
0.9393939393939394,
0.9494949494949496,
0.9595959595959597,
0.9696969696969697,
0.9797979797979799,
0.98989898989899,
1
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
{"local_extrema": [], "null": [[0.0, 0], [0.010101010101010102, 0], [0.020202020202020204, 0], [0.030303030303030304, 0], [0.04040404040404041, 0], [0.05050505050505051, 0], [0.06060606060606061, 0], [0.07070707070707072, 0], [0.08080808080808081, 0], [0.09090909090909091, 0], [0.10101010101010102, 0], [0.11111111111111112, 0], [0.12121212121212122, 0], [0.13131313131313133, 0], [0.14141414141414144, 0], [0.15151515151515152, 0], [0.16161616161616163, 0], [0.17171717171717174, 0], [0.18181818181818182, 0], [0.19191919191919193, 0], [0.20202020202020204, 0], [0.21212121212121213, 0], [0.22222222222222224, 0], [0.23232323232323235, 0], [0.24242424242424243, 0], [0.25252525252525254, 0], [0.26262626262626265, 0], [0.27272727272727276, 0], [0.2828282828282829, 0], [0.29292929292929293, 0], [0.30303030303030304, 0], [0.31313131313131315, 0], [0.32323232323232326, 0], [0.33333333333333337, 0], [0.3434343434343435, 0], [0.3535353535353536, 0], [0.36363636363636365, 0], [0.37373737373737376, 0], [0.38383838383838387, 0], [0.393939393939394, 0], [0.4040404040404041, 0], [0.4141414141414142, 0], [0.42424242424242425, 0], [0.43434343434343436, 0], [0.4444444444444445, 0], [0.4545454545454546, 0], [0.4646464646464647, 0], [0.4747474747474748, 0], [0.48484848484848486, 0], [0.494949494949495, 0], [0.5050505050505051, 0], [0.5151515151515152, 0], [0.5252525252525253, 0], [0.5353535353535354, 0], [0.5454545454545455, 0], [0.5555555555555556, 0], [0.5656565656565657, 0], [0.5757575757575758, 0], [0.5858585858585859, 0], [0.595959595959596, 0], [0.6060606060606061, 0], [0.6161616161616162, 0], [0.6262626262626263, 0], [0.6363636363636365, 0], [0.6464646464646465, 0], [0.6565656565656566, 0], [0.6666666666666667, 0], [0.6767676767676768, 0], [0.686868686868687, 0], [0.696969696969697, 0], [0.7070707070707072, 0], [0.7171717171717172, 0], [0.7272727272727273, 0], [0.7373737373737375, 0], [0.7474747474747475, 0], [0.7575757575757577, 0], [0.7676767676767677, 0], [0.7777777777777778, 0], [0.787878787878788, 0], [0.797979797979798, 0], [0.8080808080808082, 0], [0.8181818181818182, 0], [0.8282828282828284, 0], [0.8383838383838385, 0], [0.8484848484848485, 0], [0.8585858585858587, 0], [0.8686868686868687, 0], [0.8787878787878789, 0], [0.888888888888889, 0], [0.8989898989898991, 0], [0.9090909090909092, 0], [0.9191919191919192, 0], [0.9292929292929294, 0], [0.9393939393939394, 0], [0.9494949494949496, 0], [0.9595959595959597, 0], [0.9696969696969697, 0], [0.9797979797979799, 0], [0.98989898989899, 0], [1.0, 0]]}
|
{"local_extrema": [], "null": [[0.0, 0], [0.010101010101010102, 0], [0.020202020202020204, 0], [0.030303030303030304, 0], [0.04040404040404041, 0], [0.05050505050505051, 0], [0.06060606060606061, 0], [0.07070707070707072, 0], [0.08080808080808081, 0], [0.09090909090909091, 0], [0.10101010101010102, 0], [0.11111111111111112, 0], [0.12121212121212122, 0], [0.13131313131313133, 0], [0.14141414141414144, 0], [0.15151515151515152, 0], [0.16161616161616163, 0], [0.17171717171717174, 0], [0.18181818181818182, 0], [0.19191919191919193, 0], [0.20202020202020204, 0], [0.21212121212121213, 0], [0.22222222222222224, 0], [0.23232323232323235, 0], [0.24242424242424243, 0], [0.25252525252525254, 0], [0.26262626262626265, 0], [0.27272727272727276, 0], [0.2828282828282829, 0], [0.29292929292929293, 0], [0.30303030303030304, 0], [0.31313131313131315, 0], [0.32323232323232326, 0], [0.33333333333333337, 0], [0.3434343434343435, 0], [0.3535353535353536, 0], [0.36363636363636365, 0], [0.37373737373737376, 0], [0.38383838383838387, 0], [0.393939393939394, 0], [0.4040404040404041, 0], [0.4141414141414142, 0], [0.42424242424242425, 0], [0.43434343434343436, 0], [0.4444444444444445, 0], [0.4545454545454546, 0], [0.4646464646464647, 0], [0.4747474747474748, 0], [0.48484848484848486, 0], [0.494949494949495, 0], [0.5050505050505051, 0], [0.5151515151515152, 0], [0.5252525252525253, 0], [0.5353535353535354, 0], [0.5454545454545455, 0], [0.5555555555555556, 0], [0.5656565656565657, 0], [0.5757575757575758, 0], [0.5858585858585859, 0], [0.595959595959596, 0], [0.6060606060606061, 0], [0.6161616161616162, 0], [0.6262626262626263, 0], [0.6363636363636365, 0], [0.6464646464646465, 0], [0.6565656565656566, 0], [0.6666666666666667, 0], [0.6767676767676768, 0], [0.686868686868687, 0], [0.696969696969697, 0], [0.7070707070707072, 0], [0.7171717171717172, 0], [0.7272727272727273, 0], [0.7373737373737375, 0], [0.7474747474747475, 0], [0.7575757575757577, 0], [0.7676767676767677, 0], [0.7777777777777778, 0], [0.787878787878788, 0], [0.797979797979798, 0], [0.8080808080808082, 0], [0.8181818181818182, 0], [0.8282828282828284, 0], [0.8383838383838385, 0], [0.8484848484848485, 0], [0.8585858585858587, 0], [0.8686868686868687, 0], [0.8787878787878789, 0], [0.888888888888889, 0], [0.8989898989898991, 0], [0.9090909090909092, 0], [0.9191919191919192, 0], [0.9292929292929294, 0], [0.9393939393939394, 0], [0.9494949494949496, 0], [0.9595959595959597, 0], [0.9696969696969697, 0], [0.9797979797979799, 0], [0.98989898989899, 0], [1.0, 0]]}
|
{"local_extrema": [], "null": [[0.0, 0], [0.010101010101010102, 0], [0.020202020202020204, 0], [0.030303030303030304, 0], [0.04040404040404041, 0], [0.05050505050505051, 0], [0.06060606060606061, 0], [0.07070707070707072, 0], [0.08080808080808081, 0], [0.09090909090909091, 0], [0.10101010101010102, 0], [0.11111111111111112, 0], [0.12121212121212122, 0], [0.13131313131313133, 0], [0.14141414141414144, 0], [0.15151515151515152, 0], [0.16161616161616163, 0], [0.17171717171717174, 0], [0.18181818181818182, 0], [0.19191919191919193, 0], [0.20202020202020204, 0], [0.21212121212121213, 0], [0.22222222222222224, 0], [0.23232323232323235, 0], [0.24242424242424243, 0], [0.25252525252525254, 0], [0.26262626262626265, 0], [0.27272727272727276, 0], [0.2828282828282829, 0], [0.29292929292929293, 0], [0.30303030303030304, 0], [0.31313131313131315, 0], [0.32323232323232326, 0], [0.33333333333333337, 0], [0.3434343434343435, 0], [0.3535353535353536, 0], [0.36363636363636365, 0], [0.37373737373737376, 0], [0.38383838383838387, 0], [0.393939393939394, 0], [0.4040404040404041, 0], [0.4141414141414142, 0], [0.42424242424242425, 0], [0.43434343434343436, 0], [0.4444444444444445, 0], [0.4545454545454546, 0], [0.4646464646464647, 0], [0.4747474747474748, 0], [0.48484848484848486, 0], [0.494949494949495, 0], [0.5050505050505051, 0], [0.5151515151515152, 0], [0.5252525252525253, 0], [0.5353535353535354, 0], [0.5454545454545455, 0], [0.5555555555555556, 0], [0.5656565656565657, 0], [0.5757575757575758, 0], [0.5858585858585859, 0], [0.595959595959596, 0], [0.6060606060606061, 0], [0.6161616161616162, 0], [0.6262626262626263, 0], [0.6363636363636365, 0], [0.6464646464646465, 0], [0.6565656565656566, 0], [0.6666666666666667, 0], [0.6767676767676768, 0], [0.686868686868687, 0], [0.696969696969697, 0], [0.7070707070707072, 0], [0.7171717171717172, 0], [0.7272727272727273, 0], [0.7373737373737375, 0], [0.7474747474747475, 0], [0.7575757575757577, 0], [0.7676767676767677, 0], [0.7777777777777778, 0], [0.787878787878788, 0], [0.797979797979798, 0], [0.8080808080808082, 0], [0.8181818181818182, 0], [0.8282828282828284, 0], [0.8383838383838385, 0], [0.8484848484848485, 0], [0.8585858585858587, 0], [0.8686868686868687, 0], [0.8787878787878789, 0], [0.888888888888889, 0], [0.8989898989898991, 0], [0.9090909090909092, 0], [0.9191919191919192, 0], [0.9292929292929294, 0], [0.9393939393939394, 0], [0.9494949494949496, 0], [0.9595959595959597, 0], [0.9696969696969697, 0], [0.9797979797979799, 0], [0.98989898989899, 0], [1.0, 0]]}
|
{"local_extrema": [], "null": [[0.0, 0], [0.010101010101010102, 0], [0.020202020202020204, 0], [0.030303030303030304, 0], [0.04040404040404041, 0], [0.05050505050505051, 0], [0.06060606060606061, 0], [0.07070707070707072, 0], [0.08080808080808081, 0], [0.09090909090909091, 0], [0.10101010101010102, 0], [0.11111111111111112, 0], [0.12121212121212122, 0], [0.13131313131313133, 0], [0.14141414141414144, 0], [0.15151515151515152, 0], [0.16161616161616163, 0], [0.17171717171717174, 0], [0.18181818181818182, 0], [0.19191919191919193, 0], [0.20202020202020204, 0], [0.21212121212121213, 0], [0.22222222222222224, 0], [0.23232323232323235, 0], [0.24242424242424243, 0], [0.25252525252525254, 0], [0.26262626262626265, 0], [0.27272727272727276, 0], [0.2828282828282829, 0], [0.29292929292929293, 0], [0.30303030303030304, 0], [0.31313131313131315, 0], [0.32323232323232326, 0], [0.33333333333333337, 0], [0.3434343434343435, 0], [0.3535353535353536, 0], [0.36363636363636365, 0], [0.37373737373737376, 0], [0.38383838383838387, 0], [0.393939393939394, 0], [0.4040404040404041, 0], [0.4141414141414142, 0], [0.42424242424242425, 0], [0.43434343434343436, 0], [0.4444444444444445, 0], [0.4545454545454546, 0], [0.4646464646464647, 0], [0.4747474747474748, 0], [0.48484848484848486, 0], [0.494949494949495, 0], [0.5050505050505051, 0], [0.5151515151515152, 0], [0.5252525252525253, 0], [0.5353535353535354, 0], [0.5454545454545455, 0], [0.5555555555555556, 0], [0.5656565656565657, 0], [0.5757575757575758, 0], [0.5858585858585859, 0], [0.595959595959596, 0], [0.6060606060606061, 0], [0.6161616161616162, 0], [0.6262626262626263, 0], [0.6363636363636365, 0], [0.6464646464646465, 0], [0.6565656565656566, 0], [0.6666666666666667, 0], [0.6767676767676768, 0], [0.686868686868687, 0], [0.696969696969697, 0], [0.7070707070707072, 0], [0.7171717171717172, 0], [0.7272727272727273, 0], [0.7373737373737375, 0], [0.7474747474747475, 0], [0.7575757575757577, 0], [0.7676767676767677, 0], [0.7777777777777778, 0], [0.787878787878788, 0], [0.797979797979798, 0], [0.8080808080808082, 0], [0.8181818181818182, 0], [0.8282828282828284, 0], [0.8383838383838385, 0], [0.8484848484848485, 0], [0.8585858585858587, 0], [0.8686868686868687, 0], [0.8787878787878789, 0], [0.888888888888889, 0], [0.8989898989898991, 0], [0.9090909090909092, 0], [0.9191919191919192, 0], [0.9292929292929294, 0], [0.9393939393939394, 0], [0.9494949494949496, 0], [0.9595959595959597, 0], [0.9696969696969697, 0], [0.9797979797979799, 0], [0.98989898989899, 0], [1.0, 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "2*P"}, {"point": "L", "type": "Force", "value": "0"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "L"], "shear_force": "0", "bending_moment": "0"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "L"], "deflection": "0", "rotation": "0"}]}
|
[
"Calculate the reaction forces at the pin support (x=0) and the roller support (x=L) for a simply supported beam of length L with a downward point load of -2P at the pin.",
"Given a beam of length \\( L \\) with a pin support at \\( x = 0 \\) and a roller support at \\( x = L \\), and a downward point load of \\( -2P \\) at \\( x = 0 \\), calculate the reaction forces at the supports.",
"Given a beam of length \\( L \\) with a pin support at \\( x = 0 \\) and a roller support at \\( x = L \\), and a downward-point load of \\( -2P \\) at \\( x = 0 \\), calculate the reaction forces at the supports.",
"Question: \nDetermine the reaction forces at the pin support (x=0) and the roller support (x=L) for a beam of length L with a downward point load of -2P applied at x=0."
] |
[
"2P",
"0"
] |
3
| 0.5
|
{"P": "-2*P", "q": 0, "L": "L", "M": 0, "E": "E", "I": "I"}
|
[
0,
0.005050505050505051,
0.010101010101010102,
0.015151515151515152,
0.020202020202020204,
0.025252525252525256,
0.030303030303030304,
0.03535353535353536,
0.04040404040404041,
0.045454545454545456,
0.05050505050505051,
0.05555555555555556,
0.06060606060606061,
0.06565656565656566,
0.07070707070707072,
0.07575757575757576,
0.08080808080808081,
0.08585858585858587,
0.09090909090909091,
0.09595959595959597,
0.10101010101010102,
0.10606060606060606,
0.11111111111111112,
0.11616161616161617,
0.12121212121212122,
0.12626262626262627,
0.13131313131313133,
0.13636363636363638,
0.14141414141414144,
0.14646464646464646,
0.15151515151515152,
0.15656565656565657,
0.16161616161616163,
0.16666666666666669,
0.17171717171717174,
0.1767676767676768,
0.18181818181818182,
0.18686868686868688,
0.19191919191919193,
0.196969696969697,
0.20202020202020204,
0.2070707070707071,
0.21212121212121213,
0.21717171717171718,
0.22222222222222224,
0.2272727272727273,
0.23232323232323235,
0.2373737373737374,
0.24242424242424243,
0.2474747474747475,
0.25252525252525254,
0.2575757575757576,
0.26262626262626265,
0.2676767676767677,
0.27272727272727276,
0.2777777777777778,
0.2828282828282829,
0.2878787878787879,
0.29292929292929293,
0.297979797979798,
0.30303030303030304,
0.3080808080808081,
0.31313131313131315,
0.31818181818181823,
0.32323232323232326,
0.3282828282828283,
0.33333333333333337,
0.3383838383838384,
0.3434343434343435,
0.3484848484848485,
0.3535353535353536,
0.3585858585858586,
0.36363636363636365,
0.36868686868686873,
0.37373737373737376,
0.37878787878787884,
0.38383838383838387,
0.3888888888888889,
0.393939393939394,
0.398989898989899,
0.4040404040404041,
0.4090909090909091,
0.4141414141414142,
0.4191919191919192,
0.42424242424242425,
0.42929292929292934,
0.43434343434343436,
0.43939393939393945,
0.4444444444444445,
0.44949494949494956,
0.4545454545454546,
0.4595959595959596,
0.4646464646464647,
0.4696969696969697,
0.4747474747474748,
0.47979797979797983,
0.48484848484848486,
0.48989898989898994,
0.494949494949495,
0.5,
0.5,
0.5050505050505051,
0.51010101010101,
0.5151515151515151,
0.5202020202020202,
0.5252525252525253,
0.5303030303030303,
0.5353535353535354,
0.5404040404040404,
0.5454545454545454,
0.5505050505050505,
0.5555555555555556,
0.5606060606060606,
0.5656565656565656,
0.5707070707070707,
0.5757575757575758,
0.5808080808080808,
0.5858585858585859,
0.5909090909090909,
0.595959595959596,
0.601010101010101,
0.6060606060606061,
0.6111111111111112,
0.6161616161616161,
0.6212121212121212,
0.6262626262626263,
0.6313131313131313,
0.6363636363636364,
0.6414141414141414,
0.6464646464646464,
0.6515151515151515,
0.6565656565656566,
0.6616161616161617,
0.6666666666666667,
0.6717171717171717,
0.6767676767676768,
0.6818181818181819,
0.6868686868686869,
0.6919191919191919,
0.696969696969697,
0.702020202020202,
0.7070707070707071,
0.7121212121212122,
0.7171717171717171,
0.7222222222222222,
0.7272727272727273,
0.7323232323232324,
0.7373737373737375,
0.7424242424242424,
0.7474747474747475,
0.7525252525252526,
0.7575757575757576,
0.7626262626262627,
0.7676767676767677,
0.7727272727272727,
0.7777777777777778,
0.7828282828282829,
0.7878787878787878,
0.7929292929292929,
0.797979797979798,
0.803030303030303,
0.8080808080808082,
0.8131313131313131,
0.8181818181818182,
0.8232323232323233,
0.8282828282828283,
0.8333333333333334,
0.8383838383838385,
0.8434343434343434,
0.8484848484848485,
0.8535353535353536,
0.8585858585858586,
0.8636363636363636,
0.8686868686868687,
0.8737373737373737,
0.8787878787878789,
0.8838383838383839,
0.8888888888888888,
0.893939393939394,
0.898989898989899,
0.9040404040404041,
0.9090909090909092,
0.9141414141414141,
0.9191919191919192,
0.9242424242424243,
0.9292929292929293,
0.9343434343434344,
0.9393939393939394,
0.9444444444444444,
0.9494949494949496,
0.9545454545454546,
0.9595959595959596,
0.9646464646464648,
0.9696969696969697,
0.9747474747474748,
0.9797979797979799,
0.9848484848484849,
0.98989898989899,
0.994949494949495,
1
] |
[
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2
] |
[
0,
-0.010101010101010102,
-0.020202020202020204,
-0.030303030303030304,
-0.04040404040404041,
-0.05050505050505051,
-0.06060606060606061,
-0.07070707070707072,
-0.08080808080808081,
-0.09090909090909091,
-0.10101010101010102,
-0.11111111111111112,
-0.12121212121212122,
-0.13131313131313133,
-0.14141414141414144,
-0.15151515151515152,
-0.16161616161616163,
-0.17171717171717174,
-0.18181818181818182,
-0.19191919191919193,
-0.20202020202020204,
-0.21212121212121213,
-0.22222222222222224,
-0.23232323232323235,
-0.24242424242424243,
-0.25252525252525254,
-0.26262626262626265,
-0.27272727272727276,
-0.2828282828282829,
-0.29292929292929293,
-0.30303030303030304,
-0.31313131313131315,
-0.32323232323232326,
-0.33333333333333337,
-0.3434343434343435,
-0.3535353535353536,
-0.36363636363636365,
-0.37373737373737376,
-0.38383838383838387,
-0.393939393939394,
-0.4040404040404041,
-0.4141414141414142,
-0.42424242424242425,
-0.43434343434343436,
-0.4444444444444445,
-0.4545454545454546,
-0.4646464646464647,
-0.4747474747474748,
-0.48484848484848486,
-0.494949494949495,
-0.5050505050505051,
-0.5151515151515152,
-0.5252525252525253,
-0.5353535353535354,
-0.5454545454545455,
-0.5555555555555556,
-0.5656565656565657,
-0.5757575757575758,
-0.5858585858585859,
-0.595959595959596,
-0.6060606060606061,
-0.6161616161616162,
-0.6262626262626263,
-0.6363636363636365,
-0.6464646464646465,
-0.6565656565656566,
-0.6666666666666667,
-0.6767676767676768,
-0.686868686868687,
-0.696969696969697,
-0.7070707070707072,
-0.7171717171717172,
-0.7272727272727273,
-0.7373737373737375,
-0.7474747474747475,
-0.7575757575757577,
-0.7676767676767677,
-0.7777777777777778,
-0.787878787878788,
-0.797979797979798,
-0.8080808080808082,
-0.8181818181818182,
-0.8282828282828284,
-0.8383838383838385,
-0.8484848484848485,
-0.8585858585858587,
-0.8686868686868687,
-0.8787878787878789,
-0.888888888888889,
-0.8989898989898991,
-0.9090909090909092,
-0.9191919191919192,
-0.9292929292929294,
-0.9393939393939394,
-0.9494949494949496,
-0.9595959595959597,
-0.9696969696969697,
-0.9797979797979799,
-0.98989898989899,
-1,
-1,
-0.9898989898989898,
-0.9797979797979799,
-0.9696969696969697,
-0.9595959595959596,
-0.9494949494949494,
-0.9393939393939394,
-0.9292929292929293,
-0.9191919191919191,
-0.9090909090909092,
-0.898989898989899,
-0.8888888888888888,
-0.8787878787878789,
-0.8686868686868687,
-0.8585858585858586,
-0.8484848484848484,
-0.8383838383838385,
-0.8282828282828283,
-0.8181818181818181,
-0.808080808080808,
-0.797979797979798,
-0.7878787878787878,
-0.7777777777777777,
-0.7676767676767677,
-0.7575757575757576,
-0.7474747474747474,
-0.7373737373737375,
-0.7272727272727273,
-0.7171717171717171,
-0.7070707070707072,
-0.696969696969697,
-0.6868686868686869,
-0.6767676767676767,
-0.6666666666666665,
-0.6565656565656566,
-0.6464646464646464,
-0.6363636363636362,
-0.6262626262626263,
-0.6161616161616161,
-0.606060606060606,
-0.595959595959596,
-0.5858585858585859,
-0.5757575757575757,
-0.5656565656565657,
-0.5555555555555556,
-0.5454545454545454,
-0.5353535353535352,
-0.5252525252525251,
-0.5151515151515151,
-0.505050505050505,
-0.4949494949494948,
-0.48484848484848486,
-0.4747474747474747,
-0.46464646464646453,
-0.4545454545454546,
-0.4444444444444444,
-0.43434343434343425,
-0.4242424242424243,
-0.41414141414141414,
-0.404040404040404,
-0.39393939393939403,
-0.38383838383838365,
-0.3737373737373737,
-0.36363636363636354,
-0.35353535353535337,
-0.3434343434343434,
-0.33333333333333326,
-0.3232323232323231,
-0.31313131313131315,
-0.303030303030303,
-0.2929292929292928,
-0.2828282828282829,
-0.2727272727272727,
-0.26262626262626254,
-0.2525252525252526,
-0.2424242424242422,
-0.23232323232323226,
-0.22222222222222232,
-0.21212121212121193,
-0.202020202020202,
-0.19191919191919182,
-0.18181818181818166,
-0.1717171717171717,
-0.16161616161616155,
-0.15151515151515138,
-0.14141414141414144,
-0.13131313131313127,
-0.1212121212121211,
-0.11111111111111116,
-0.10101010101010077,
-0.09090909090909083,
-0.08080808080808088,
-0.0707070707070705,
-0.06060606060606055,
-0.050505050505050386,
-0.04040404040404022,
-0.030303030303030276,
-0.02020202020202011,
-0.010101010101009944,
0
] |
[
0.25,
0.24997449239873482,
0.2498979695949393,
0.2497704315886134,
0.24959187837975716,
0.24936230996837058,
0.24908172635445364,
0.24875012753800632,
0.24836751351902867,
0.24793388429752067,
0.2474492398734823,
0.24691358024691357,
0.24632690541781452,
0.24568921538618507,
0.2450005101520253,
0.24426078971533516,
0.2434700540761147,
0.24262830323436385,
0.24173553719008264,
0.2407917559432711,
0.23979695949392918,
0.23875114784205692,
0.23765432098765432,
0.23650647893072135,
0.23530762167125804,
0.23405774920926437,
0.23275686154474032,
0.23140495867768596,
0.2300020406081012,
0.22854810733598613,
0.2270431588613407,
0.22548719518416488,
0.22388021630445873,
0.2222222222222222,
0.22051321293745535,
0.21875318845015815,
0.21694214876033058,
0.21508009386797267,
0.21316702377308439,
0.21120293847566574,
0.20918783797571674,
0.2071217222732374,
0.20500459136822774,
0.20283644526068767,
0.2006172839506173,
0.19834710743801653,
0.1960259157228854,
0.19365370880522395,
0.19123048668503212,
0.18875624936230995,
0.18623099683705743,
0.18365472910927455,
0.18102744617896133,
0.17834914804611773,
0.17561983471074377,
0.1728395061728395,
0.17000816243240482,
0.16712580348943984,
0.1641924293439445,
0.16120803999591876,
0.1581726354453627,
0.15508621569227626,
0.15194878073665952,
0.14876033057851235,
0.14552086521783492,
0.14223038465462706,
0.13888888888888887,
0.13549637792062033,
0.1320528517498214,
0.12855831037649218,
0.12501275380063254,
0.12141618202224261,
0.11776859504132231,
0.11406999285787162,
0.11032037547189061,
0.1065197428833792,
0.10266809509233749,
0.09876543209876543,
0.09481175390266297,
0.0908070605040302,
0.08675135190286701,
0.08264462809917353,
0.07848688909294965,
0.07427813488419546,
0.0700183654729109,
0.06570758085909598,
0.06134578104275071,
0.05693296602387507,
0.05246913580246912,
0.04795429037853274,
0.04338842975206608,
0.03877155392306905,
0.034103662891541625,
0.029384756657483913,
0.024614835220895775,
0.019793898581777325,
0.014921946740128533,
0.009998979695949345,
0.005024997449239843,
0,
0,
-0.0050249974492398986,
-0.009998979695949428,
-0.014921946740128478,
-0.01979389858177738,
-0.024614835220895914,
-0.029384756657483857,
-0.03410366289154165,
-0.03877155392306908,
-0.04338842975206614,
-0.04795429037853283,
-0.05246913580246915,
-0.0569329660238751,
-0.06134578104275068,
-0.065707580859096,
-0.07001836547291096,
-0.07427813488419543,
-0.07848688909294976,
-0.0826446280991735,
-0.08675135190286709,
-0.0908070605040302,
-0.09481175390266294,
-0.09876543209876543,
-0.10266809509233754,
-0.10651974288337929,
-0.11032037547189066,
-0.11406999285787167,
-0.11776859504132231,
-0.12141618202224258,
-0.12501275380063248,
-0.12855831037649224,
-0.1320528517498214,
-0.13549637792062041,
-0.13888888888888895,
-0.14223038465462712,
-0.14552086521783492,
-0.14876033057851246,
-0.15194878073665952,
-0.15508621569227632,
-0.15817263544536275,
-0.16120803999591882,
-0.1641924293439445,
-0.16712580348943984,
-0.1700081624324048,
-0.1728395061728395,
-0.17561983471074383,
-0.1783491480461178,
-0.18102744617896138,
-0.1836547291092746,
-0.18623099683705746,
-0.18875624936231006,
-0.19123048668503217,
-0.19365370880522392,
-0.1960259157228854,
-0.19834710743801653,
-0.2006172839506173,
-0.20283644526068767,
-0.20500459136822768,
-0.20712172227323744,
-0.20918783797571683,
-0.21120293847566574,
-0.21316702377308439,
-0.21508009386797267,
-0.21694214876033058,
-0.21875318845015823,
-0.2205132129374554,
-0.2222222222222222,
-0.22388021630445876,
-0.22548719518416482,
-0.22704315886134063,
-0.22854810733598618,
-0.23000204060810125,
-0.23140495867768596,
-0.2327568615447403,
-0.23405774920926437,
-0.23530762167125807,
-0.2365064789307214,
-0.23765432098765427,
-0.23875114784205698,
-0.2397969594939292,
-0.24079175594327107,
-0.24173553719008267,
-0.2426283032343638,
-0.24347005407611466,
-0.24426078971533516,
-0.24500051015202529,
-0.24568921538618504,
-0.24632690541781455,
-0.24691358024691357,
-0.24744923987348233,
-0.2479338842975206,
-0.24836751351902864,
-0.2487501275380063,
-0.24908172635445358,
-0.2493623099683706,
-0.24959187837975716,
-0.24977043158861345,
-0.24989796959493926,
-0.24997449239873482,
-0.25
] |
[
0,
0.0012625833205365908,
0.0025249089885351493,
0.0037867193514576434,
0.005047756756766042,
0.006307763551922312,
0.007566482084388421,
0.008823654701626339,
0.01007902375109803,
0.011332331580265465,
0.012583320536590612,
0.013831732967535438,
0.01507731122056191,
0.016319797643132,
0.01755893458270767,
0.01879446438675089,
0.02002612940272363,
0.021253671978087856,
0.022476834460305534,
0.02369535919683864,
0.024908988535149133,
0.026117464822698982,
0.02732053040695016,
0.028517927635364634,
0.029709398855404367,
0.03089468641453133,
0.032073532660207495,
0.03324567993989482,
0.03441087060105528,
0.035568846991150836,
0.03671935145764347,
0.03786212634799514,
0.038996914009667816,
0.04012345679012346,
0.04124149703682405,
0.04235077709723155,
0.043451039318807914,
0.04454202604901514,
0.04562347963531516,
0.04669514242516998,
0.04775675676604154,
0.04880806500539182,
0.04984880949068277,
0.05087873256937638,
0.05189757658893462,
0.05290508389681944,
0.053900996840492814,
0.054885057767416714,
0.055857009025053105,
0.05681659296086396,
0.05776355192231124,
0.05869762825685691,
0.05961856431196295,
0.060526102435091315,
0.06141998497370399,
0.06229995427526292,
0.0631657526872301,
0.06401712255706746,
0.06485380623223701,
0.06567554606020069,
0.06648208438842047,
0.06727316356435835,
0.06804852593547625,
0.06880791384923617,
0.06955106965310007,
0.0702777356945299,
0.07098765432098766,
0.07168056787993529,
0.07235621871883478,
0.07301434918514808,
0.07365470162633718,
0.07427701838986402,
0.07488104182319058,
0.07546651427377885,
0.07603317808909076,
0.0765807756165883,
0.07710904920373343,
0.07761774119798812,
0.07810659394681434,
0.07857534979767405,
0.07902375109802924,
0.07945154019534185,
0.07985845943707387,
0.08024425117068726,
0.08060865774364398,
0.08095142150340601,
0.0812722847974353,
0.08157098997319384,
0.08184727937814358,
0.0821008953597465,
0.08233158026546457,
0.08253907644275973,
0.082723126239094,
0.0828834720019293,
0.08301985607872762,
0.08313202081695092,
0.08321970856406119,
0.08328266166752035,
0.08332062247479041,
0.08333333333333334,
0.08333333333333336,
0.0833206224747904,
0.08328266166752042,
0.0832197085640612,
0.08313202081695091,
0.08301985607872762,
0.08288347200192935,
0.08272312623909402,
0.08253907644275978,
0.0823315802654646,
0.08210089535974648,
0.08184727937814358,
0.08157098997319386,
0.08127228479743533,
0.08095142150340602,
0.08060865774364402,
0.08024425117068719,
0.07985845943707394,
0.07945154019534191,
0.07902375109802924,
0.07857534979767412,
0.07810659394681436,
0.07761774119798816,
0.07710904920373342,
0.07658077561658834,
0.07603317808909078,
0.07546651427377883,
0.07488104182319062,
0.07427701838986402,
0.07365470162633721,
0.07301434918514811,
0.07235621871883481,
0.07168056787993528,
0.0709876543209876,
0.0702777356945299,
0.06955106965310005,
0.06880791384923625,
0.06804852593547629,
0.06727316356435838,
0.06648208438842047,
0.06567554606020072,
0.06485380623223698,
0.0640171225570675,
0.06316575268723008,
0.06229995427526293,
0.06141998497370395,
0.060526102435091336,
0.059618564311962954,
0.05869762825685705,
0.057763551922311265,
0.05681659296086401,
0.0558570090250531,
0.054885057767416714,
0.05390099684049278,
0.05290508389681954,
0.05189757658893464,
0.050878732569376375,
0.049848809490682724,
0.04880806500539188,
0.04775675676604159,
0.04669514242517005,
0.04562347963531517,
0.04454202604901515,
0.04345103931880785,
0.04235077709723152,
0.041241497036824074,
0.04012345679012337,
0.03899691400966794,
0.03786212634799509,
0.03671935145764345,
0.035568846991150774,
0.03441087060105537,
0.03324567993989476,
0.032073532660207474,
0.030894686414531372,
0.029709398855404426,
0.028517927635364607,
0.027320530406950108,
0.026117464822699013,
0.024908988535149182,
0.023695359196838586,
0.02247683446030553,
0.021253671978087765,
0.020026129402723705,
0.018794464386750878,
0.0175589345827077,
0.01631979764313203,
0.015077311220561954,
0.01383173296753544,
0.012583320536590573,
0.011332331580265434,
0.010079023751098107,
0.00882365470162634,
0.007566482084388329,
0.006307763551922266,
0.0050477567567659,
0.0037867193514576486,
0.002524908988535038,
0.001262583320536595,
-4.163336342344337e-17
] |
{"local_extrema": [], "null": [[0.5, 0]]}
|
{"local_extrema": [[0.0, -0.0], [0.5, -1.0], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, 0.25], [1.0, -0.25]], "null": [[0.5, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.5, 0.08333333333333334], [1.0, -4.163336342344337e-17]], "null": [[0.0, 0], [0.9999999999999998, 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.5*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.5*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.5*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "P"}, {"point": "L", "type": "Force", "value": "P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.5*L"], "shear_force": "-P", "bending_moment": "P*x"}, {"span": ["0.5*L", "L"], "shear_force": "P", "bending_moment": "L*P - P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.5*L"], "deflection": "-0.125*L**2*P*x/(E*I) + P*x**3/(6*E*I)", "rotation": "-0.125*L**2*P/(E*I) + P*x**2/(2*E*I)"}, {"span": ["0.5*L", "L"], "deflection": "0.0416666666666667*L**3*P/(E*I) - 0.375*L**2*P*x/(E*I) + L*P*x**2/(2*E*I) - P*x**3/(6*E*I)", "rotation": "-0.375*L**2*P/(E*I) + L*P*x/(E*I) - P*x**2/(2*E*I)"}]}
|
[
"Question: Determine the reaction forces at the pin and roller supports of a beam with length L, supported at x=0 (pin) and x=L (roller), subjected to a downward point load of -2P at x=0.5L.",
"Calculate the reaction forces at the pin support (x=0) and the roller support (x=L) for a statically loaded beam of length L, with a point downward load of -2P applied at x=0.5L.",
"Question: \nDetermine the reaction forces at the pin support (x=0) and the roller support (x=L) for a statically loaded beam of length L with a downward-point load of -2P applied at x=0.5L.",
"Given a beam of length L with a pin support at x=0 and a roller support at x=L, and a downward point load of -2P at x=0.5L, calculate the reaction forces at the supports."
] |
[
"P",
"P"
] |
4
| 0
|
{"P": "-P", "q": 0, "L": "2*L", "M": 0, "E": "E", "I": "I"}
|
[
0,
0.04040404040404041,
0.08080808080808081,
0.12121212121212122,
0.16161616161616163,
0.20202020202020204,
0.24242424242424243,
0.2828282828282829,
0.32323232323232326,
0.36363636363636365,
0.4040404040404041,
0.4444444444444445,
0.48484848484848486,
0.5252525252525253,
0.5656565656565657,
0.6060606060606061,
0.6464646464646465,
0.686868686868687,
0.7272727272727273,
0.7676767676767677,
0.8080808080808082,
0.8484848484848485,
0.888888888888889,
0.9292929292929294,
0.9696969696969697,
1.0101010101010102,
1.0505050505050506,
1.090909090909091,
1.1313131313131315,
1.1717171717171717,
1.2121212121212122,
1.2525252525252526,
1.292929292929293,
1.3333333333333335,
1.373737373737374,
1.4141414141414144,
1.4545454545454546,
1.494949494949495,
1.5353535353535355,
1.575757575757576,
1.6161616161616164,
1.6565656565656568,
1.696969696969697,
1.7373737373737375,
1.777777777777778,
1.8181818181818183,
1.8585858585858588,
1.8989898989898992,
1.9393939393939394,
1.97979797979798,
2.0202020202020203,
2.060606060606061,
2.101010101010101,
2.1414141414141414,
2.181818181818182,
2.2222222222222223,
2.262626262626263,
2.303030303030303,
2.3434343434343434,
2.383838383838384,
2.4242424242424243,
2.464646464646465,
2.505050505050505,
2.545454545454546,
2.585858585858586,
2.6262626262626263,
2.666666666666667,
2.707070707070707,
2.747474747474748,
2.787878787878788,
2.8282828282828287,
2.868686868686869,
2.909090909090909,
2.94949494949495,
2.98989898989899,
3.0303030303030307,
3.070707070707071,
3.111111111111111,
3.151515151515152,
3.191919191919192,
3.2323232323232327,
3.272727272727273,
3.3131313131313136,
3.353535353535354,
3.393939393939394,
3.4343434343434347,
3.474747474747475,
3.5151515151515156,
3.555555555555556,
3.5959595959595965,
3.6363636363636367,
3.676767676767677,
3.7171717171717176,
3.757575757575758,
3.7979797979797985,
3.8383838383838387,
3.878787878787879,
3.9191919191919196,
3.95959595959596,
4
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
{"local_extrema": [], "null": [[0.0, 0], [0.04040404040404041, 0], [0.08080808080808081, 0], [0.12121212121212122, 0], [0.16161616161616163, 0], [0.20202020202020204, 0], [0.24242424242424243, 0], [0.2828282828282829, 0], [0.32323232323232326, 0], [0.36363636363636365, 0], [0.4040404040404041, 0], [0.4444444444444445, 0], [0.48484848484848486, 0], [0.5252525252525253, 0], [0.5656565656565657, 0], [0.6060606060606061, 0], [0.6464646464646465, 0], [0.686868686868687, 0], [0.7272727272727273, 0], [0.7676767676767677, 0], [0.8080808080808082, 0], [0.8484848484848485, 0], [0.888888888888889, 0], [0.9292929292929294, 0], [0.9696969696969697, 0], [1.0101010101010102, 0], [1.0505050505050506, 0], [1.090909090909091, 0], [1.1313131313131315, 0], [1.1717171717171717, 0], [1.2121212121212122, 0], [1.2525252525252526, 0], [1.292929292929293, 0], [1.3333333333333335, 0], [1.373737373737374, 0], [1.4141414141414144, 0], [1.4545454545454546, 0], [1.494949494949495, 0], [1.5353535353535355, 0], [1.575757575757576, 0], [1.6161616161616164, 0], [1.6565656565656568, 0], [1.696969696969697, 0], [1.7373737373737375, 0], [1.777777777777778, 0], [1.8181818181818183, 0], [1.8585858585858588, 0], [1.8989898989898992, 0], [1.9393939393939394, 0], [1.97979797979798, 0], [2.0202020202020203, 0], [2.060606060606061, 0], [2.101010101010101, 0], [2.1414141414141414, 0], [2.181818181818182, 0], [2.2222222222222223, 0], [2.262626262626263, 0], [2.303030303030303, 0], [2.3434343434343434, 0], [2.383838383838384, 0], [2.4242424242424243, 0], [2.464646464646465, 0], [2.505050505050505, 0], [2.545454545454546, 0], [2.585858585858586, 0], [2.6262626262626263, 0], [2.666666666666667, 0], [2.707070707070707, 0], [2.747474747474748, 0], [2.787878787878788, 0], [2.8282828282828287, 0], [2.868686868686869, 0], [2.909090909090909, 0], [2.94949494949495, 0], [2.98989898989899, 0], [3.0303030303030307, 0], [3.070707070707071, 0], [3.111111111111111, 0], [3.151515151515152, 0], [3.191919191919192, 0], [3.2323232323232327, 0], [3.272727272727273, 0], [3.3131313131313136, 0], [3.353535353535354, 0], [3.393939393939394, 0], [3.4343434343434347, 0], [3.474747474747475, 0], [3.5151515151515156, 0], [3.555555555555556, 0], [3.5959595959595965, 0], [3.6363636363636367, 0], [3.676767676767677, 0], [3.7171717171717176, 0], [3.757575757575758, 0], [3.7979797979797985, 0], [3.8383838383838387, 0], [3.878787878787879, 0], [3.9191919191919196, 0], [3.95959595959596, 0], [4.0, 0]]}
|
{"local_extrema": [], "null": [[0.0, 0], [0.04040404040404041, 0], [0.08080808080808081, 0], [0.12121212121212122, 0], [0.16161616161616163, 0], [0.20202020202020204, 0], [0.24242424242424243, 0], [0.2828282828282829, 0], [0.32323232323232326, 0], [0.36363636363636365, 0], [0.4040404040404041, 0], [0.4444444444444445, 0], [0.48484848484848486, 0], [0.5252525252525253, 0], [0.5656565656565657, 0], [0.6060606060606061, 0], [0.6464646464646465, 0], [0.686868686868687, 0], [0.7272727272727273, 0], [0.7676767676767677, 0], [0.8080808080808082, 0], [0.8484848484848485, 0], [0.888888888888889, 0], [0.9292929292929294, 0], [0.9696969696969697, 0], [1.0101010101010102, 0], [1.0505050505050506, 0], [1.090909090909091, 0], [1.1313131313131315, 0], [1.1717171717171717, 0], [1.2121212121212122, 0], [1.2525252525252526, 0], [1.292929292929293, 0], [1.3333333333333335, 0], [1.373737373737374, 0], [1.4141414141414144, 0], [1.4545454545454546, 0], [1.494949494949495, 0], [1.5353535353535355, 0], [1.575757575757576, 0], [1.6161616161616164, 0], [1.6565656565656568, 0], [1.696969696969697, 0], [1.7373737373737375, 0], [1.777777777777778, 0], [1.8181818181818183, 0], [1.8585858585858588, 0], [1.8989898989898992, 0], [1.9393939393939394, 0], [1.97979797979798, 0], [2.0202020202020203, 0], [2.060606060606061, 0], [2.101010101010101, 0], [2.1414141414141414, 0], [2.181818181818182, 0], [2.2222222222222223, 0], [2.262626262626263, 0], [2.303030303030303, 0], [2.3434343434343434, 0], [2.383838383838384, 0], [2.4242424242424243, 0], [2.464646464646465, 0], [2.505050505050505, 0], [2.545454545454546, 0], [2.585858585858586, 0], [2.6262626262626263, 0], [2.666666666666667, 0], [2.707070707070707, 0], [2.747474747474748, 0], [2.787878787878788, 0], [2.8282828282828287, 0], [2.868686868686869, 0], [2.909090909090909, 0], [2.94949494949495, 0], [2.98989898989899, 0], [3.0303030303030307, 0], [3.070707070707071, 0], [3.111111111111111, 0], [3.151515151515152, 0], [3.191919191919192, 0], [3.2323232323232327, 0], [3.272727272727273, 0], [3.3131313131313136, 0], [3.353535353535354, 0], [3.393939393939394, 0], [3.4343434343434347, 0], [3.474747474747475, 0], [3.5151515151515156, 0], [3.555555555555556, 0], [3.5959595959595965, 0], [3.6363636363636367, 0], [3.676767676767677, 0], [3.7171717171717176, 0], [3.757575757575758, 0], [3.7979797979797985, 0], [3.8383838383838387, 0], [3.878787878787879, 0], [3.9191919191919196, 0], [3.95959595959596, 0], [4.0, 0]]}
|
{"local_extrema": [], "null": [[0.0, 0], [0.04040404040404041, 0], [0.08080808080808081, 0], [0.12121212121212122, 0], [0.16161616161616163, 0], [0.20202020202020204, 0], [0.24242424242424243, 0], [0.2828282828282829, 0], [0.32323232323232326, 0], [0.36363636363636365, 0], [0.4040404040404041, 0], [0.4444444444444445, 0], [0.48484848484848486, 0], [0.5252525252525253, 0], [0.5656565656565657, 0], [0.6060606060606061, 0], [0.6464646464646465, 0], [0.686868686868687, 0], [0.7272727272727273, 0], [0.7676767676767677, 0], [0.8080808080808082, 0], [0.8484848484848485, 0], [0.888888888888889, 0], [0.9292929292929294, 0], [0.9696969696969697, 0], [1.0101010101010102, 0], [1.0505050505050506, 0], [1.090909090909091, 0], [1.1313131313131315, 0], [1.1717171717171717, 0], [1.2121212121212122, 0], [1.2525252525252526, 0], [1.292929292929293, 0], [1.3333333333333335, 0], [1.373737373737374, 0], [1.4141414141414144, 0], [1.4545454545454546, 0], [1.494949494949495, 0], [1.5353535353535355, 0], [1.575757575757576, 0], [1.6161616161616164, 0], [1.6565656565656568, 0], [1.696969696969697, 0], [1.7373737373737375, 0], [1.777777777777778, 0], [1.8181818181818183, 0], [1.8585858585858588, 0], [1.8989898989898992, 0], [1.9393939393939394, 0], [1.97979797979798, 0], [2.0202020202020203, 0], [2.060606060606061, 0], [2.101010101010101, 0], [2.1414141414141414, 0], [2.181818181818182, 0], [2.2222222222222223, 0], [2.262626262626263, 0], [2.303030303030303, 0], [2.3434343434343434, 0], [2.383838383838384, 0], [2.4242424242424243, 0], [2.464646464646465, 0], [2.505050505050505, 0], [2.545454545454546, 0], [2.585858585858586, 0], [2.6262626262626263, 0], [2.666666666666667, 0], [2.707070707070707, 0], [2.747474747474748, 0], [2.787878787878788, 0], [2.8282828282828287, 0], [2.868686868686869, 0], [2.909090909090909, 0], [2.94949494949495, 0], [2.98989898989899, 0], [3.0303030303030307, 0], [3.070707070707071, 0], [3.111111111111111, 0], [3.151515151515152, 0], [3.191919191919192, 0], [3.2323232323232327, 0], [3.272727272727273, 0], [3.3131313131313136, 0], [3.353535353535354, 0], [3.393939393939394, 0], [3.4343434343434347, 0], [3.474747474747475, 0], [3.5151515151515156, 0], [3.555555555555556, 0], [3.5959595959595965, 0], [3.6363636363636367, 0], [3.676767676767677, 0], [3.7171717171717176, 0], [3.757575757575758, 0], [3.7979797979797985, 0], [3.8383838383838387, 0], [3.878787878787879, 0], [3.9191919191919196, 0], [3.95959595959596, 0], [4.0, 0]]}
|
{"local_extrema": [], "null": [[0.0, 0], [0.04040404040404041, 0], [0.08080808080808081, 0], [0.12121212121212122, 0], [0.16161616161616163, 0], [0.20202020202020204, 0], [0.24242424242424243, 0], [0.2828282828282829, 0], [0.32323232323232326, 0], [0.36363636363636365, 0], [0.4040404040404041, 0], [0.4444444444444445, 0], [0.48484848484848486, 0], [0.5252525252525253, 0], [0.5656565656565657, 0], [0.6060606060606061, 0], [0.6464646464646465, 0], [0.686868686868687, 0], [0.7272727272727273, 0], [0.7676767676767677, 0], [0.8080808080808082, 0], [0.8484848484848485, 0], [0.888888888888889, 0], [0.9292929292929294, 0], [0.9696969696969697, 0], [1.0101010101010102, 0], [1.0505050505050506, 0], [1.090909090909091, 0], [1.1313131313131315, 0], [1.1717171717171717, 0], [1.2121212121212122, 0], [1.2525252525252526, 0], [1.292929292929293, 0], [1.3333333333333335, 0], [1.373737373737374, 0], [1.4141414141414144, 0], [1.4545454545454546, 0], [1.494949494949495, 0], [1.5353535353535355, 0], [1.575757575757576, 0], [1.6161616161616164, 0], [1.6565656565656568, 0], [1.696969696969697, 0], [1.7373737373737375, 0], [1.777777777777778, 0], [1.8181818181818183, 0], [1.8585858585858588, 0], [1.8989898989898992, 0], [1.9393939393939394, 0], [1.97979797979798, 0], [2.0202020202020203, 0], [2.060606060606061, 0], [2.101010101010101, 0], [2.1414141414141414, 0], [2.181818181818182, 0], [2.2222222222222223, 0], [2.262626262626263, 0], [2.303030303030303, 0], [2.3434343434343434, 0], [2.383838383838384, 0], [2.4242424242424243, 0], [2.464646464646465, 0], [2.505050505050505, 0], [2.545454545454546, 0], [2.585858585858586, 0], [2.6262626262626263, 0], [2.666666666666667, 0], [2.707070707070707, 0], [2.747474747474748, 0], [2.787878787878788, 0], [2.8282828282828287, 0], [2.868686868686869, 0], [2.909090909090909, 0], [2.94949494949495, 0], [2.98989898989899, 0], [3.0303030303030307, 0], [3.070707070707071, 0], [3.111111111111111, 0], [3.151515151515152, 0], [3.191919191919192, 0], [3.2323232323232327, 0], [3.272727272727273, 0], [3.3131313131313136, 0], [3.353535353535354, 0], [3.393939393939394, 0], [3.4343434343434347, 0], [3.474747474747475, 0], [3.5151515151515156, 0], [3.555555555555556, 0], [3.5959595959595965, 0], [3.6363636363636367, 0], [3.676767676767677, 0], [3.7171717171717176, 0], [3.757575757575758, 0], [3.7979797979797985, 0], [3.8383838383838387, 0], [3.878787878787879, 0], [3.9191919191919196, 0], [3.95959595959596, 0], [4.0, 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "-P", "moment": "0"}, {"coordinate": "2*L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "2*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "P"}, {"point": "2*L", "type": "Force", "value": "0"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "2*L"], "shear_force": "0", "bending_moment": "0"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "2*L"], "deflection": "0", "rotation": "0"}]}
|
[
"Question: \nGiven a beam of length 2*L with a pin support at x=0 and a roller support at x=2*L, and a downward point load of -P at x=0.0*L, calculate the reaction forces at the supports.",
"Question: Determine the reaction forces at the pin and roller supports of a simply supported beam with a length of 2*L, subjected to a downward point load of magnitude P at the pin support location.",
"What are the reaction forces at the pin and roller supports of a beam with a length of 2*L, supported at x=0 (pin) and x=2*L (roller), with a downward point load of -P at x=0?",
"Given a beam of length 2*L with a pin support at x=0 and a roller support at x=2*L, and a downward point load of -P at x=0.0*L, calculate the reaction forces at the supports."
] |
[
"P",
"0"
] |
5
| 0.5
|
{"P": "-P", "q": 0, "L": "2*L", "M": 0, "E": "E", "I": "I"}
|
[
0,
0.020202020202020204,
0.04040404040404041,
0.06060606060606061,
0.08080808080808081,
0.10101010101010102,
0.12121212121212122,
0.14141414141414144,
0.16161616161616163,
0.18181818181818182,
0.20202020202020204,
0.22222222222222224,
0.24242424242424243,
0.26262626262626265,
0.2828282828282829,
0.30303030303030304,
0.32323232323232326,
0.3434343434343435,
0.36363636363636365,
0.38383838383838387,
0.4040404040404041,
0.42424242424242425,
0.4444444444444445,
0.4646464646464647,
0.48484848484848486,
0.5050505050505051,
0.5252525252525253,
0.5454545454545455,
0.5656565656565657,
0.5858585858585859,
0.6060606060606061,
0.6262626262626263,
0.6464646464646465,
0.6666666666666667,
0.686868686868687,
0.7070707070707072,
0.7272727272727273,
0.7474747474747475,
0.7676767676767677,
0.787878787878788,
0.8080808080808082,
0.8282828282828284,
0.8484848484848485,
0.8686868686868687,
0.888888888888889,
0.9090909090909092,
0.9292929292929294,
0.9494949494949496,
0.9696969696969697,
0.98989898989899,
1.0101010101010102,
1.0303030303030305,
1.0505050505050506,
1.0707070707070707,
1.090909090909091,
1.1111111111111112,
1.1313131313131315,
1.1515151515151516,
1.1717171717171717,
1.191919191919192,
1.2121212121212122,
1.2323232323232325,
1.2525252525252526,
1.272727272727273,
1.292929292929293,
1.3131313131313131,
1.3333333333333335,
1.3535353535353536,
1.373737373737374,
1.393939393939394,
1.4141414141414144,
1.4343434343434345,
1.4545454545454546,
1.474747474747475,
1.494949494949495,
1.5151515151515154,
1.5353535353535355,
1.5555555555555556,
1.575757575757576,
1.595959595959596,
1.6161616161616164,
1.6363636363636365,
1.6565656565656568,
1.676767676767677,
1.696969696969697,
1.7171717171717173,
1.7373737373737375,
1.7575757575757578,
1.777777777777778,
1.7979797979797982,
1.8181818181818183,
1.8383838383838385,
1.8585858585858588,
1.878787878787879,
1.8989898989898992,
1.9191919191919193,
1.9393939393939394,
1.9595959595959598,
1.97979797979798,
2,
2,
2.0202020202020203,
2.04040404040404,
2.0606060606060606,
2.080808080808081,
2.101010101010101,
2.121212121212121,
2.1414141414141414,
2.1616161616161618,
2.1818181818181817,
2.202020202020202,
2.2222222222222223,
2.242424242424242,
2.2626262626262625,
2.282828282828283,
2.303030303030303,
2.323232323232323,
2.3434343434343434,
2.3636363636363638,
2.383838383838384,
2.404040404040404,
2.4242424242424243,
2.4444444444444446,
2.4646464646464645,
2.484848484848485,
2.505050505050505,
2.525252525252525,
2.5454545454545454,
2.5656565656565657,
2.5858585858585856,
2.606060606060606,
2.6262626262626263,
2.6464646464646466,
2.666666666666667,
2.686868686868687,
2.707070707070707,
2.7272727272727275,
2.7474747474747474,
2.7676767676767677,
2.787878787878788,
2.808080808080808,
2.8282828282828283,
2.8484848484848486,
2.8686868686868685,
2.888888888888889,
2.909090909090909,
2.9292929292929295,
2.94949494949495,
2.9696969696969697,
2.98989898989899,
3.0101010101010104,
3.0303030303030303,
3.0505050505050506,
3.070707070707071,
3.090909090909091,
3.111111111111111,
3.1313131313131315,
3.1515151515151514,
3.1717171717171717,
3.191919191919192,
3.212121212121212,
3.2323232323232327,
3.2525252525252526,
3.272727272727273,
3.2929292929292933,
3.313131313131313,
3.3333333333333335,
3.353535353535354,
3.3737373737373737,
3.393939393939394,
3.4141414141414144,
3.4343434343434343,
3.4545454545454546,
3.474747474747475,
3.494949494949495,
3.5151515151515156,
3.5353535353535355,
3.5555555555555554,
3.575757575757576,
3.595959595959596,
3.6161616161616164,
3.6363636363636367,
3.6565656565656566,
3.676767676767677,
3.6969696969696972,
3.717171717171717,
3.7373737373737375,
3.757575757575758,
3.7777777777777777,
3.7979797979797985,
3.8181818181818183,
3.8383838383838382,
3.858585858585859,
3.878787878787879,
3.8989898989898992,
3.9191919191919196,
3.9393939393939394,
3.95959595959596,
3.97979797979798,
4
] |
[
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5,
-0.5
] |
[
0,
-0.010101010101010102,
-0.020202020202020204,
-0.030303030303030304,
-0.04040404040404041,
-0.05050505050505051,
-0.06060606060606061,
-0.07070707070707072,
-0.08080808080808081,
-0.09090909090909091,
-0.10101010101010102,
-0.11111111111111112,
-0.12121212121212122,
-0.13131313131313133,
-0.14141414141414144,
-0.15151515151515152,
-0.16161616161616163,
-0.17171717171717174,
-0.18181818181818182,
-0.19191919191919193,
-0.20202020202020204,
-0.21212121212121213,
-0.22222222222222224,
-0.23232323232323235,
-0.24242424242424243,
-0.25252525252525254,
-0.26262626262626265,
-0.27272727272727276,
-0.2828282828282829,
-0.29292929292929293,
-0.30303030303030304,
-0.31313131313131315,
-0.32323232323232326,
-0.33333333333333337,
-0.3434343434343435,
-0.3535353535353536,
-0.36363636363636365,
-0.37373737373737376,
-0.38383838383838387,
-0.393939393939394,
-0.4040404040404041,
-0.4141414141414142,
-0.42424242424242425,
-0.43434343434343436,
-0.4444444444444445,
-0.4545454545454546,
-0.4646464646464647,
-0.4747474747474748,
-0.48484848484848486,
-0.494949494949495,
-0.5050505050505051,
-0.5151515151515152,
-0.5252525252525253,
-0.5353535353535354,
-0.5454545454545455,
-0.5555555555555556,
-0.5656565656565657,
-0.5757575757575758,
-0.5858585858585859,
-0.595959595959596,
-0.6060606060606061,
-0.6161616161616162,
-0.6262626262626263,
-0.6363636363636365,
-0.6464646464646465,
-0.6565656565656566,
-0.6666666666666667,
-0.6767676767676768,
-0.686868686868687,
-0.696969696969697,
-0.7070707070707072,
-0.7171717171717172,
-0.7272727272727273,
-0.7373737373737375,
-0.7474747474747475,
-0.7575757575757577,
-0.7676767676767677,
-0.7777777777777778,
-0.787878787878788,
-0.797979797979798,
-0.8080808080808082,
-0.8181818181818182,
-0.8282828282828284,
-0.8383838383838385,
-0.8484848484848485,
-0.8585858585858587,
-0.8686868686868687,
-0.8787878787878789,
-0.888888888888889,
-0.8989898989898991,
-0.9090909090909092,
-0.9191919191919192,
-0.9292929292929294,
-0.9393939393939394,
-0.9494949494949496,
-0.9595959595959597,
-0.9696969696969697,
-0.9797979797979799,
-0.98989898989899,
-1,
-1,
-0.9898989898989898,
-0.9797979797979799,
-0.9696969696969697,
-0.9595959595959596,
-0.9494949494949494,
-0.9393939393939394,
-0.9292929292929293,
-0.9191919191919191,
-0.9090909090909092,
-0.898989898989899,
-0.8888888888888888,
-0.8787878787878789,
-0.8686868686868687,
-0.8585858585858586,
-0.8484848484848484,
-0.8383838383838385,
-0.8282828282828283,
-0.8181818181818181,
-0.808080808080808,
-0.797979797979798,
-0.7878787878787878,
-0.7777777777777777,
-0.7676767676767677,
-0.7575757575757576,
-0.7474747474747474,
-0.7373737373737375,
-0.7272727272727273,
-0.7171717171717171,
-0.7070707070707072,
-0.696969696969697,
-0.6868686868686869,
-0.6767676767676767,
-0.6666666666666665,
-0.6565656565656566,
-0.6464646464646464,
-0.6363636363636362,
-0.6262626262626263,
-0.6161616161616161,
-0.606060606060606,
-0.595959595959596,
-0.5858585858585859,
-0.5757575757575757,
-0.5656565656565657,
-0.5555555555555556,
-0.5454545454545454,
-0.5353535353535352,
-0.5252525252525251,
-0.5151515151515151,
-0.505050505050505,
-0.4949494949494948,
-0.48484848484848486,
-0.4747474747474747,
-0.46464646464646453,
-0.4545454545454546,
-0.4444444444444444,
-0.43434343434343425,
-0.4242424242424243,
-0.41414141414141414,
-0.404040404040404,
-0.39393939393939403,
-0.38383838383838365,
-0.3737373737373737,
-0.36363636363636354,
-0.35353535353535337,
-0.3434343434343434,
-0.33333333333333326,
-0.3232323232323231,
-0.31313131313131315,
-0.303030303030303,
-0.2929292929292928,
-0.2828282828282829,
-0.2727272727272727,
-0.26262626262626254,
-0.2525252525252526,
-0.2424242424242422,
-0.23232323232323226,
-0.22222222222222232,
-0.21212121212121193,
-0.202020202020202,
-0.19191919191919182,
-0.18181818181818166,
-0.1717171717171717,
-0.16161616161616155,
-0.15151515151515138,
-0.14141414141414144,
-0.13131313131313127,
-0.1212121212121211,
-0.11111111111111116,
-0.10101010101010077,
-0.09090909090909083,
-0.08080808080808088,
-0.0707070707070705,
-0.06060606060606055,
-0.050505050505050386,
-0.04040404040404022,
-0.030303030303030276,
-0.02020202020202011,
-0.010101010101009944,
0
] |
[
1,
0.9998979695949393,
0.9995918783797572,
0.9990817263544536,
0.9983675135190286,
0.9974492398734823,
0.9963269054178145,
0.9950005101520253,
0.9934700540761147,
0.9917355371900827,
0.9897969594939292,
0.9876543209876543,
0.9853076216712581,
0.9827568615447403,
0.9800020406081013,
0.9770431588613406,
0.9738802163044588,
0.9705132129374554,
0.9669421487603306,
0.9631670237730844,
0.9591878379757167,
0.9550045913682277,
0.9506172839506173,
0.9460259157228854,
0.9412304866850322,
0.9362309968370575,
0.9310274461789613,
0.9256198347107438,
0.9200081624324048,
0.9141924293439445,
0.9081726354453628,
0.9019487807366595,
0.8955208652178349,
0.8888888888888888,
0.8820528517498214,
0.8750127538006326,
0.8677685950413223,
0.8603203754718907,
0.8526680950923375,
0.8448117539026629,
0.836751351902867,
0.8284868890929497,
0.820018365472911,
0.8113457810427507,
0.8024691358024691,
0.7933884297520661,
0.7841036628915417,
0.7746148352208958,
0.7649219467401285,
0.7550249974492398,
0.7449239873482297,
0.7346189164370982,
0.7241097847158453,
0.7133965921844709,
0.7024793388429751,
0.691358024691358,
0.6800326497296193,
0.6685032139577594,
0.656769717375778,
0.644832159983675,
0.6326905417814508,
0.620344862769105,
0.6077951229466381,
0.5950413223140494,
0.5820834608713397,
0.5689215386185082,
0.5555555555555555,
0.5419855116824813,
0.5282114069992856,
0.5142332415059687,
0.5000510152025301,
0.48566472808897043,
0.47107438016528924,
0.45627997143148646,
0.44128150188756243,
0.4260789715335168,
0.41067238036934994,
0.3950617283950617,
0.3792470156106519,
0.3632282420161208,
0.34700540761146803,
0.3305785123966941,
0.3139475563717986,
0.29711253953678185,
0.2800734618916436,
0.2628303234363839,
0.24538312417100283,
0.22773186409550028,
0.20987654320987648,
0.19181716151413097,
0.17355371900826433,
0.1550862156922762,
0.1364146515661665,
0.11753902662993565,
0.0984593408835831,
0.0791755943271093,
0.05968778696051413,
0.03999591878379738,
0.020099989796959372,
0,
0,
-0.020099989796959594,
-0.03999591878379771,
-0.05968778696051391,
-0.07917559432710952,
-0.09845934088358366,
-0.11753902662993543,
-0.1364146515661666,
-0.15508621569227632,
-0.17355371900826455,
-0.1918171615141313,
-0.2098765432098766,
-0.2277318640955004,
-0.24538312417100272,
-0.262830323436384,
-0.28007346189164384,
-0.29711253953678174,
-0.31394755637179905,
-0.330578512396694,
-0.34700540761146836,
-0.3632282420161208,
-0.37924701561065177,
-0.3950617283950617,
-0.41067238036935017,
-0.42607897153351715,
-0.44128150188756265,
-0.4562799714314867,
-0.47107438016528924,
-0.4856647280889703,
-0.5000510152025299,
-0.5142332415059689,
-0.5282114069992856,
-0.5419855116824817,
-0.5555555555555558,
-0.5689215386185085,
-0.5820834608713397,
-0.5950413223140498,
-0.6077951229466381,
-0.6203448627691053,
-0.632690541781451,
-0.6448321599836753,
-0.656769717375778,
-0.6685032139577594,
-0.6800326497296192,
-0.691358024691358,
-0.7024793388429753,
-0.7133965921844712,
-0.7241097847158455,
-0.7346189164370984,
-0.7449239873482298,
-0.7550249974492402,
-0.7649219467401287,
-0.7746148352208957,
-0.7841036628915417,
-0.7933884297520661,
-0.8024691358024691,
-0.8113457810427507,
-0.8200183654729107,
-0.8284868890929498,
-0.8367513519028673,
-0.8448117539026629,
-0.8526680950923375,
-0.8603203754718907,
-0.8677685950413223,
-0.8750127538006329,
-0.8820528517498216,
-0.8888888888888888,
-0.895520865217835,
-0.9019487807366593,
-0.9081726354453625,
-0.9141924293439447,
-0.920008162432405,
-0.9256198347107438,
-0.9310274461789612,
-0.9362309968370575,
-0.9412304866850323,
-0.9460259157228856,
-0.9506172839506171,
-0.9550045913682279,
-0.9591878379757168,
-0.9631670237730843,
-0.9669421487603307,
-0.9705132129374552,
-0.9738802163044586,
-0.9770431588613406,
-0.9800020406081011,
-0.9827568615447402,
-0.9853076216712582,
-0.9876543209876543,
-0.9897969594939293,
-0.9917355371900825,
-0.9934700540761146,
-0.9950005101520252,
-0.9963269054178143,
-0.9974492398734824,
-0.9983675135190286,
-0.9990817263544538,
-0.999591878379757,
-0.9998979695949393,
-1
] |
[
0,
0.020201333128585453,
0.04039854381656239,
0.060587509623322294,
0.08076410810825667,
0.10092421683075699,
0.12106371335021474,
0.14117847522602142,
0.1612643800175685,
0.18131730528424744,
0.2013331285854498,
0.221307727480567,
0.24123697952899056,
0.261116762290112,
0.2809429533233227,
0.3007114301880142,
0.32041807044357806,
0.3400587516494057,
0.35962935136488855,
0.3791257471494182,
0.39854381656238613,
0.4178794371631837,
0.4371284865112026,
0.45628684216583415,
0.47535038168646987,
0.4943149826325013,
0.5131765225633199,
0.5319308790383172,
0.5505739296168846,
0.5691015518584134,
0.5875096233222955,
0.6057940215679223,
0.623950624154685,
0.6419753086419754,
0.6598639525891848,
0.6776124335557048,
0.6952166291009266,
0.7126724167842422,
0.7299756741650426,
0.7471222788027196,
0.7641081082566646,
0.7809290400862691,
0.7975809518509244,
0.8140597211100221,
0.8303612254229539,
0.846481342349111,
0.862415949447885,
0.8781609242786674,
0.8937121444008497,
0.9090654873738233,
0.9242168307569798,
0.9391620521097107,
0.9538970289914073,
0.968417638961461,
0.9827197595792638,
0.9967992684042067,
1.0106520429956816,
1.0242739609130795,
1.0376608997157921,
1.050808736963211,
1.0637133502147278,
1.0763706170297336,
1.08877641496762,
1.1009266215877789,
1.112817114449601,
1.1244437711124784,
1.1358024691358026,
1.1468890860789647,
1.1576994995013568,
1.1682295869623696,
1.178475226021395,
1.1884322942378245,
1.1980966691710495,
1.2074642283804615,
1.216530849425452,
1.2252924098654128,
1.233744787259735,
1.2418838591678099,
1.2497055031490296,
1.2572055967627849,
1.2643800175684679,
1.2712246431254697,
1.2777353509931821,
1.2839080187309961,
1.2897385238983037,
1.2952227440544961,
1.300356556758965,
1.3051358395711015,
1.3095564700502975,
1.3136143257559443,
1.3173052842474333,
1.320625223084156,
1.323570019825504,
1.326135552030869,
1.3283176972596422,
1.3301123330712152,
1.331515337024979,
1.332522586680326,
1.333129959596647,
1.3333333333333335,
1.3333333333333366,
1.3331299595966493,
1.3325225866803296,
1.3315153370249817,
1.3301123330712175,
1.3283176972596449,
1.326135552030872,
1.3235700198255071,
1.3206252230841593,
1.317305284247436,
1.313614325755946,
1.3095564700503002,
1.3051358395711037,
1.3003565567589672,
1.2952227440544983,
1.2897385238983063,
1.283908018730998,
1.277735350993185,
1.2712246431254726,
1.2643800175684707,
1.257205596762788,
1.2497055031490327,
1.2418838591678125,
1.2337447872597376,
1.2252924098654154,
1.2165308494254554,
1.2074642283804642,
1.1980966691710528,
1.1884322942378271,
1.1784752260213973,
1.1682295869623727,
1.157699499501359,
1.1468890860789664,
1.1358024691358044,
1.1244437711124813,
1.1128171144496029,
1.100926621587782,
1.0887764149676227,
1.076370617029736,
1.0637133502147296,
1.0508087369632135,
1.0376608997157946,
1.024273960913082,
1.0106520429956833,
0.9967992684042088,
0.9827197595792652,
0.9684176389614643,
0.9538970289914102,
0.9391620521097139,
0.9242168307569831,
0.9090654873738271,
0.8937121444008516,
0.8781609242786694,
0.8624159494478865,
0.8464813423491147,
0.8303612254229571,
0.814059721110024,
0.7975809518509256,
0.7809290400862721,
0.7641081082566683,
0.7471222788027228,
0.7299756741650456,
0.7126724167842444,
0.6952166291009285,
0.6776124335557072,
0.6598639525891881,
0.6419753086419768,
0.6239506241546882,
0.6057940215679243,
0.5875096233222963,
0.5691015518584153,
0.550573929616887,
0.531930879038319,
0.5131765225633225,
0.49431498263250306,
0.4753503816864719,
0.4562868421658366,
0.43712848651120284,
0.4178794371631853,
0.3985438165623898,
0.37912574714942027,
0.3596293513648896,
0.34005875164940713,
0.3204180704435804,
0.30071143018801516,
0.2809429533233243,
0.2611167622901118,
0.24123697952899237,
0.22130772748056637,
0.20133312858545027,
0.18131730528424805,
0.16126438001757082,
0.14117847522602256,
0.12106371335021615,
0.10092421683075914,
0.0807641081082573,
0.060587509623325264,
0.04039854381656349,
0.020201333128588406,
2.220446049250313e-15
] |
{"local_extrema": [], "null": [[2.0, 0]]}
|
{"local_extrema": [[0.0, -0.0], [2.0, -1.0], [4.0, 0.0]], "null": [[0.0, 0], [4.0, 0]]}
|
{"local_extrema": [[0.0, 1.0], [4.0, -1.0]], "null": [[2.0, 0]]}
|
{"local_extrema": [[0.0, 0.0], [2.0, 1.3333333333333335], [4.0, 2.220446049250313e-15]], "null": [[0.0, 0], [4.0, 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "1.0*L", "type": "Continuity point", "load": "-P", "moment": "0"}, {"coordinate": "2*L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "1.0*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["1.0*L", "2*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "0.5*P"}, {"point": "2*L", "type": "Force", "value": "0.5*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "1.0*L"], "shear_force": "-0.5*P", "bending_moment": "0.5*P*x"}, {"span": ["1.0*L", "2*L"], "shear_force": "0.5*P", "bending_moment": "L*P - 0.5*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "1.0*L"], "deflection": "-0.25*L**2*P*x/(E*I) + 0.0833333333333333*P*x**3/(E*I)", "rotation": "-0.25*L**2*P/(E*I) + 0.25*P*x**2/(E*I)"}, {"span": ["1.0*L", "2*L"], "deflection": "0.166666666666667*L**3*P/(E*I) - 0.75*L**2*P*x/(E*I) + 0.5*L*P*x**2/(E*I) - 0.0833333333333333*P*x**3/(E*I)", "rotation": "-0.75*L**2*P/(E*I) + 1.0*L*P*x/(E*I) - 0.25*P*x**2/(E*I)"}]}
|
[
"What are the reaction forces at the pin support (R_A) and the roller support (R_B) of a beam with a length of 2*L, supported at x=0 and x=2*L respectively, with a downward point load of P at x=L?",
"What are the reaction forces at the supports of a beam with a length of 2*L, supported at x=0 (pin) and x=2*L (roller), with a downward point load of -P applied at x=1.0*L?",
"Given a beam with a length of 2*L, supported by a pin at x=0 and a roller at x=2*L, and subjected to a downward point load of -P at x=1.0*L, calculate the reaction forces at the supports.",
"What are the reaction forces at the pin support (x=0) and roller support (x=2*L) for a beam of length 2*L with a downward point load of P at x=1*L?"
] |
[
"0.5P",
"0.5P"
] |
6
| 0
|
{"P": "-2*P", "q": 0, "L": "2*L", "M": 0, "E": "E", "I": "I"}
|
[
0,
0.04040404040404041,
0.08080808080808081,
0.12121212121212122,
0.16161616161616163,
0.20202020202020204,
0.24242424242424243,
0.2828282828282829,
0.32323232323232326,
0.36363636363636365,
0.4040404040404041,
0.4444444444444445,
0.48484848484848486,
0.5252525252525253,
0.5656565656565657,
0.6060606060606061,
0.6464646464646465,
0.686868686868687,
0.7272727272727273,
0.7676767676767677,
0.8080808080808082,
0.8484848484848485,
0.888888888888889,
0.9292929292929294,
0.9696969696969697,
1.0101010101010102,
1.0505050505050506,
1.090909090909091,
1.1313131313131315,
1.1717171717171717,
1.2121212121212122,
1.2525252525252526,
1.292929292929293,
1.3333333333333335,
1.373737373737374,
1.4141414141414144,
1.4545454545454546,
1.494949494949495,
1.5353535353535355,
1.575757575757576,
1.6161616161616164,
1.6565656565656568,
1.696969696969697,
1.7373737373737375,
1.777777777777778,
1.8181818181818183,
1.8585858585858588,
1.8989898989898992,
1.9393939393939394,
1.97979797979798,
2.0202020202020203,
2.060606060606061,
2.101010101010101,
2.1414141414141414,
2.181818181818182,
2.2222222222222223,
2.262626262626263,
2.303030303030303,
2.3434343434343434,
2.383838383838384,
2.4242424242424243,
2.464646464646465,
2.505050505050505,
2.545454545454546,
2.585858585858586,
2.6262626262626263,
2.666666666666667,
2.707070707070707,
2.747474747474748,
2.787878787878788,
2.8282828282828287,
2.868686868686869,
2.909090909090909,
2.94949494949495,
2.98989898989899,
3.0303030303030307,
3.070707070707071,
3.111111111111111,
3.151515151515152,
3.191919191919192,
3.2323232323232327,
3.272727272727273,
3.3131313131313136,
3.353535353535354,
3.393939393939394,
3.4343434343434347,
3.474747474747475,
3.5151515151515156,
3.555555555555556,
3.5959595959595965,
3.6363636363636367,
3.676767676767677,
3.7171717171717176,
3.757575757575758,
3.7979797979797985,
3.8383838383838387,
3.878787878787879,
3.9191919191919196,
3.95959595959596,
4
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] |
{"local_extrema": [], "null": [[0.0, 0], [0.04040404040404041, 0], [0.08080808080808081, 0], [0.12121212121212122, 0], [0.16161616161616163, 0], [0.20202020202020204, 0], [0.24242424242424243, 0], [0.2828282828282829, 0], [0.32323232323232326, 0], [0.36363636363636365, 0], [0.4040404040404041, 0], [0.4444444444444445, 0], [0.48484848484848486, 0], [0.5252525252525253, 0], [0.5656565656565657, 0], [0.6060606060606061, 0], [0.6464646464646465, 0], [0.686868686868687, 0], [0.7272727272727273, 0], [0.7676767676767677, 0], [0.8080808080808082, 0], [0.8484848484848485, 0], [0.888888888888889, 0], [0.9292929292929294, 0], [0.9696969696969697, 0], [1.0101010101010102, 0], [1.0505050505050506, 0], [1.090909090909091, 0], [1.1313131313131315, 0], [1.1717171717171717, 0], [1.2121212121212122, 0], [1.2525252525252526, 0], [1.292929292929293, 0], [1.3333333333333335, 0], [1.373737373737374, 0], [1.4141414141414144, 0], [1.4545454545454546, 0], [1.494949494949495, 0], [1.5353535353535355, 0], [1.575757575757576, 0], [1.6161616161616164, 0], [1.6565656565656568, 0], [1.696969696969697, 0], [1.7373737373737375, 0], [1.777777777777778, 0], [1.8181818181818183, 0], [1.8585858585858588, 0], [1.8989898989898992, 0], [1.9393939393939394, 0], [1.97979797979798, 0], [2.0202020202020203, 0], [2.060606060606061, 0], [2.101010101010101, 0], [2.1414141414141414, 0], [2.181818181818182, 0], [2.2222222222222223, 0], [2.262626262626263, 0], [2.303030303030303, 0], [2.3434343434343434, 0], [2.383838383838384, 0], [2.4242424242424243, 0], [2.464646464646465, 0], [2.505050505050505, 0], [2.545454545454546, 0], [2.585858585858586, 0], [2.6262626262626263, 0], [2.666666666666667, 0], [2.707070707070707, 0], [2.747474747474748, 0], [2.787878787878788, 0], [2.8282828282828287, 0], [2.868686868686869, 0], [2.909090909090909, 0], [2.94949494949495, 0], [2.98989898989899, 0], [3.0303030303030307, 0], [3.070707070707071, 0], [3.111111111111111, 0], [3.151515151515152, 0], [3.191919191919192, 0], [3.2323232323232327, 0], [3.272727272727273, 0], [3.3131313131313136, 0], [3.353535353535354, 0], [3.393939393939394, 0], [3.4343434343434347, 0], [3.474747474747475, 0], [3.5151515151515156, 0], [3.555555555555556, 0], [3.5959595959595965, 0], [3.6363636363636367, 0], [3.676767676767677, 0], [3.7171717171717176, 0], [3.757575757575758, 0], [3.7979797979797985, 0], [3.8383838383838387, 0], [3.878787878787879, 0], [3.9191919191919196, 0], [3.95959595959596, 0], [4.0, 0]]}
|
{"local_extrema": [], "null": [[0.0, 0], [0.04040404040404041, 0], [0.08080808080808081, 0], [0.12121212121212122, 0], [0.16161616161616163, 0], [0.20202020202020204, 0], [0.24242424242424243, 0], [0.2828282828282829, 0], [0.32323232323232326, 0], [0.36363636363636365, 0], [0.4040404040404041, 0], [0.4444444444444445, 0], [0.48484848484848486, 0], [0.5252525252525253, 0], [0.5656565656565657, 0], [0.6060606060606061, 0], [0.6464646464646465, 0], [0.686868686868687, 0], [0.7272727272727273, 0], [0.7676767676767677, 0], [0.8080808080808082, 0], [0.8484848484848485, 0], [0.888888888888889, 0], [0.9292929292929294, 0], [0.9696969696969697, 0], [1.0101010101010102, 0], [1.0505050505050506, 0], [1.090909090909091, 0], [1.1313131313131315, 0], [1.1717171717171717, 0], [1.2121212121212122, 0], [1.2525252525252526, 0], [1.292929292929293, 0], [1.3333333333333335, 0], [1.373737373737374, 0], [1.4141414141414144, 0], [1.4545454545454546, 0], [1.494949494949495, 0], [1.5353535353535355, 0], [1.575757575757576, 0], [1.6161616161616164, 0], [1.6565656565656568, 0], [1.696969696969697, 0], [1.7373737373737375, 0], [1.777777777777778, 0], [1.8181818181818183, 0], [1.8585858585858588, 0], [1.8989898989898992, 0], [1.9393939393939394, 0], [1.97979797979798, 0], [2.0202020202020203, 0], [2.060606060606061, 0], [2.101010101010101, 0], [2.1414141414141414, 0], [2.181818181818182, 0], [2.2222222222222223, 0], [2.262626262626263, 0], [2.303030303030303, 0], [2.3434343434343434, 0], [2.383838383838384, 0], [2.4242424242424243, 0], [2.464646464646465, 0], [2.505050505050505, 0], [2.545454545454546, 0], [2.585858585858586, 0], [2.6262626262626263, 0], [2.666666666666667, 0], [2.707070707070707, 0], [2.747474747474748, 0], [2.787878787878788, 0], [2.8282828282828287, 0], [2.868686868686869, 0], [2.909090909090909, 0], [2.94949494949495, 0], [2.98989898989899, 0], [3.0303030303030307, 0], [3.070707070707071, 0], [3.111111111111111, 0], [3.151515151515152, 0], [3.191919191919192, 0], [3.2323232323232327, 0], [3.272727272727273, 0], [3.3131313131313136, 0], [3.353535353535354, 0], [3.393939393939394, 0], [3.4343434343434347, 0], [3.474747474747475, 0], [3.5151515151515156, 0], [3.555555555555556, 0], [3.5959595959595965, 0], [3.6363636363636367, 0], [3.676767676767677, 0], [3.7171717171717176, 0], [3.757575757575758, 0], [3.7979797979797985, 0], [3.8383838383838387, 0], [3.878787878787879, 0], [3.9191919191919196, 0], [3.95959595959596, 0], [4.0, 0]]}
|
{"local_extrema": [], "null": [[0.0, 0], [0.04040404040404041, 0], [0.08080808080808081, 0], [0.12121212121212122, 0], [0.16161616161616163, 0], [0.20202020202020204, 0], [0.24242424242424243, 0], [0.2828282828282829, 0], [0.32323232323232326, 0], [0.36363636363636365, 0], [0.4040404040404041, 0], [0.4444444444444445, 0], [0.48484848484848486, 0], [0.5252525252525253, 0], [0.5656565656565657, 0], [0.6060606060606061, 0], [0.6464646464646465, 0], [0.686868686868687, 0], [0.7272727272727273, 0], [0.7676767676767677, 0], [0.8080808080808082, 0], [0.8484848484848485, 0], [0.888888888888889, 0], [0.9292929292929294, 0], [0.9696969696969697, 0], [1.0101010101010102, 0], [1.0505050505050506, 0], [1.090909090909091, 0], [1.1313131313131315, 0], [1.1717171717171717, 0], [1.2121212121212122, 0], [1.2525252525252526, 0], [1.292929292929293, 0], [1.3333333333333335, 0], [1.373737373737374, 0], [1.4141414141414144, 0], [1.4545454545454546, 0], [1.494949494949495, 0], [1.5353535353535355, 0], [1.575757575757576, 0], [1.6161616161616164, 0], [1.6565656565656568, 0], [1.696969696969697, 0], [1.7373737373737375, 0], [1.777777777777778, 0], [1.8181818181818183, 0], [1.8585858585858588, 0], [1.8989898989898992, 0], [1.9393939393939394, 0], [1.97979797979798, 0], [2.0202020202020203, 0], [2.060606060606061, 0], [2.101010101010101, 0], [2.1414141414141414, 0], [2.181818181818182, 0], [2.2222222222222223, 0], [2.262626262626263, 0], [2.303030303030303, 0], [2.3434343434343434, 0], [2.383838383838384, 0], [2.4242424242424243, 0], [2.464646464646465, 0], [2.505050505050505, 0], [2.545454545454546, 0], [2.585858585858586, 0], [2.6262626262626263, 0], [2.666666666666667, 0], [2.707070707070707, 0], [2.747474747474748, 0], [2.787878787878788, 0], [2.8282828282828287, 0], [2.868686868686869, 0], [2.909090909090909, 0], [2.94949494949495, 0], [2.98989898989899, 0], [3.0303030303030307, 0], [3.070707070707071, 0], [3.111111111111111, 0], [3.151515151515152, 0], [3.191919191919192, 0], [3.2323232323232327, 0], [3.272727272727273, 0], [3.3131313131313136, 0], [3.353535353535354, 0], [3.393939393939394, 0], [3.4343434343434347, 0], [3.474747474747475, 0], [3.5151515151515156, 0], [3.555555555555556, 0], [3.5959595959595965, 0], [3.6363636363636367, 0], [3.676767676767677, 0], [3.7171717171717176, 0], [3.757575757575758, 0], [3.7979797979797985, 0], [3.8383838383838387, 0], [3.878787878787879, 0], [3.9191919191919196, 0], [3.95959595959596, 0], [4.0, 0]]}
|
{"local_extrema": [], "null": [[0.0, 0], [0.04040404040404041, 0], [0.08080808080808081, 0], [0.12121212121212122, 0], [0.16161616161616163, 0], [0.20202020202020204, 0], [0.24242424242424243, 0], [0.2828282828282829, 0], [0.32323232323232326, 0], [0.36363636363636365, 0], [0.4040404040404041, 0], [0.4444444444444445, 0], [0.48484848484848486, 0], [0.5252525252525253, 0], [0.5656565656565657, 0], [0.6060606060606061, 0], [0.6464646464646465, 0], [0.686868686868687, 0], [0.7272727272727273, 0], [0.7676767676767677, 0], [0.8080808080808082, 0], [0.8484848484848485, 0], [0.888888888888889, 0], [0.9292929292929294, 0], [0.9696969696969697, 0], [1.0101010101010102, 0], [1.0505050505050506, 0], [1.090909090909091, 0], [1.1313131313131315, 0], [1.1717171717171717, 0], [1.2121212121212122, 0], [1.2525252525252526, 0], [1.292929292929293, 0], [1.3333333333333335, 0], [1.373737373737374, 0], [1.4141414141414144, 0], [1.4545454545454546, 0], [1.494949494949495, 0], [1.5353535353535355, 0], [1.575757575757576, 0], [1.6161616161616164, 0], [1.6565656565656568, 0], [1.696969696969697, 0], [1.7373737373737375, 0], [1.777777777777778, 0], [1.8181818181818183, 0], [1.8585858585858588, 0], [1.8989898989898992, 0], [1.9393939393939394, 0], [1.97979797979798, 0], [2.0202020202020203, 0], [2.060606060606061, 0], [2.101010101010101, 0], [2.1414141414141414, 0], [2.181818181818182, 0], [2.2222222222222223, 0], [2.262626262626263, 0], [2.303030303030303, 0], [2.3434343434343434, 0], [2.383838383838384, 0], [2.4242424242424243, 0], [2.464646464646465, 0], [2.505050505050505, 0], [2.545454545454546, 0], [2.585858585858586, 0], [2.6262626262626263, 0], [2.666666666666667, 0], [2.707070707070707, 0], [2.747474747474748, 0], [2.787878787878788, 0], [2.8282828282828287, 0], [2.868686868686869, 0], [2.909090909090909, 0], [2.94949494949495, 0], [2.98989898989899, 0], [3.0303030303030307, 0], [3.070707070707071, 0], [3.111111111111111, 0], [3.151515151515152, 0], [3.191919191919192, 0], [3.2323232323232327, 0], [3.272727272727273, 0], [3.3131313131313136, 0], [3.353535353535354, 0], [3.393939393939394, 0], [3.4343434343434347, 0], [3.474747474747475, 0], [3.5151515151515156, 0], [3.555555555555556, 0], [3.5959595959595965, 0], [3.6363636363636367, 0], [3.676767676767677, 0], [3.7171717171717176, 0], [3.757575757575758, 0], [3.7979797979797985, 0], [3.8383838383838387, 0], [3.878787878787879, 0], [3.9191919191919196, 0], [3.95959595959596, 0], [4.0, 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "-2*P", "moment": "0"}, {"coordinate": "2*L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "2*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "2*P"}, {"point": "2*L", "type": "Force", "value": "0"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "2*L"], "shear_force": "0", "bending_moment": "0"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "2*L"], "deflection": "0", "rotation": "0"}]}
|
[
"Question: \nGiven a beam of length 2*L with a pin support at x=0 and a roller support at x=2*L, and a downward point load of -2*P at x=0, calculate the reaction forces at both supports.",
"Given a beam with a length of 2*L, supported by a pin at x=0 and a roller at x=2*L, and subjected to a downward point load of -2*P at x=0.0*L, calculate the reaction forces at the supports.",
"Calculate the reaction forces at the pin and roller support of a 2*L beam with a downward point load of -2*P at x=0.",
"Question: Calculate the reaction forces at the pin support (x=0) and the roller support (x=2*L) for a beam of length 2*L with a downward point load of -2*P at the fixed end."
] |
[
"2P",
"0"
] |
7
| 0.5
|
{"P": "-2*P", "q": 0, "L": "2*L", "M": 0, "E": "E", "I": "I"}
|
[
0,
0.020202020202020204,
0.04040404040404041,
0.06060606060606061,
0.08080808080808081,
0.10101010101010102,
0.12121212121212122,
0.14141414141414144,
0.16161616161616163,
0.18181818181818182,
0.20202020202020204,
0.22222222222222224,
0.24242424242424243,
0.26262626262626265,
0.2828282828282829,
0.30303030303030304,
0.32323232323232326,
0.3434343434343435,
0.36363636363636365,
0.38383838383838387,
0.4040404040404041,
0.42424242424242425,
0.4444444444444445,
0.4646464646464647,
0.48484848484848486,
0.5050505050505051,
0.5252525252525253,
0.5454545454545455,
0.5656565656565657,
0.5858585858585859,
0.6060606060606061,
0.6262626262626263,
0.6464646464646465,
0.6666666666666667,
0.686868686868687,
0.7070707070707072,
0.7272727272727273,
0.7474747474747475,
0.7676767676767677,
0.787878787878788,
0.8080808080808082,
0.8282828282828284,
0.8484848484848485,
0.8686868686868687,
0.888888888888889,
0.9090909090909092,
0.9292929292929294,
0.9494949494949496,
0.9696969696969697,
0.98989898989899,
1.0101010101010102,
1.0303030303030305,
1.0505050505050506,
1.0707070707070707,
1.090909090909091,
1.1111111111111112,
1.1313131313131315,
1.1515151515151516,
1.1717171717171717,
1.191919191919192,
1.2121212121212122,
1.2323232323232325,
1.2525252525252526,
1.272727272727273,
1.292929292929293,
1.3131313131313131,
1.3333333333333335,
1.3535353535353536,
1.373737373737374,
1.393939393939394,
1.4141414141414144,
1.4343434343434345,
1.4545454545454546,
1.474747474747475,
1.494949494949495,
1.5151515151515154,
1.5353535353535355,
1.5555555555555556,
1.575757575757576,
1.595959595959596,
1.6161616161616164,
1.6363636363636365,
1.6565656565656568,
1.676767676767677,
1.696969696969697,
1.7171717171717173,
1.7373737373737375,
1.7575757575757578,
1.777777777777778,
1.7979797979797982,
1.8181818181818183,
1.8383838383838385,
1.8585858585858588,
1.878787878787879,
1.8989898989898992,
1.9191919191919193,
1.9393939393939394,
1.9595959595959598,
1.97979797979798,
2,
2,
2.0202020202020203,
2.04040404040404,
2.0606060606060606,
2.080808080808081,
2.101010101010101,
2.121212121212121,
2.1414141414141414,
2.1616161616161618,
2.1818181818181817,
2.202020202020202,
2.2222222222222223,
2.242424242424242,
2.2626262626262625,
2.282828282828283,
2.303030303030303,
2.323232323232323,
2.3434343434343434,
2.3636363636363638,
2.383838383838384,
2.404040404040404,
2.4242424242424243,
2.4444444444444446,
2.4646464646464645,
2.484848484848485,
2.505050505050505,
2.525252525252525,
2.5454545454545454,
2.5656565656565657,
2.5858585858585856,
2.606060606060606,
2.6262626262626263,
2.6464646464646466,
2.666666666666667,
2.686868686868687,
2.707070707070707,
2.7272727272727275,
2.7474747474747474,
2.7676767676767677,
2.787878787878788,
2.808080808080808,
2.8282828282828283,
2.8484848484848486,
2.8686868686868685,
2.888888888888889,
2.909090909090909,
2.9292929292929295,
2.94949494949495,
2.9696969696969697,
2.98989898989899,
3.0101010101010104,
3.0303030303030303,
3.0505050505050506,
3.070707070707071,
3.090909090909091,
3.111111111111111,
3.1313131313131315,
3.1515151515151514,
3.1717171717171717,
3.191919191919192,
3.212121212121212,
3.2323232323232327,
3.2525252525252526,
3.272727272727273,
3.2929292929292933,
3.313131313131313,
3.3333333333333335,
3.353535353535354,
3.3737373737373737,
3.393939393939394,
3.4141414141414144,
3.4343434343434343,
3.4545454545454546,
3.474747474747475,
3.494949494949495,
3.5151515151515156,
3.5353535353535355,
3.5555555555555554,
3.575757575757576,
3.595959595959596,
3.6161616161616164,
3.6363636363636367,
3.6565656565656566,
3.676767676767677,
3.6969696969696972,
3.717171717171717,
3.7373737373737375,
3.757575757575758,
3.7777777777777777,
3.7979797979797985,
3.8181818181818183,
3.8383838383838382,
3.858585858585859,
3.878787878787879,
3.8989898989898992,
3.9191919191919196,
3.9393939393939394,
3.95959595959596,
3.97979797979798,
4
] |
[
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2,
-2
] |
[
0,
-0.04040404040404041,
-0.08080808080808081,
-0.12121212121212122,
-0.16161616161616163,
-0.20202020202020204,
-0.24242424242424243,
-0.2828282828282829,
-0.32323232323232326,
-0.36363636363636365,
-0.4040404040404041,
-0.4444444444444445,
-0.48484848484848486,
-0.5252525252525253,
-0.5656565656565657,
-0.6060606060606061,
-0.6464646464646465,
-0.686868686868687,
-0.7272727272727273,
-0.7676767676767677,
-0.8080808080808082,
-0.8484848484848485,
-0.888888888888889,
-0.9292929292929294,
-0.9696969696969697,
-1.0101010101010102,
-1.0505050505050506,
-1.090909090909091,
-1.1313131313131315,
-1.1717171717171717,
-1.2121212121212122,
-1.2525252525252526,
-1.292929292929293,
-1.3333333333333335,
-1.373737373737374,
-1.4141414141414144,
-1.4545454545454546,
-1.494949494949495,
-1.5353535353535355,
-1.575757575757576,
-1.6161616161616164,
-1.6565656565656568,
-1.696969696969697,
-1.7373737373737375,
-1.777777777777778,
-1.8181818181818183,
-1.8585858585858588,
-1.8989898989898992,
-1.9393939393939394,
-1.97979797979798,
-2.0202020202020203,
-2.060606060606061,
-2.101010101010101,
-2.1414141414141414,
-2.181818181818182,
-2.2222222222222223,
-2.262626262626263,
-2.303030303030303,
-2.3434343434343434,
-2.383838383838384,
-2.4242424242424243,
-2.464646464646465,
-2.505050505050505,
-2.545454545454546,
-2.585858585858586,
-2.6262626262626263,
-2.666666666666667,
-2.707070707070707,
-2.747474747474748,
-2.787878787878788,
-2.8282828282828287,
-2.868686868686869,
-2.909090909090909,
-2.94949494949495,
-2.98989898989899,
-3.0303030303030307,
-3.070707070707071,
-3.111111111111111,
-3.151515151515152,
-3.191919191919192,
-3.2323232323232327,
-3.272727272727273,
-3.3131313131313136,
-3.353535353535354,
-3.393939393939394,
-3.4343434343434347,
-3.474747474747475,
-3.5151515151515156,
-3.555555555555556,
-3.5959595959595965,
-3.6363636363636367,
-3.676767676767677,
-3.7171717171717176,
-3.757575757575758,
-3.7979797979797985,
-3.8383838383838387,
-3.878787878787879,
-3.9191919191919196,
-3.95959595959596,
-4,
-4,
-3.9595959595959593,
-3.9191919191919196,
-3.878787878787879,
-3.8383838383838382,
-3.7979797979797976,
-3.757575757575758,
-3.717171717171717,
-3.6767676767676765,
-3.6363636363636367,
-3.595959595959596,
-3.5555555555555554,
-3.5151515151515156,
-3.474747474747475,
-3.4343434343434343,
-3.3939393939393936,
-3.353535353535354,
-3.313131313131313,
-3.2727272727272725,
-3.232323232323232,
-3.191919191919192,
-3.1515151515151514,
-3.1111111111111107,
-3.070707070707071,
-3.0303030303030303,
-2.9898989898989896,
-2.94949494949495,
-2.909090909090909,
-2.8686868686868685,
-2.8282828282828287,
-2.787878787878788,
-2.7474747474747474,
-2.7070707070707067,
-2.666666666666666,
-2.6262626262626263,
-2.5858585858585856,
-2.545454545454545,
-2.505050505050505,
-2.4646464646464645,
-2.424242424242424,
-2.383838383838384,
-2.3434343434343434,
-2.3030303030303028,
-2.262626262626263,
-2.2222222222222223,
-2.1818181818181817,
-2.141414141414141,
-2.1010101010101003,
-2.0606060606060606,
-2.02020202020202,
-1.9797979797979792,
-1.9393939393939394,
-1.8989898989898988,
-1.8585858585858581,
-1.8181818181818183,
-1.7777777777777777,
-1.737373737373737,
-1.6969696969696972,
-1.6565656565656566,
-1.616161616161616,
-1.5757575757575761,
-1.5353535353535346,
-1.4949494949494948,
-1.4545454545454541,
-1.4141414141414135,
-1.3737373737373737,
-1.333333333333333,
-1.2929292929292924,
-1.2525252525252526,
-1.212121212121212,
-1.1717171717171713,
-1.1313131313131315,
-1.0909090909090908,
-1.0505050505050502,
-1.0101010101010104,
-0.9696969696969688,
-0.9292929292929291,
-0.8888888888888893,
-0.8484848484848477,
-0.808080808080808,
-0.7676767676767673,
-0.7272727272727266,
-0.6868686868686869,
-0.6464646464646462,
-0.6060606060606055,
-0.5656565656565657,
-0.5252525252525251,
-0.4848484848484844,
-0.44444444444444464,
-0.4040404040404031,
-0.3636363636363633,
-0.32323232323232354,
-0.282828282828282,
-0.2424242424242422,
-0.20202020202020154,
-0.16161616161616088,
-0.1212121212121211,
-0.08080808080808044,
-0.040404040404039776,
0
] |
[
4,
3.999591878379757,
3.9983675135190286,
3.9963269054178143,
3.9934700540761146,
3.9897969594939293,
3.985307621671258,
3.980002040608101,
3.9738802163044586,
3.9669421487603307,
3.959187837975717,
3.950617283950617,
3.9412304866850323,
3.931027446178961,
3.920008162432405,
3.9081726354453625,
3.895520865217835,
3.8820528517498216,
3.8677685950413223,
3.8526680950923375,
3.836751351902867,
3.8200183654729107,
3.802469135802469,
3.7841036628915417,
3.7649219467401287,
3.74492398734823,
3.724109784715845,
3.7024793388429753,
3.680032649729619,
3.656769717375778,
3.632690541781451,
3.607795122946638,
3.5820834608713397,
3.5555555555555554,
3.5282114069992856,
3.5000510152025304,
3.4710743801652892,
3.4412815018875627,
3.41067238036935,
3.3792470156106518,
3.347005407611468,
3.3139475563717986,
3.280073461891644,
3.2453831241710027,
3.2098765432098766,
3.1735537190082646,
3.1364146515661666,
3.098459340883583,
3.059687786960514,
3.020099989796959,
2.979695949392919,
2.938475665748393,
2.8964391388633812,
2.8535863687378837,
2.8099173553719003,
2.765432098765432,
2.720130598918477,
2.6740128558310374,
2.627078869503112,
2.5793286399347,
2.530762167125803,
2.48137945107642,
2.4311804917865523,
2.3801652892561975,
2.3283338434853587,
2.275686154474033,
2.222222222222222,
2.1679420467299253,
2.1128456279971424,
2.056932966023875,
2.0002040608101206,
1.9426589123558817,
1.884297520661157,
1.8251198857259459,
1.7651260075502497,
1.7043158861340673,
1.6426895214773998,
1.5802469135802468,
1.5169880624426075,
1.4529129680644832,
1.3880216304458721,
1.3223140495867765,
1.2557902254871944,
1.1884501581471274,
1.1202938475665745,
1.0513212937455356,
0.9815324966840113,
0.9109274563820011,
0.8395061728395059,
0.7672686460565239,
0.6942148760330573,
0.6203448627691048,
0.545658606264666,
0.4701561065197426,
0.3938373635343324,
0.3167023773084372,
0.23875114784205653,
0.15998367513518952,
0.08039995918783749,
0,
0,
-0.08039995918783838,
-0.15998367513519085,
-0.23875114784205564,
-0.3167023773084381,
-0.39383736353433463,
-0.4701561065197417,
-0.5456586062646664,
-0.6203448627691053,
-0.6942148760330582,
-0.7672686460565252,
-0.8395061728395063,
-0.9109274563820016,
-0.9815324966840109,
-1.051321293745536,
-1.1202938475665754,
-1.188450158147127,
-1.2557902254871962,
-1.322314049586776,
-1.3880216304458735,
-1.4529129680644832,
-1.516988062442607,
-1.5802469135802468,
-1.6426895214774007,
-1.7043158861340686,
-1.7651260075502506,
-1.8251198857259467,
-1.884297520661157,
-1.9426589123558813,
-2.0002040608101197,
-2.0569329660238758,
-2.1128456279971424,
-2.1679420467299266,
-2.222222222222223,
-2.275686154474034,
-2.3283338434853587,
-2.3801652892561993,
-2.4311804917865523,
-2.481379451076421,
-2.530762167125804,
-2.579328639934701,
-2.627078869503112,
-2.6740128558310374,
-2.7201305989184767,
-2.765432098765432,
-2.8099173553719012,
-2.8535863687378846,
-2.896439138863382,
-2.9384756657483937,
-2.9796959493929194,
-3.020099989796961,
-3.059687786960515,
-3.0984593408835828,
-3.1364146515661666,
-3.1735537190082646,
-3.2098765432098766,
-3.2453831241710027,
-3.280073461891643,
-3.313947556371799,
-3.3470054076114693,
-3.3792470156106518,
-3.41067238036935,
-3.4412815018875627,
-3.4710743801652892,
-3.5000510152025317,
-3.5282114069992865,
-3.5555555555555554,
-3.58208346087134,
-3.607795122946637,
-3.63269054178145,
-3.656769717375779,
-3.68003264972962,
-3.7024793388429753,
-3.7241097847158446,
-3.74492398734823,
-3.764921946740129,
-3.7841036628915425,
-3.8024691358024683,
-3.8200183654729116,
-3.8367513519028673,
-3.852668095092337,
-3.8677685950413228,
-3.8820528517498207,
-3.8955208652178346,
-3.9081726354453625,
-3.9200081624324046,
-3.9310274461789607,
-3.9412304866850327,
-3.950617283950617,
-3.9591878379757173,
-3.96694214876033,
-3.973880216304458,
-3.9800020406081007,
-3.9853076216712573,
-3.9897969594939298,
-3.9934700540761146,
-3.996326905417815,
-3.998367513519028,
-3.999591878379757,
-4
] |
[
0,
0.08080533251434181,
0.16159417526624956,
0.24235003849328918,
0.3230564324330267,
0.40369686732302795,
0.48425485340085894,
0.5647139009040857,
0.645057520070274,
0.7252692211369898,
0.8053325143417992,
0.885230909922268,
0.9649479181159623,
1.044467049160448,
1.1237718132932908,
1.2028457207520569,
1.2816722817743122,
1.3602350065976228,
1.4385174054595542,
1.5165029885976729,
1.5941752662495445,
1.6715177486527348,
1.7485139460448103,
1.8251473686633366,
1.9014015267458795,
1.9772599305300051,
2.0527060902532797,
2.1277235161532686,
2.202295718467538,
2.2764062074336535,
2.350038493289182,
2.423176086271689,
2.49580249661874,
2.5679012345679015,
2.6394558103567394,
2.710449734222819,
2.7808665164037065,
2.850689667136969,
2.9199026966601704,
2.9884891152108786,
3.0564324330266586,
3.1237161603450763,
3.1903238074036975,
3.2562388844400885,
3.3214449016918155,
3.385925369396444,
3.44966379779154,
3.5126436971146697,
3.5748485776033987,
3.6362619494952932,
3.696867323027919,
3.7566482084388424,
3.8155881159656286,
3.873670555845844,
3.9308790383170553,
3.987197073616827,
4.042608171982726,
4.097095843652317,
4.1506435988631685,
4.203234947852844,
4.25485340085891,
4.305482468118934,
4.35510565987048,
4.403706486351115,
4.451268457798404,
4.497775084449914,
4.5432098765432105,
4.587556344315859,
4.630797998005426,
4.672918347849477,
4.7139009040855795,
4.753729176951297,
4.792386676684197,
4.829856913521846,
4.866123397701808,
4.901169639461651,
4.93497914903894,
4.967535436671239,
4.998822012596118,
5.0288223870511395,
5.057520070273871,
5.084898572501879,
5.110941403972728,
5.1356320749239845,
5.158954095593215,
5.1808909762179844,
5.201426227035859,
5.220543358284406,
5.238225880201189,
5.254457303023776,
5.269221136989732,
5.282500892336623,
5.294280079302016,
5.304542208123475,
5.313270789038568,
5.320449332284859,
5.326061348099916,
5.3300903467213026,
5.332519838386586,
5.333333333333334,
5.333333333333334,
5.332519838386585,
5.330090346721306,
5.326061348099914,
5.320449332284857,
5.313270789038567,
5.304542208123475,
5.294280079302014,
5.282500892336625,
5.2692211369897315,
5.254457303023772,
5.2382258802011865,
5.2205433582844005,
5.201426227035858,
5.180890976217983,
5.158954095593215,
5.135632074923981,
5.110941403972726,
5.084898572501876,
5.057520070273869,
5.028822387051138,
4.998822012596117,
4.967535436671239,
4.934979149038936,
4.9011696394616475,
4.866123397701804,
4.8298569135218425,
4.792386676684197,
4.753729176951294,
4.713900904085575,
4.6729183478494765,
4.630797998005422,
4.587556344315852,
4.543209876543203,
4.497775084449911,
4.451268457798397,
4.403706486351114,
4.3551056598704765,
4.30548246811893,
4.254853400858904,
4.20323494785284,
4.1506435988631605,
4.097095843652314,
4.042608171982719,
3.9871970736168176,
3.9308790383170464,
3.8736705558458393,
3.815588115965623,
3.7566482084388415,
3.6968673230279148,
3.6362619494952906,
3.5748485776033885,
3.51264369711466,
3.449663797791528,
3.385925369396441,
3.3214449016918106,
3.2562388844400783,
3.1903238074036846,
3.1237161603450705,
3.0564324330266555,
2.9884891152108732,
2.9199026966601647,
2.85068966713696,
2.7808665164036928,
2.7104497342228075,
2.639455810356731,
2.5679012345678895,
2.495802496618735,
2.4231760862716794,
2.3500384932891674,
2.2764062074336433,
2.2022957184675302,
2.1277235161532584,
2.052706090253265,
1.9772599305299945,
1.90140152674587,
1.8251473686633215,
1.7485139460447936,
1.6715177486527235,
1.5941752662495343,
1.5165029885976562,
1.4385174054595407,
1.3602350065976037,
1.2816722817742967,
1.2028457207520429,
1.1237718132932795,
1.0444670491604295,
0.9649479181159517,
0.8852309099222477,
0.8053325143417833,
0.7252692211369673,
0.6450575200702584,
0.5647139009040654,
0.48425485340083974,
0.4036968673230117,
0.3230564324330043,
0.2423500384932762,
0.1615941752662291,
0.08080533251432875,
-1.5987211554602254e-14
] |
{"local_extrema": [], "null": [[2.0, 0]]}
|
{"local_extrema": [[0.0, -0.0], [2.0, -4.0], [4.0, 0.0]], "null": [[0.0, 0], [4.0, 0]]}
|
{"local_extrema": [[0.0, 4.0], [4.0, -4.0]], "null": [[2.0, 0]]}
|
{"local_extrema": [[0.0, 0.0], [2.0, 5.333333333333334], [4.0, -1.5987211554602254e-14]], "null": [[0.0, 0], [3.999999999999996, 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "1.0*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "2*L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "1.0*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["1.0*L", "2*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "P"}, {"point": "2*L", "type": "Force", "value": "P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "1.0*L"], "shear_force": "-P", "bending_moment": "P*x"}, {"span": ["1.0*L", "2*L"], "shear_force": "P", "bending_moment": "2.0*L*P - P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "1.0*L"], "deflection": "-0.5*L**2*P*x/(E*I) + P*x**3/(6*E*I)", "rotation": "-0.5*L**2*P/(E*I) + P*x**2/(2*E*I)"}, {"span": ["1.0*L", "2*L"], "deflection": "0.333333333333333*L**3*P/(E*I) - 1.5*L**2*P*x/(E*I) + 1.0*L*P*x**2/(E*I) - 0.166666666666667*P*x**3/(E*I)", "rotation": "-1.5*L**2*P/(E*I) + 2.0*L*P*x/(E*I) - 0.5*P*x**2/(E*I)"}]}
|
[
"Given a beam with a length of 2*L, supported by a pin at x=0 and a roller at x=2*L, and subjected to a downward point load of -2*P at x=1.0*L, calculate the reaction forces at the supports.",
"To calculate the reaction forces at the supports of a simply supported beam with a point load applied at its midpoint.",
"What are the reaction forces at the supports of a beam with a length of 2*L, supported by a pin at x=0 and a roller at x=2*L, with a downward point load of 2*P at x=1.0*L?",
"Question: \nDetermine the reaction forces at the pin support (x=0) and the roller support (x=2*L) for a beam of length 2*L with a downward point load of 2P at x=L."
] |
[
"P",
"P"
] |
README.md exists but content is empty.
- Downloads last month
- 23