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[
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{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.95*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
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{"local_extrema": [], "null": [[0.95, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.95, 0.095], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.00611599570947535j"], [1.0, "-0.01135827774616821j"]], "null": [["(0.5766215877786183+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.5757575757575757, "0.002351095410714278j"], [1.0, "-3.469446951953614e-16j"]], "null": [[0.0, 0], ["(0.9999999999999695+0j)", 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.95*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.95*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.95*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "0.1*P"}, {"point": "L", "type": "Force", "value": "1.9*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.95*L"], "shear_force": "-0.1*P", "bending_moment": "0.1*P*x"}, {"span": ["0.95*L", "L"], "shear_force": "1.9*P", "bending_moment": "1.9*L*P - 1.9*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.95*L"], "deflection": "0.00611599570947535*I*L**2*P*x - 0.0166666666666667*I*P*x**3*exp(-1)", "rotation": "0.00611599570947535*I*L**2*P - 0.05*I*P*x**2*exp(-1)"}, {"span": ["0.95*L", "L"], "deflection": "-0.105136878624789*I*L**3*P + 0.338127191366702*I*L**2*P*x - 0.95*I*L*P*x**2*exp(-1) + 0.316666666666667*I*P*x**3*exp(-1)", "rotation": "0.338127191366702*I*L**2*P - 1.9*I*L*P*x*exp(-1) + 0.95*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.95*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Alright, I need to create a question based on the given setup of a statically loaded beam. Let me go through the details provided. \n\nThe beam has a length of L. It's supported by a pin at the left end (x=0) and a roller at the right end (x=L). There's a downward point load of -2P applied at 0.95L. My task is to ask the reader to calculate the reaction forces at the supports.\n\nI should include all necessary details: beam length, type and location of supports, and the load's magnitude, location, and direction. The question needs to be concise and self-contained. \n\nSo, I'll start by stating the beam's length as L. Then mention the pin support at one end and the roller at the other. Next, I'll note the applied load: it's a point load of -2P at 0.95L. Finally, I'll ask for the reaction forces at the supports.\n\nPutting it all together, the question should be clear and include all the required information without being too wordy. I need to make sure it's straightforward and directly asks for the reaction forces without any extra details.\n</think>\n\nGiven 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 = 0.95L \\), calculate the reaction forces at the supports."
] |
1
|
[
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{"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"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I need to generate a question based on the setup of a statically loaded beam. The user provided some details about the beam, supports, and loads. Let me break this down.\n\nFirst, the beam has a length of L. That's straightforward. Then, the supports: there's a pin support at x=0 and a roller support at x=L. I remember that pin supports can resist both vertical and horizontal forces, while roller supports can only resist vertical forces, allowing rotation.\n\nNext, the load: there's a point load of -2P at x=0. The negative sign indicates it's downward. So, it's a downward force applied at the pin support. That's interesting because it might cause reactions at the supports.\n\nMy task is to create a question asking the reader to calculate the reaction forces at the supports. I should include all the necessary details: beam length, support locations and types, and load details.\n\nI need to make sure the question is clear and concise. It should state everything needed without being too wordy. Let me structure it step by step.\n\n1. Beam length: L\n2. Supports: pin at 0, roller at L\n3. Load: -2P at x=0\n\nPutting it all together, the question should ask for the reaction forces at the supports, mentioning the beam length, the type of supports, their locations, and the applied load.\n\nI should avoid any unnecessary information, like Young's modulus E and moment of inertia I, since the question is only about reaction forces, not deflection or stress.\n\nSo, the final question should be something like: \"Calculate the reaction forces at the pin and roller supports of a beam of length L with a downward point load of -2P at its left end.\"\n\nThat covers all the required details concisely.\n</think>\n\nCalculate the reaction forces at the pin and roller supports of a beam of length L with a downward point load of -2P at its left end."
] |
2
|
[
"0.25*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.25*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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] |
{"local_extrema": [], "null": [[0.25, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.25, 0.375], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.0402368138781265j"], [1.0, "-0.02874058134151898j"]], "null": [["(0.4409915481344048+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.25, "0.008622174402455678j"], [0.4393939393939394, "0.010710852318538442j"], [1.0, "-5.572799166575493e-17j"]], "null": [[0.0, 0], ["(0.9999999999999981+0j)", 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.25*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.25*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.25*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "1.5*P"}, {"point": "L", "type": "Force", "value": "0.5*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.25*L"], "shear_force": "-1.5*P", "bending_moment": "1.5*P*x"}, {"span": ["0.25*L", "L"], "shear_force": "0.5*P", "bending_moment": "0.5*L*P - 0.5*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.25*L"], "deflection": "0.0402368138781265*I*L**2*P*x - 0.25*I*P*x**3*exp(-1)", "rotation": "0.0402368138781265*I*L**2*P - 0.75*I*P*x**2*exp(-1)"}, {"span": ["0.25*L", "L"], "deflection": "-0.00191603875610126*I*L**3*P + 0.0632292789513416*I*L**2*P*x - 0.25*I*L*P*x**2*exp(-1) + 0.0833333333333333*I*P*x**3*exp(-1)", "rotation": "0.0632292789513416*I*L**2*P - 0.5*I*L*P*x*exp(-1) + 0.25*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.25*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Alright, I need to help the user by generating a question based on the given setup of a statically loaded beam. The user has provided specific details about the beam, supports, and loads. My task is to create a concise, self-contained question that asks the reader to calculate the reaction forces at the supports.\n\nFirst, I'll review the setup details. The beam has a length of L. It has a pin support at x=0 and a roller support at x=L. There's an applied point load of -2P at x=0.25L, indicating it's downward. The material properties like Young's modulus E and moment of inertia I are given, but they might not be directly relevant to the question about reactions, so perhaps I can omit them unless they're necessary for context.\n\nThe question should include the length of the beam, the location and type of supports, and the location and magnitude of the load. It needs to be short and concise. I should structure it clearly, stating each piece of information succinctly.\n\nI should make sure to mention the supports: pin at one end and roller at the other. The load is a downward force at a specific point. The goal is to find the reaction forces, so I'll phrase it directly.\n\nPutting it all together, the question should clearly state the beam's length, support locations and types, and the load's position and magnitude. I'll avoid any unnecessary details and keep it focused on the reaction forces.\n\nSo, the final question will ask for the reaction forces at the pin and roller supports, given the beam's setup and the applied load.\n</think>\n\nGiven 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 = 0.25L \\), calculate the reaction forces at the supports."
] |
3
|
[
"0.15*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.15*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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] |
{"local_extrema": [], "null": [[0.15, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.15, 0.255], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.0289245210621047j"], [1.0, "-0.01798010768725425j"]], "null": [["(0.4291979949874687+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.15, "0.0039868934436955135j"], [0.42474747474747476, "0.006841626593639739j"], [1.0, "-8.131516293641283e-19j"]], "null": [[0.0, 0], ["(1+0j)", 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.15*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.15*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.15*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "1.7*P"}, {"point": "L", "type": "Force", "value": "0.3*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.15*L"], "shear_force": "-1.7*P", "bending_moment": "1.7*P*x"}, {"span": ["0.15*L", "L"], "shear_force": "0.3*P", "bending_moment": "0.3*L*P - 0.3*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.15*L"], "deflection": "0.0289245210621047*I*L**2*P*x - 0.283333333333333*I*P*x**3*exp(-1)", "rotation": "0.0289245210621047*I*L**2*P - 0.85*I*P*x**2*exp(-1)"}, {"span": ["0.15*L", "L"], "deflection": "-0.000413864371317873*I*L**3*P + 0.0372018084884621*I*L**2*P*x - 0.15*I*L*P*x**2*exp(-1) + 0.05*I*P*x**3*exp(-1)", "rotation": "0.0372018084884621*I*L**2*P - 0.3*I*L*P*x*exp(-1) + 0.15*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.15*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I need to figure out how to generate a question based on the setup of a statically loaded beam. The user provided a detailed setup with specific parameters, so I should make sure to include all of that in the question.\n\nFirst, I'll look at the given information. The beam has a length of L, with a pin support at x=0 and a roller support at x=L. There's a point load of -2P applied at 0.15L, which is downward because of the negative sign.\n\nI need to ask the reader to calculate the reaction forces at the supports. That makes sense because in statics, reaction forces are typically what you solve for when dealing with supports.\n\nI should make the question concise and self-contained, so it includes all the necessary details: beam length, support locations and types, and the load's position and magnitude.\n\nPutting it all together, the question should state the beam's length, the supports at each end with their types, and the applied load's position and value. Then, it should ask for the reaction forces at the supports.\n\nI think that covers everything the user provided. Now, I just need to write it clearly and concisely without any extra information.\n</think>\n\nGiven 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 applied at x=0.15L, calculate the reaction forces at the supports."
] |
4
|
[
"0.95*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.95*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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{"local_extrema": [], "null": [[0.95, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.95, 0.095], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.00611599570947535j"], [1.0, "-0.01135827774616821j"]], "null": [["(0.5766215877786183+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.5757575757575757, "0.002351095410714278j"], [1.0, "-3.469446951953614e-16j"]], "null": [[0.0, 0], ["(0.9999999999999695+0j)", 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.95*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.95*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.95*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "0.1*P"}, {"point": "L", "type": "Force", "value": "1.9*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.95*L"], "shear_force": "-0.1*P", "bending_moment": "0.1*P*x"}, {"span": ["0.95*L", "L"], "shear_force": "1.9*P", "bending_moment": "1.9*L*P - 1.9*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.95*L"], "deflection": "0.00611599570947535*I*L**2*P*x - 0.0166666666666667*I*P*x**3*exp(-1)", "rotation": "0.00611599570947535*I*L**2*P - 0.05*I*P*x**2*exp(-1)"}, {"span": ["0.95*L", "L"], "deflection": "-0.105136878624789*I*L**3*P + 0.338127191366702*I*L**2*P*x - 0.95*I*L*P*x**2*exp(-1) + 0.316666666666667*I*P*x**3*exp(-1)", "rotation": "0.338127191366702*I*L**2*P - 1.9*I*L*P*x*exp(-1) + 0.95*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.95*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I need to create a question that asks someone to calculate the reaction forces at the supports of a beam. Let me look at the setup provided. The beam is statically loaded, which means it's in equilibrium, so statics can be used here.\n\nThe beam has a length of L. The supports are a pin at x=0 and a roller at x=L. There's a point load of -2P at 0.95L. The negative sign indicates it's downward.\n\nI should include all these details in the question. It needs to be concise and self-contained. So, I'll mention the length, the type and position of the supports, and the load's position and magnitude.\n\nPutting it all together, the question should ask for the reaction forces at the pin and roller. I'll make sure to specify the direction of the load to clarify its effect.\n\nI think that covers everything. Now, I'll formulate the question.\n</think>\n\nQuestion: \nDetermine 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=0.95L."
] |
5
|
[
"0.85*L",
"0.55*L"
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{"local_extrema": [], "null": [[0.55, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.55, 0.66], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.0619876858373878j"], [1.0, "-0.07596710460190326j"]], "null": [["(0.5299301919720758+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.5277777777777778, "0.02189917178199701j"], [0.55, "0.021852038805583545j"], [0.85, "0.010815655570440185j"], [1.0, "-6.938893903907228e-17j"]], "null": [[0.0, 0], ["(0.9999999999999991+0j)", 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.55*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.85*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.55*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.55*L", "0.85*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.85*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "1.2*P"}, {"point": "L", "type": "Force", "value": "2.8*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.55*L"], "shear_force": "-1.2*P", "bending_moment": "1.2*P*x"}, {"span": ["0.55*L", "0.85*L"], "shear_force": "0.8*P", "bending_moment": "1.1*L*P - 0.8*P*x"}, {"span": ["0.85*L", "L"], "shear_force": "2.8*P", "bending_moment": "2.8*L*P - 2.8*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.55*L"], "deflection": "0.0619876858373878*I*L**2*P*x - 0.2*I*P*x**3*exp(-1)", "rotation": "0.0619876858373878*I*L**2*P - 0.6*I*P*x**2*exp(-1)"}, {"span": ["0.55*L", "0.85*L"], "deflection": "-0.0204019806749661*I*L**3*P + 0.173271216791749*I*L**2*P*x - 0.55*I*L*P*x**2*exp(-1) + 0.133333333333333*I*P*x**3*exp(-1)", "rotation": "0.173271216791749*I*L**2*P - 1.1*I*L*P*x*exp(-1) + 0.4*I*P*x**2*exp(-1)"}, {"span": ["0.85*L", "L"], "deflection": "-0.09570996794477*I*L**3*P + 0.439064113038116*I*L**2*P*x - 1.4*I*L*P*x**2*exp(-1) + 0.466666666666667*I*P*x**3*exp(-1)", "rotation": "0.439064113038116*I*L**2*P - 2.8*I*L*P*x*exp(-1) + 1.4*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.85*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.55*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I'm trying to figure out how to generate a question based on the setup provided. The setup describes a beam with certain properties and loads applied. Let me break it down step by step.\n\nFirst, the beam has a length of L. That's straightforward. The supports are a pin at the very start (x=0) and a roller at the end (x=L). So, the beam is simply supported at both ends, but one end is a pin and the other is a roller. That means the pin can resist vertical and horizontal forces but not moments, while the roller can resist vertical forces but not moments or horizontal forces.\n\nNext, there are two point loads applied. Both are downward, as indicated by the negative signs. The first load is at 0.55*L, and the second is at 0.85*L, each with a magnitude of -2*P. So, these are two downward forces acting on the beam at specific points along its length.\n\nThe question needs to ask for the reaction forces at the supports. Since it's a statics problem, I can use the equations of equilibrium to find these reactions. The sum of forces in the vertical direction should be zero, and the sum of moments about any point should also be zero.\n\nLet me visualize the beam. At x=0, there's a pin support, so it will have a vertical reaction force, let's call it R_A. At x=L, the roller support will have a vertical reaction force, R_B. Since there are no horizontal forces acting on the beam, the horizontal reactions are zero.\n\nTo find R_A and R_B, I can sum the moments about one of the supports. Let's take moments about x=0 to find R_B first. The moment due to R_B is zero because it's at the point we're taking moments about. The moments due to the point loads will be their respective forces multiplied by their distances from x=0.\n\nSo, the moment equation would be: R_B * L = (-2P) * 0.55L + (-2P) * 0.85L. Simplifying that, R_B * L = -2P*(0.55L + 0.85L) = -2P*(1.4L). Therefore, R_B = (-2P*1.4L)/L = -2.8P. But since we're looking for the magnitude, R_B is 2.8P upwards.\n\nSimilarly, to find R_A, I can sum the vertical forces. The sum of vertical forces is R_A + R_B - (-2P) - (-2P) = 0. So, R_A + R_B + 4P = 0. Plugging in R_B as 2.8P, we get R_A + 2.8P + 4P = 0, which simplifies to R_A = -6.8P. The negative sign indicates the direction; since R_A is at x=0 (a pin), it's a downward force, so R_A is 6.8P downward.\n\nWait, but the question only asks for the reaction forces, not their directions. So, I should present them as magnitudes with their directions implied by the support type. The pin at x=0 will have a downward force, and the roller at x=L will have an upward force.\n\nPutting it all together, the question should state the beam's length, the supports, the loads' locations and magnitudes, and then ask for the reaction forces at the supports. It should be concise and self-contained.\n</think>\n\nQuestion: \nGiven a beam of length L with a pin support at x=0 and a roller support at x=L, and subjected to downward point loads of -2P at x=0.55L and x=0.85L, calculate the reaction forces at the supports."
] |
6
|
[
"0.05*L",
"0.25*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.05*L", "magnitude": "-2*P"}, "P2": {"location": "0.25*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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{"local_extrema": [], "null": [[0.25, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.05, 0.17], [0.25, 0.44999999999999996], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.0515950916242948j"], [1.0, "-0.034856577050994195j"]], "null": [["(0.4380170835875531+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.25, "0.010622518863825401j"], [0.4318181818181818, "0.013056990778053832j"], [1.0, "-2.2985086056692694e-17j"]], "null": [[0.0, 0], ["(0.9999999999999993+0j)", 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.05*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.25*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.05*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.05*L", "0.25*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.25*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "3.4*P"}, {"point": "L", "type": "Force", "value": "0.6*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.05*L"], "shear_force": "-3.4*P", "bending_moment": "3.4*P*x"}, {"span": ["0.05*L", "0.25*L"], "shear_force": "-1.4*P", "bending_moment": "0.1*L*P + 1.4*P*x"}, {"span": ["0.25*L", "L"], "shear_force": "0.6*P", "bending_moment": "0.6*L*P - 0.6*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.05*L"], "deflection": "0.0515950916242948*I*L**2*P*x - 0.566666666666667*I*P*x**3*exp(-1)", "rotation": "0.0515950916242948*I*L**2*P - 1.7*I*P*x**2*exp(-1)"}, {"span": ["0.05*L", "0.25*L"], "deflection": "-1.53283100488101e-5*I*L**3*P + 0.0525147902272234*I*L**2*P*x - 0.05*I*L*P*x**2*exp(-1) - 0.233333333333333*I*P*x**3*exp(-1)", "rotation": "0.0525147902272234*I*L**2*P - 0.1*I*L*P*x*exp(-1) - 0.7*I*P*x**2*exp(-1)"}, {"span": ["0.25*L", "L"], "deflection": "-0.00193136706615007*I*L**3*P + 0.0755072553004385*I*L**2*P*x - 0.3*I*L*P*x**2*exp(-1) + 0.1*I*P*x**3*exp(-1)", "rotation": "0.0755072553004385*I*L**2*P - 0.6*I*L*P*x*exp(-1) + 0.3*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.05*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.25*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I need to figure out how to create a question based on the given setup of a statically loaded beam. Let me start by going through the details provided.\n\nFirst, the beam has a length of L. That's straightforward. Then, it has a Young's modulus E and a moment of inertia I, but I don't think those are needed for the question since it's about reaction forces, not the beam's deflection or stress.\n\nNext, there are two point loads: both are -2P, meaning they're downward forces. The first one is at 0.05L from the left end, and the second is at 0.25L. So, these are located pretty close to the left side, with the first one closer to the support at x=0.\n\nThe supports are a pin at x=0 and a roller at x=L. A pin support can provide both vertical and horizontal reactions, but since it's at the end, I think it can't have a horizontal reaction. A roller support can only provide a vertical reaction because it can't resist horizontal movement.\n\nNow, the question needs to ask for the reaction forces at the supports. Since it's a statically determinate beam, I can use the equations of equilibrium to find these reactions. The sum of vertical forces should be zero, and the sum of moments about any point should also be zero.\n\nI should make sure the question is self-contained and includes all necessary details: beam length, support locations and types, and load locations and magnitudes. It should be concise and short, as per the instructions.\n\nPutting it all together, the question should state the beam's length, the support conditions (pin at one end, roller at the other), and the applied downward loads at specific points. Then, it should ask for the reaction forces at the supports.\n\nI think that covers everything. Let me make sure I didn't miss anything. Beam length L, pin at 0, roller at L, two downward loads at 0.05L and 0.25L with magnitude 2P each. The question should ask for the reaction forces at the supports.\n\nYes, that seems right. I should present this as the final question without any additional text.\n</think>\n\nWhat are the reaction forces at the pin support (at x=0) and the roller support (at x=L) for a beam of length L with pin support at x=0, roller support at x=L, and two downward point loads of magnitude 2P each at x=0.05L and x=0.25L?"
] |
7
|
[
"0.75*L",
"0.25*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.75*L", "magnitude": "-2*P"}, "P2": {"location": "0.25*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.25*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.75*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.25*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.25*L", "0.75*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.75*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "2.0*P"}, {"point": "L", "type": "Force", "value": "2.0*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.25*L"], "shear_force": "-2.0*P", "bending_moment": "2.0*P*x"}, {"span": ["0.25*L", "0.75*L"], "shear_force": "0", "bending_moment": "0.5*L*P"}, {"span": ["0.75*L", "L"], "shear_force": "2*P", "bending_moment": "2.0*L*P - 2*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.25*L"], "deflection": "0.0689773952196454*I*L**2*P*x - 0.333333333333333*I*P*x**3*exp(-1)", "rotation": "0.0689773952196454*I*L**2*P - 1.0*I*P*x**2*exp(-1)"}, {"span": ["0.25*L", "0.75*L"], "deflection": "-0.00191603875610126*I*L**3*P + 0.0919698602928606*I*L**2*P*x - 0.25*I*L*P*x**2*exp(-1)", "rotation": "0.0919698602928606*I*L**2*P - 0.5*I*L*P*x*exp(-1)"}, {"span": ["0.75*L", "L"], "deflection": "-0.0536490851708353*I*L**3*P + 0.298902045951797*I*L**2*P*x - 1.0*I*L*P*x**2*exp(-1) + 0.333333333333333*I*P*x**3*exp(-1)", "rotation": "0.298902045951797*I*L**2*P - 2.0*I*L*P*x*exp(-1) + 1.0*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.75*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.25*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I need to help the user generate a question about calculating reaction forces in a beam setup. Let me start by understanding the given information. The beam has a length L, with a pin support at x=0 and a roller at x=L. There are two downward point loads of -2P each at 0.25L and 0.75L. \n\nI remember that for statics problems, reaction forces can be found using equilibrium equations. Since the beam is statically determinate, there are only two reactions: at the pin (Ay) and the roller (By). \n\nFirst, I'll consider the sum of moments about one of the supports. Let's choose the pin at x=0 because it eliminates Ay from the equation. The moments from By and the two point loads should balance each other. \n\nSo, the moment from By at x=L is By*L. The moment from the 0.75L load is -2P*0.75L, and from the 0.25L load is -2P*0.25L. Setting the sum of moments to zero gives: By*L - 2P*(0.75L + 0.25L) = 0. Simplifying, By*L = 2P*L, so By = 2P.\n\nNext, using the sum of vertical forces, Ay + By = 0 (since the total downward load is -4P). Wait, no, the total downward load is -2P -2P = -4P. So, Ay + By = 4P. Since By is 2P, Ay must be 2P as well.\n\nSo the reaction forces at both supports are 2P each. But the question doesn't need the values; it just needs to ask for calculating the reaction forces. \n\nI should structure the question to include all necessary details: beam length, supports, and load positions and magnitudes. It should be concise and self-contained. \n\nPutting it all together, the question should state the beam's length, the type and location of supports, and the applied loads. Then ask the reader to calculate the reaction forces at the supports. \n\nI think that's clear and covers all the required information without being too wordy. It's straightforward for someone to understand the setup and apply the equilibrium equations.\n</think>\n\nUse the given setup of a statically loaded beam to calculate the reaction forces at the supports. The beam has a length of L, with a pin support at x=0 and a roller support at x=L. There are two downward point loads of -2P at x=0.25L and x=0.75L. \n\nQuestion: \nCalculate the reaction forces at the pin support (Ay) and the roller support (By) for the beam with a length of L, supported at x=0 (pin) and x=L (roller), subjected to two downward point loads of -2P at x=0.25L and x=0.75L."
] |
8
|
[
"0.65*L",
"0.85*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.65*L", "magnitude": "-2*P"}, "P2": {"location": "0.85*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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] |
{"local_extrema": [], "null": [[0.65, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.65, 0.65], [0.85, 0.45000000000000007], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.055641765477181j"], [0.85, "-0.06253950499914526j"], [1.0, "-0.0749554361386805j"]], "null": [["(0.5499930209511065+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.544949494949495, "0.020399408050145163j"], [0.85, "0.0106225188638253j"], [1.0, "6.661338147750939e-16j"]], "null": [[0.0, 0], [1.0, 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.65*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.85*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.65*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.65*L", "0.85*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.85*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": "3.0*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.65*L"], "shear_force": "-P", "bending_moment": "P*x"}, {"span": ["0.65*L", "0.85*L"], "shear_force": "P", "bending_moment": "1.3*L*P - P*x"}, {"span": ["0.85*L", "L"], "shear_force": "3*P", "bending_moment": "3.0*L*P - 3*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.65*L"], "deflection": "0.055641765477181*I*L**2*P*x - I*P*x**3*exp(-1)/6", "rotation": "0.055641765477181*I*L**2*P - I*P*x**2*exp(-1)/2"}, {"span": ["0.65*L", "0.85*L"], "deflection": "-0.0336762971772359*I*L**3*P + 0.211070829372115*I*L**2*P*x - 0.65*I*L*P*x**2*exp(-1) + 0.166666666666667*I*P*x**3*exp(-1)", "rotation": "0.211070829372115*I*L**2*P - 1.3*I*L*P*x*exp(-1) + 0.5*I*P*x**2*exp(-1)"}, {"span": ["0.85*L", "L"], "deflection": "-0.10898428444704*I*L**3*P + 0.476863725618483*I*L**2*P*x - 1.5*I*L*P*x**2*exp(-1) + 0.5*I*P*x**3*exp(-1)", "rotation": "0.476863725618483*I*L**2*P - 3.0*I*L*P*x*exp(-1) + 1.5*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.65*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.85*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I need to help the user by generating a question based on the provided setup of a statically loaded beam. Let me read through the details again to make sure I understand everything correctly.\n\nThe beam has a length of L. It has a pin support at x=0 and a roller support at x=L. There are two downward point loads, each of magnitude -2P, applied at x=0.65L and x=0.85L. The user wants a question that asks the reader to calculate the reaction forces at the supports.\n\nFirst, I should identify all the necessary components to include in the question. The beam's length is L, the supports are a pin at one end and a roller at the other. The loads are both downward and located at specific points along the beam. \n\nI need to make sure the question is self-contained and concise. It should clearly state the beam's setup, the type and location of the supports, and the nature and location of the applied loads. \n\nI should also consider the units and any specific notation used, like the negative sign indicating downward direction. The question should ask specifically for the reaction forces at the supports, which are typically denoted as R_A and R_B in such problems.\n\nPutting it all together, the question should succinctly present all these elements without unnecessary details. I should avoid any mention of Young's modulus, moment of inertia, or bending moment since those aren't required for calculating the reaction forces in this statics problem.\n\nI think I've covered all the necessary points. Now, I'll draft the question accordingly.\n</think>\n\nGiven a beam of length \\( L \\) with a pin support at \\( x = 0 \\) and a roller support at \\( x = L \\), and subjected to two downward point loads of magnitude \\( -2P \\) at \\( x = 0.65L \\) and \\( x = 0.85L \\), calculate the reaction forces at the supports."
] |
9
|
[
"0.15*L",
"0.55*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.15*L", "magnitude": "-2*P"}, "P2": {"location": "0.55*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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{"local_extrema": [], "null": [[0.55, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.55, 0.63], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.0729320992122383j"], [0.15, "0.062171625557973606j"], [1.0, "-0.06502269122705262j"]], "null": [["(0.4928904428904424+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.4893939393939394, "0.021801068559805663j"], [0.55, "0.021438174434265746j"], [1.0, "-1.9081958235744878e-16j"]], "null": [[0.0, 0], ["(0.9999999999999971+0j)", 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.15*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.55*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.15*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.15*L", "0.55*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.55*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "2.6*P"}, {"point": "L", "type": "Force", "value": "1.4*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.15*L"], "shear_force": "-2.6*P", "bending_moment": "2.6*P*x"}, {"span": ["0.15*L", "0.55*L"], "shear_force": "-0.6*P", "bending_moment": "0.3*L*P + 0.6*P*x"}, {"span": ["0.55*L", "L"], "shear_force": "1.4*P", "bending_moment": "1.4*L*P - 1.4*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.15*L"], "deflection": "0.0729320992122383*I*L**2*P*x - 0.433333333333333*I*P*x**3*exp(-1)", "rotation": "0.0729320992122383*I*L**2*P - 1.3*I*P*x**2*exp(-1)"}, {"span": ["0.15*L", "0.55*L"], "deflection": "-0.000413864371317873*I*L**3*P + 0.0812093866385958*I*L**2*P*x - 0.15*I*L*P*x**2*exp(-1) - 0.1*I*P*x**3*exp(-1)", "rotation": "0.0812093866385958*I*L**2*P - 0.3*I*L*P*x*exp(-1) - 0.3*I*P*x**2*exp(-1)"}, {"span": ["0.55*L", "L"], "deflection": "-0.020815845046284*I*L**3*P + 0.192492917592957*I*L**2*P*x - 0.7*I*L*P*x**2*exp(-1) + 0.233333333333333*I*P*x**3*exp(-1)", "rotation": "0.192492917592957*I*L**2*P - 1.4*I*L*P*x*exp(-1) + 0.7*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.15*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.55*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I need to figure out how to generate a question based on the given setup of a statically loaded beam. Let me start by reading through the provided information carefully.\n\nThe beam has a length of L. It's supported at x=0 with a pin and at x=L with a roller. There are two downward point loads, each of magnitude -2P, applied at x=0.15L and x=0.55L. The question should ask the reader to calculate the reaction forces at the supports.\n\nI remember that for a simply supported beam with point loads, the reaction forces can be found using the equations of equilibrium. The sum of moments about one support should equal zero, and the sum of vertical forces should also equal zero. \n\nSo, the question needs to include all the necessary details: the length of the beam, the locations and types of supports, and the specifics of the loads. It should be concise and self-contained, so the reader has all the information they need to solve it without additional context.\n\nPutting it all together, the question should state the beam's length, the pin and roller supports at the ends, and the two downward loads at the given positions. Then, it should ask for the reaction forces at the supports.\n\nI think that's all the information needed. The question is clear and includes everything required to calculate the reactions using statics.\n</think>\n\nA beam of length \\( L \\) is supported at \\( x = 0 \\) with a pin and at \\( x = L \\) with a roller. There are two downward point loads of magnitude \\(-2P\\) at \\( x = 0.15L \\) and \\( x = 0.55L \\). Calculate the reaction forces at the supports."
] |
10
|
[
"0.15*L",
"0.25*L",
"0.45*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.15*L", "magnitude": "-2*P"}, "P2": {"location": "0.25*L", "magnitude": "-2*P"}, "P3": {"location": "0.45*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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] |
{"local_extrema": [], "null": [[0.45, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.45, 0.935], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.116203918480029j"], [0.15, "0.09840775051336048j"], [1.0, "-0.09072826717890695j"]], "null": [["(0.4613481662094889+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.25, "0.02505412277478016j"], [0.45, "0.03255886337467755j"], [0.46111111111111114, "0.0325806930749418j"], [1.0, "-1.1622647289044608e-16j"]], "null": [[0.0, 0], ["(0.9999999999999987+0j)", 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.15*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.25*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.45*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.15*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.15*L", "0.25*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.25*L", "0.45*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.45*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "4.3*P"}, {"point": "L", "type": "Force", "value": "1.7*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.15*L"], "shear_force": "-4.3*P", "bending_moment": "4.3*P*x"}, {"span": ["0.15*L", "0.25*L"], "shear_force": "-2.3*P", "bending_moment": "0.3*L*P + 2.3*P*x"}, {"span": ["0.25*L", "0.45*L"], "shear_force": "-0.3*P", "bending_moment": "0.8*L*P + 0.3*P*x"}, {"span": ["0.45*L", "L"], "shear_force": "1.7*P", "bending_moment": "1.7*L*P - 1.7*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.15*L"], "deflection": "0.116203918480029*I*L**2*P*x - 0.716666666666667*I*P*x**3*exp(-1)", "rotation": "0.116203918480029*I*L**2*P - 2.15*I*P*x**2*exp(-1)"}, {"span": ["0.15*L", "0.25*L"], "deflection": "-0.000413864371317873*I*L**3*P + 0.124481205906387*I*L**2*P*x - 0.15*I*L*P*x**2*exp(-1) - 0.383333333333333*I*P*x**3*exp(-1)", "rotation": "0.124481205906387*I*L**2*P - 0.3*I*L*P*x*exp(-1) - 1.15*I*P*x**2*exp(-1)"}, {"span": ["0.25*L", "0.45*L"], "deflection": "-0.00232990312741913*I*L**3*P + 0.147473670979602*I*L**2*P*x - 0.4*I*L*P*x**2*exp(-1) - 0.05*I*P*x**3*exp(-1)", "rotation": "0.147473670979602*I*L**2*P - 0.8*I*L*P*x*exp(-1) - 0.15*I*P*x**2*exp(-1)"}, {"span": ["0.45*L", "L"], "deflection": "-0.0135042411530017*I*L**3*P + 0.221969257816819*I*L**2*P*x - 0.85*I*L*P*x**2*exp(-1) + 0.283333333333333*I*P*x**3*exp(-1)", "rotation": "0.221969257816819*I*L**2*P - 1.7*I*L*P*x*exp(-1) + 0.85*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.15*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.25*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.45*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I need to create a question about calculating reaction forces in a beam setup. Let me see what details are given. The beam is statically loaded, which means it's in equilibrium. The beam has a length L, which is important for setting up the problem. The supports are at x=0 (a pin) and x=L (a roller). So, the beam is simply supported at both ends, but one end can't rotate because it's a pin, and the other can because it's a roller.\n\nThere are three point loads applied, all downward since they're negative. Each is -2P, and they're located at 0.15L, 0.25L, and 0.45L along the beam. So, these are the positions where the forces are acting. I need to make sure the question includes all these details.\n\nThe question should ask for the reaction forces at the supports. Since it's a statics problem, the sum of forces and moments should be zero. I can use the equations of equilibrium to find the reactions. I'll have to set up the equations considering the loads and the reactions at the supports.\n\nI should make sure to include all the given specifics: the length L, the supports at 0 and L, and the three downward loads at their respective positions. The question needs to be concise and self-contained, so it should clearly state what needs to be calculated without extra information.\n\nI think I've got all the parts. Now, I'll phrase it as a question that asks for the reaction forces, including all the necessary details.\n</think>\n\nGiven a beam of length L with a pin support at x=0 and a roller support at x=L, and three downward point loads of -2P each at x=0.15L, x=0.25L, and x=0.45L, calculate the reaction forces at the supports."
] |
11
|
[
"0.05*L",
"0.45*L",
"0.85*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.05*L", "magnitude": "-2*P"}, "P2": {"location": "0.45*L", "magnitude": "-2*P"}, "P3": {"location": "0.85*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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] |
{"local_extrema": [], "null": [[0.45, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.45, 0.685], [0.85, 0.405], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.0763809689732206j"], [1.0, "-0.07904809492171416j"]], "null": [["(0.500194473695988+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.05, "0.0037937567370804936j"], [0.45, "0.023781873040728797j"], [0.4984848484848485, "0.024088094944410388j"], [1.0, "-3.7470027081099033e-16j"]], "null": [[0.0, 0], ["(0.9999999999999952+0j)", 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.05*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.45*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.85*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.05*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.05*L", "0.45*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.45*L", "0.85*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.85*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "3.3*P"}, {"point": "L", "type": "Force", "value": "2.7*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.05*L"], "shear_force": "-3.3*P", "bending_moment": "3.3*P*x"}, {"span": ["0.05*L", "0.45*L"], "shear_force": "-1.3*P", "bending_moment": "0.1*L*P + 1.3*P*x"}, {"span": ["0.45*L", "0.85*L"], "shear_force": "0.7*P", "bending_moment": "L*P - 0.7*P*x"}, {"span": ["0.85*L", "L"], "shear_force": "2.7*P", "bending_moment": "2.7*L*P - 2.7*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.05*L"], "deflection": "0.0763809689732206*I*L**2*P*x - 0.55*I*P*x**3*exp(-1)", "rotation": "0.0763809689732206*I*L**2*P - 1.65*I*P*x**2*exp(-1)"}, {"span": ["0.05*L", "0.45*L"], "deflection": "-1.53283100488101e-5*I*L**3*P + 0.0773006675761492*I*L**2*P*x - 0.05*I*L*P*x**2*exp(-1) - 0.216666666666667*I*P*x**3*exp(-1)", "rotation": "0.0773006675761492*I*L**2*P - 0.1*I*L*P*x*exp(-1) - 0.65*I*P*x**2*exp(-1)"}, {"span": ["0.45*L", "0.85*L"], "deflection": "-0.0111896663356314*I*L**3*P + 0.151796254413366*I*L**2*P*x - 0.5*I*L*P*x**2*exp(-1) + 0.116666666666667*I*P*x**3*exp(-1)", "rotation": "0.151796254413366*I*L**2*P - 1.0*I*L*P*x*exp(-1) + 0.35*I*P*x**2*exp(-1)"}, {"span": ["0.85*L", "L"], "deflection": "-0.0864976536054353*I*L**3*P + 0.417589150659733*I*L**2*P*x - 1.35*I*L*P*x**2*exp(-1) + 0.45*I*P*x**3*exp(-1)", "rotation": "0.417589150659733*I*L**2*P - 2.7*I*L*P*x*exp(-1) + 1.35*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.05*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.45*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.85*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I need to generate a question based on the setup provided about a statically loaded beam. Let me start by understanding all the details given.\n\nFirst, the beam has a length of L. That's straightforward. Then, it has a Young's modulus of E and a moment of inertia of I. Hmm, but wait, for calculating reaction forces, do I need E and I? I think E and I are more relevant for deflection or stress calculations, not for reactions. So maybe the question doesn't need to include E and I.\n\nNext, there are three point loads, all downward with a magnitude of -2P. They're located at x=0.05L, x=0.45L, and x=0.85L. Since all the loads are downward, the reactions at the supports must counteract these to keep the beam static.\n\nThe supports are a pin at x=0 and a roller at x=L. A pin support can provide both vertical and horizontal reactions, while a roller can only provide a vertical reaction. But since the beam is horizontal and the loads are vertical, I think the horizontal reaction at the pin might be zero. So, the pin only has a vertical reaction, and the roller has a vertical reaction as well.\n\nThe question needs to ask for the reaction forces at the supports. So, I should state all the given information concisely in the question. Let me make sure to include the beam length, the supports, and the loads.\n\nWait, do I need to mention the magnitudes as -2P? Or can I just state they are downward? Since the question is about reaction forces, which are typically positive values, using -2P might be confusing. Maybe it's better to say \"downward point loads of 2P\" to avoid negative signs.\n\nPutting it all together, the question should state the beam's length, the type of supports, the number and location of the downward loads, and then ask for the reaction forces at the supports. Let me structure that into a clear and concise question.\n</think>\n\nQuestion: \nGiven a beam of length L with a pin support at one end and a roller support at the other, and three downward point loads of 2P each located at 5% (x=0.05L), 45% (x=0.45L), and 85% (x=0.85L) of its length, calculate the reaction forces at the supports."
] |
12
|
[
"0.75*L",
"0.05*L",
"0.55*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.75*L", "magnitude": "-2*P"}, "P2": {"location": "0.05*L", "magnitude": "-2*P"}, "P3": {"location": "0.55*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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0
] |
{"local_extrema": [], "null": [[0.55, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.55, 0.8150000000000001], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.0841064372378209j"], [0.55, "-0.0075415285440147j"], [1.0, "-0.0933953931274002j"]], "null": [["(0.5243190562085643+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.5196969696969698, "0.028016672351402514j"], [0.55, "0.02792358241591727j"], [1.0, "-9.71445146547012e-17j"]], "null": [[0.0, 0], ["(0.999999999999999+0j)", 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.05*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.55*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.75*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.05*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.05*L", "0.55*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.55*L", "0.75*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.75*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "3.3*P"}, {"point": "L", "type": "Force", "value": "2.7*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.05*L"], "shear_force": "-3.3*P", "bending_moment": "3.3*P*x"}, {"span": ["0.05*L", "0.55*L"], "shear_force": "-1.3*P", "bending_moment": "0.1*L*P + 1.3*P*x"}, {"span": ["0.55*L", "0.75*L"], "shear_force": "0.7*P", "bending_moment": "1.2*L*P - 0.7*P*x"}, {"span": ["0.75*L", "L"], "shear_force": "2.7*P", "bending_moment": "2.7*L*P - 2.7*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.05*L"], "deflection": "0.0841064372378209*I*L**2*P*x - 0.55*I*P*x**3*exp(-1)", "rotation": "0.0841064372378209*I*L**2*P - 1.65*I*P*x**2*exp(-1)"}, {"span": ["0.05*L", "0.55*L"], "deflection": "-1.53283100488101e-5*I*L**3*P + 0.0850261358407495*I*L**2*P*x - 0.05*I*L*P*x**2*exp(-1) - 0.216666666666667*I*P*x**3*exp(-1)", "rotation": "0.0850261358407495*I*L**2*P - 0.1*I*L*P*x*exp(-1) - 0.65*I*P*x**2*exp(-1)"}, {"span": ["0.55*L", "0.75*L"], "deflection": "-0.0204173089850149*I*L**3*P + 0.196309666795111*I*L**2*P*x - 0.6*I*L*P*x**2*exp(-1) + 0.116666666666667*I*P*x**3*exp(-1)", "rotation": "0.196309666795111*I*L**2*P - 1.2*I*L*P*x*exp(-1) + 0.35*I*P*x**2*exp(-1)"}, {"span": ["0.75*L", "L"], "deflection": "-0.072150355399749*I*L**3*P + 0.403241852454047*I*L**2*P*x - 1.35*I*L*P*x**2*exp(-1) + 0.45*I*P*x**3*exp(-1)", "rotation": "0.403241852454047*I*L**2*P - 2.7*I*L*P*x*exp(-1) + 1.35*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.75*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.05*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.55*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Alright, so I need to generate a question based on the setup of a statically loaded beam. The user has provided details about the beam's length, supports, and the applied loads. Let me break this down step by step.\n\nFirst, the beam's length is given as L. The supports are a pin at x=0 and a roller at x=L. That means the beam is simply supported at both ends, with one end having a fixed pivot (pin) and the other a free roller. \n\nNext, there are three point loads applied, each with a magnitude of -2P. The negative sign indicates that these are downward forces. The loads are located at x=0.05L, x=0.55L, and x=0.75L. So, they're distributed along the beam, with the first and third being closer to the ends and the middle one near the center.\n\nThe task is to calculate the reaction forces at the supports. Since the beam is statically loaded, it's in equilibrium, so the sum of forces and moments should be zero. \n\nI need to structure the question to include all these elements: beam length, support locations and types, and the specifics of the loads. It should be concise and self-contained, so the reader knows exactly what to calculate without additional context.\n\nI should mention the pin support at the start (x=0) and the roller at the end (x=L). Then, list the three downward forces with their positions and magnitudes. Finally, ask for the reaction forces at both supports.\n\nPutting it all together, the question should clearly state the beam's setup and the applied loads, leading the reader to calculate the reactions at the pin and roller supports.\n</think>\n\nGiven a beam of length \\( L \\) with a pin support at \\( x = 0 \\) and a roller support at \\( x = L \\), and three downward forces of magnitude \\( -2P \\) applied at \\( x = 0.05L \\), \\( x = 0.55L \\), and \\( x = 0.75L \\), calculate the reaction forces at the supports."
] |
13
|
[
"0.85*L",
"0.25*L",
"0.05*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.85*L", "magnitude": "-2*P"}, "P2": {"location": "0.25*L", "magnitude": "-2*P"}, "P3": {"location": "0.05*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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{"header": "Internal Loads", "segments": [{"span": ["0", "0.05*L"], "shear_force": "-3.7*P", "bending_moment": "3.7*P*x"}, {"span": ["0.05*L", "0.25*L"], "shear_force": "-1.7*P", "bending_moment": "0.1*L*P + 1.7*P*x"}, {"span": ["0.25*L", "0.85*L"], "shear_force": "0.3*P", "bending_moment": "0.6*L*P - 0.3*P*x"}, {"span": ["0.85*L", "L"], "shear_force": "2.3*P", "bending_moment": "2.3*L*P - 2.3*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.05*L"], "deflection": "0.0695751993115489*I*L**2*P*x - 0.616666666666667*I*P*x**3*exp(-1)", "rotation": "0.0695751993115489*I*L**2*P - 1.85*I*P*x**2*exp(-1)"}, {"span": ["0.05*L", "0.25*L"], "deflection": "-1.53283100488101e-5*I*L**3*P + 0.0704948979144775*I*L**2*P*x - 0.05*I*L*P*x**2*exp(-1) - 0.283333333333333*I*P*x**3*exp(-1)", "rotation": "0.0704948979144775*I*L**2*P - 0.1*I*L*P*x*exp(-1) - 0.85*I*P*x**2*exp(-1)"}, {"span": ["0.25*L", "0.85*L"], "deflection": "-0.00193136706615007*I*L**3*P + 0.0934873629876927*I*L**2*P*x - 0.3*I*L*P*x**2*exp(-1) + 0.05*I*P*x**3*exp(-1)", "rotation": "0.0934873629876927*I*L**2*P - 0.6*I*L*P*x*exp(-1) + 0.15*I*P*x**2*exp(-1)"}, {"span": ["0.85*L", "L"], "deflection": "-0.077239354335954*I*L**3*P + 0.35928025923406*I*L**2*P*x - 1.15*I*L*P*x**2*exp(-1) + 0.383333333333333*I*P*x**3*exp(-1)", "rotation": "0.35928025923406*I*L**2*P - 2.3*I*L*P*x*exp(-1) + 1.15*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.85*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.25*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.05*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so the user provided a setup of a statically loaded beam and wants a question about calculating the reaction forces. Let me break this down.\n\nFirst, I need to extract all the necessary details from the setup. The beam's length is L, with a pin support at x=0 and a roller at x=L. There are three downward point loads at x=0.05L, 0.25L, and 0.85L, each with a magnitude of 2P.\n\nThe question should be concise and include all these elements. I should mention the beam's supports, their locations, the type (pin and roller), and the applied loads with their positions and magnitudes.\n\nI should phrase it in a way that clearly asks for the reaction forces at the supports. Using the given details, I can structure the question to be self-contained and straightforward for the reader.\n\nPutting it all together, the question will state the beam's length, supports, and loads, then ask to find the reaction forces at the pin and roller. That should cover all the provided information succinctly.\n</think>\n\nGiven a beam of length \\( L \\) with a pin support at \\( x = 0 \\) and a roller support at \\( x = L \\), and three downward point loads of \\( -2P \\) at \\( x = 0.05L \\), \\( x = 0.25L \\), and \\( x = 0.85L \\), calculate the reaction forces at the supports."
] |
14
|
[
"0.05*L",
"0.25*L",
"0.95*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.05*L", "magnitude": "-2*P"}, "P2": {"location": "0.25*L", "magnitude": "-2*P"}, "P3": {"location": "0.95*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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] |
{"local_extrema": [], "null": [[0.25, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.25, 0.475], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.0577110873337701j"], [0.25, "0.032189451102501286j"], [0.95, "-0.04506523154350155j"], [1.0, "-0.04621485479716192j"]], "null": [["(0.45670258442738104+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.05, "0.002858729824103088j"], [0.45505050505050504, "0.015246893787465144j"], [1.0, "1.942890293094024e-16j"]], "null": [[0.0, 0], [1.0, 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.05*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.25*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.95*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.05*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.05*L", "0.25*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.25*L", "0.95*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.95*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "3.5*P"}, {"point": "L", "type": "Force", "value": "2.5*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.05*L"], "shear_force": "-3.5*P", "bending_moment": "3.5*P*x"}, {"span": ["0.05*L", "0.25*L"], "shear_force": "-1.5*P", "bending_moment": "0.1*L*P + 1.5*P*x"}, {"span": ["0.25*L", "0.95*L"], "shear_force": "0.5*P", "bending_moment": "0.6*L*P - 0.5*P*x"}, {"span": ["0.95*L", "L"], "shear_force": "2.5*P", "bending_moment": "2.5*L*P - 2.5*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.05*L"], "deflection": "0.0577110873337701*I*L**2*P*x - 0.583333333333333*I*P*x**3*exp(-1)", "rotation": "0.0577110873337701*I*L**2*P - 1.75*I*P*x**2*exp(-1)"}, {"span": ["0.05*L", "0.25*L"], "deflection": "-1.53283100488101e-5*I*L**3*P + 0.0586307859366987*I*L**2*P*x - 0.05*I*L*P*x**2*exp(-1) - 0.25*I*P*x**3*exp(-1)", "rotation": "0.0586307859366987*I*L**2*P - 0.1*I*L*P*x*exp(-1) - 0.75*I*P*x**2*exp(-1)"}, {"span": ["0.25*L", "0.95*L"], "deflection": "-0.00193136706615007*I*L**3*P + 0.0816232510099139*I*L**2*P*x - 0.3*I*L*P*x**2*exp(-1) + 0.0833333333333333*I*P*x**3*exp(-1)", "rotation": "0.0816232510099139*I*L**2*P - 0.6*I*L*P*x*exp(-1) + 0.25*I*P*x**2*exp(-1)"}, {"span": ["0.95*L", "L"], "deflection": "-0.107068245690939*I*L**3*P + 0.413634446667141*I*L**2*P*x - 1.25*I*L*P*x**2*exp(-1) + 0.416666666666667*I*P*x**3*exp(-1)", "rotation": "0.413634446667141*I*L**2*P - 2.5*I*L*P*x*exp(-1) + 1.25*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.05*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.25*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.95*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so the user wants me to generate a question about calculating reaction forces on a beam. They provided a setup with a beam of length L, supported by a pin at one end and a roller at the other. There are three downward point loads at specific positions along the beam.\n\nFirst, I need to make sure the question is self-contained and includes all necessary details. The beam's length, the positions and types of supports, and the locations and magnitudes of the loads are all crucial. I should mention the pin support at x=0 and the roller at x=L. The loads are each -2P at 0.05L, 0.25L, and 0.95L, so I'll note that.\n\nI should structure the question to ask for the reaction forces at the supports. Since it's a statically loaded beam, equilibrium equations should suffice. I'll mention using free-body diagrams and equations of equilibrium to solve it.\n\nI need to keep the question concise and clear, avoiding any unnecessary details. Make sure to include all the provided specifics without making it too long. Also, the question should be standalone, so readers don't need to refer back to the setup.\n\nLet me put it all together: state the beam's length, supports, loads, and ask for the reaction forces. Use the correct terminology for each part to ensure clarity.\n</think>\n\nThink: The question should ask the reader to calculate the reaction forces at the supports of a beam with specific details provided. The beam has a length of L, with a pin support at x=0 and a roller support at x=L. There are three downward point loads of -2P each applied at x=0.05L, x=0.25L, and x=0.95L. The question should instruct the reader to use free-body diagrams and equilibrium equations to solve for the reaction forces at the supports.\n\nQuestion: \nCalculate the reaction forces at the pin and roller supports of a beam with length L, subjected to downward point loads of -2P at x=0.05L, x=0.25L, and x=0.95L, with a pin support at x=0 and a roller support at x=L."
] |
15
|
[
"0.95*L",
"0.45*L",
"0.15*L",
"0.85*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.95*L", "magnitude": "-2*P"}, "P2": {"location": "0.45*L", "magnitude": "-2*P"}, "P3": {"location": "0.15*L", "magnitude": "-2*P"}, "P4": {"location": "0.85*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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{"local_extrema": [[0.0, "0.100063207998632j"], [0.85, "-0.08608378923411836j"], [1.0, "-0.10227048464566157j"]], "null": [["(0.496259016943463+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.15, "0.014347298205686202j"], [0.45, "0.030460417728995083j"], [0.49444444444444446, "0.0307808277699385j"], [0.85, "0.014469924686075962j"], [1.0, "-6.38378239159465e-16j"]], "null": [[0.0, 0], ["(0.9999999999999938+0j)", 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.15*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.45*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.85*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.95*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.15*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.15*L", "0.45*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.45*L", "0.85*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.85*L", "0.95*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.95*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "3.2*P"}, {"point": "L", "type": "Force", "value": "4.8*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.15*L"], "shear_force": "-3.2*P", "bending_moment": "3.2*P*x"}, {"span": ["0.15*L", "0.45*L"], "shear_force": "-1.2*P", "bending_moment": "0.3*L*P + 1.2*P*x"}, {"span": ["0.45*L", "0.85*L"], "shear_force": "0.8*P", "bending_moment": "1.2*L*P - 0.8*P*x"}, {"span": ["0.85*L", "0.95*L"], "shear_force": "2.8*P", "bending_moment": "2.9*L*P - 2.8*P*x"}, {"span": ["0.95*L", "L"], "shear_force": "4.8*P", "bending_moment": "4.8*L*P - 4.8*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.15*L"], "deflection": "0.100063207998632*I*L**2*P*x - 0.533333333333333*I*P*x**3*exp(-1)", "rotation": "0.100063207998632*I*L**2*P - 1.6*I*P*x**2*exp(-1)"}, {"span": ["0.15*L", "0.45*L"], "deflection": "-0.000413864371317873*I*L**3*P + 0.108340495424989*I*L**2*P*x - 0.15*I*L*P*x**2*exp(-1) - 0.2*I*P*x**3*exp(-1)", "rotation": "0.108340495424989*I*L**2*P - 0.3*I*L*P*x*exp(-1) - 0.6*I*P*x**2*exp(-1)"}, {"span": ["0.45*L", "0.85*L"], "deflection": "-0.0115882023969004*I*L**3*P + 0.182836082262206*I*L**2*P*x - 0.6*I*L*P*x**2*exp(-1) + 0.133333333333333*I*P*x**3*exp(-1)", "rotation": "0.182836082262206*I*L**2*P - 1.2*I*L*P*x*exp(-1) + 0.4*I*P*x**2*exp(-1)"}, {"span": ["0.85*L", "0.95*L"], "deflection": "-0.0868961896667043*I*L**3*P + 0.448628978508574*I*L**2*P*x - 1.45*I*L*P*x**2*exp(-1) + 0.466666666666667*I*P*x**3*exp(-1)", "rotation": "0.448628978508574*I*L**2*P - 2.9*I*L*P*x*exp(-1) + 1.4*I*P*x**2*exp(-1)"}, {"span": ["0.95*L", "L"], "deflection": "-0.192033068291493*I*L**3*P + 0.7806401741658*I*L**2*P*x - 2.4*I*L*P*x**2*exp(-1) + 0.8*I*P*x**3*exp(-1)", "rotation": "0.7806401741658*I*L**2*P - 4.8*I*L*P*x*exp(-1) + 2.4*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.95*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.45*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.15*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.85*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I need to generate a question based on the setup provided. Let me read through the details again to make sure I understand everything. The beam has a length of L, with a pin support at the start (x=0) and a roller support at the end (x=L). There are four downward point loads, each with a magnitude of -2P, applied at different positions along the beam: 0.15L, 0.45L, 0.85L, and 0.95L. \n\nMy task is to create a question that asks the reader to calculate the reaction forces at the supports. I should include all the necessary details: the length of the beam, the type and location of the supports, and the magnitude and location of the applied loads. The question needs to be concise and self-contained, so I don't want to include unnecessary information.\n\nLet me think about how to structure this. I should mention the beam's length as L, the pin support at x=0, and the roller support at x=L. Then, I need to list the four point loads, each with their specific positions and magnitudes. Since the loads are all downward, they're negative, but I don't need to mention that in the question as it's already implied by the negative sign in the setup.\n\nI should make sure the question is clear and direct. Maybe something like, \"Determine the reaction forces at the pin and roller supports of a beam with given point loads.\" Then, I can list all the specifics in the question body. Wait, but the question should be a single statement. So perhaps I can combine the setup details into the question.\n\nLet me try drafting it: \"Determine the reaction forces at the pin and roller supports of a beam with a length L, subjected to four downward point loads of magnitude 2P each at x = 0.15L, 0.45L, 0.85L, and 0.95L.\" Hmm, that seems to include all the necessary information. The pin is at x=0, and the roller at x=L, and the loads are correctly placed.\n\nI think that's a good start. I should make sure the question is clear and all details are included without being too wordy. Let me check if I missed anything. Beam length, supports, and all four load positions and magnitudes are there. Yes, that should be sufficient for someone to calculate the reactions.\n</think>\n\nDetermine the reaction forces at the pin and roller supports of a beam with a length L, subjected to four downward point loads of magnitude 2P each at x = 0.15L, 0.45L, 0.85L, and 0.95L."
] |
16
|
[
"0.85*L",
"0.15*L",
"0.75*L",
"0.25*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.85*L", "magnitude": "-2*P"}, "P2": {"location": "0.15*L", "magnitude": "-2*P"}, "P3": {"location": "0.75*L", "magnitude": "-2*P"}, "P4": {"location": "0.25*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.15*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.25*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.75*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.85*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.15*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.15*L", "0.25*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.25*L", "0.75*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.75*L", "0.85*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.85*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "4.0*P"}, {"point": "L", "type": "Force", "value": "4.0*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.15*L"], "shear_force": "-4.0*P", "bending_moment": "4.0*P*x"}, {"span": ["0.15*L", "0.25*L"], "shear_force": "-2.0*P", "bending_moment": "0.3*L*P + 2.0*P*x"}, {"span": ["0.25*L", "0.75*L"], "shear_force": "0", "bending_moment": "0.8*L*P"}, {"span": ["0.75*L", "0.85*L"], "shear_force": "2*P", "bending_moment": "2.3*L*P - 2*P*x"}, {"span": ["0.85*L", "L"], "shear_force": "4*P", "bending_moment": "4.0*L*P - 4*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.15*L"], "deflection": "0.115882023969004*I*L**2*P*x - 0.666666666666667*I*P*x**3*exp(-1)", "rotation": "0.115882023969004*I*L**2*P - 2.0*I*P*x**2*exp(-1)"}, {"span": ["0.15*L", "0.25*L"], "deflection": "-0.000413864371317873*I*L**3*P + 0.124159311395362*I*L**2*P*x - 0.15*I*L*P*x**2*exp(-1) - 0.333333333333333*I*P*x**3*exp(-1)", "rotation": "0.124159311395362*I*L**2*P - 0.3*I*L*P*x*exp(-1) - 1.0*I*P*x**2*exp(-1)"}, {"span": ["0.25*L", "0.75*L"], "deflection": "-0.00232990312741913*I*L**3*P + 0.147151776468577*I*L**2*P*x - 0.4*I*L*P*x**2*exp(-1)", "rotation": "0.147151776468577*I*L**2*P - 0.8*I*L*P*x*exp(-1)"}, {"span": ["0.75*L", "0.85*L"], "deflection": "-0.0540629495421532*I*L**3*P + 0.354083962127513*I*L**2*P*x - 1.15*I*L*P*x**2*exp(-1) + 0.333333333333333*I*P*x**3*exp(-1)", "rotation": "0.354083962127513*I*L**2*P - 2.3*I*L*P*x*exp(-1) + 1.0*I*P*x**2*exp(-1)"}, {"span": ["0.85*L", "L"], "deflection": "-0.129370936811957*I*L**3*P + 0.61987685837388*I*L**2*P*x - 2.0*I*L*P*x**2*exp(-1) + 0.666666666666667*I*P*x**3*exp(-1)", "rotation": "0.61987685837388*I*L**2*P - 4.0*I*L*P*x*exp(-1) + 2.0*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.85*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.15*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.75*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.25*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I need to figure out how to generate a question based on the setup provided. The setup is about a statically loaded beam, and the task is to calculate the reaction forces at the supports. Let me start by understanding all the details given.\n\nThe beam has a length of L. It's supported at two points: a pin support at x=0 and a roller support at x=L. So, the supports are at the very start and the very end of the beam. Now, there are four point loads applied at different positions along the beam. Each load is -2P, meaning they're downward forces. The positions are at 0.15L, 0.25L, 0.75L, and 0.85L. \n\nI remember that for a beam with these supports and loads, the reaction forces can be found using static equilibrium equations. Since it's a statically determinate structure, the reactions can be calculated without considering deflection or material properties like Young's modulus or moment of inertia. But the question only asks for the reaction forces, so I don't need to involve those details.\n\nSo, the question should state the length of the beam, the type of supports (pin at one end, roller at the other), and the location and magnitude of each applied load. It should be concise and self-contained. I should make sure to mention that the loads are downward, indicated by the negative sign.\n\nPutting it all together, the question should ask for the reaction forces at the supports, including both the magnitudes and their directions. Since the pin support can have both vertical and horizontal reactions, and the roller only vertical, I should specify that. But maybe it's enough to just ask for the reaction forces without specifying direction if it's clear from the context.\n\nWait, the user's example answer was a question that included all the details. Let me check that. Yes, it included the beam length, support locations and types, and the point loads with their positions and magnitudes. So, I should follow that structure.\n\nI think I have all the elements. Now, I'll formulate the question accordingly.\n</think>\n\nWhat are the reaction forces at the pin support (at x=0) and the roller support (at x=L) for a beam of length L with downward point loads of -2P at x=0.15L, x=0.25L, x=0.75L, and x=0.85L?"
] |
17
|
[
"0.95*L",
"0.75*L",
"0.25*L",
"0.45*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.95*L", "magnitude": "-2*P"}, "P2": {"location": "0.75*L", "magnitude": "-2*P"}, "P3": {"location": "0.25*L", "magnitude": "-2*P"}, "P4": {"location": "0.45*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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] |
{"local_extrema": [], "null": [[0.45, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.45, 1.04], [0.75, 0.7999999999999998], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.122135974468919j"], [0.95, "-0.12213597446891922j"], [1.0, "-0.12434325111594757j"]], "null": [["(0.49700450698032306+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.25, "0.02746833160746773j"], [0.45, "0.03806325951320523j"], [0.4954545454545455, "0.03847526974634287j"], [0.95, "0.006180374611679945j"], [1.0, "3.608224830031759e-16j"]], "null": [[0.0, 0], [1.0, 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.25*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.45*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.75*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.95*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.25*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.25*L", "0.45*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.45*L", "0.75*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.75*L", "0.95*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.95*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "3.2*P"}, {"point": "L", "type": "Force", "value": "4.8*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.25*L"], "shear_force": "-3.2*P", "bending_moment": "3.2*P*x"}, {"span": ["0.25*L", "0.45*L"], "shear_force": "-1.2*P", "bending_moment": "0.5*L*P + 1.2*P*x"}, {"span": ["0.45*L", "0.75*L"], "shear_force": "0.8*P", "bending_moment": "1.4*L*P - 0.8*P*x"}, {"span": ["0.75*L", "0.95*L"], "shear_force": "2.8*P", "bending_moment": "2.9*L*P - 2.8*P*x"}, {"span": ["0.95*L", "L"], "shear_force": "4.8*P", "bending_moment": "4.8*L*P - 4.8*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.25*L"], "deflection": "0.122135974468919*I*L**2*P*x - 0.533333333333333*I*P*x**3*exp(-1)", "rotation": "0.122135974468919*I*L**2*P - 1.6*I*P*x**2*exp(-1)"}, {"span": ["0.25*L", "0.45*L"], "deflection": "-0.00191603875610126*I*L**3*P + 0.145128439542134*I*L**2*P*x - 0.25*I*L*P*x**2*exp(-1) - 0.2*I*P*x**3*exp(-1)", "rotation": "0.145128439542134*I*L**2*P - 0.5*I*L*P*x*exp(-1) - 0.6*I*P*x**2*exp(-1)"}, {"span": ["0.45*L", "0.75*L"], "deflection": "-0.0130903767816838*I*L**3*P + 0.219624026379351*I*L**2*P*x - 0.7*I*L*P*x**2*exp(-1) + 0.133333333333333*I*P*x**3*exp(-1)", "rotation": "0.219624026379351*I*L**2*P - 1.4*I*L*P*x*exp(-1) + 0.4*I*P*x**2*exp(-1)"}, {"span": ["0.75*L", "0.95*L"], "deflection": "-0.0648234231964179*I*L**3*P + 0.426556212038287*I*L**2*P*x - 1.45*I*L*P*x**2*exp(-1) + 0.466666666666667*I*P*x**3*exp(-1)", "rotation": "0.426556212038287*I*L**2*P - 2.9*I*L*P*x*exp(-1) + 1.4*I*P*x**2*exp(-1)"}, {"span": ["0.95*L", "L"], "deflection": "-0.169960301821206*I*L**3*P + 0.758567407695514*I*L**2*P*x - 2.4*I*L*P*x**2*exp(-1) + 0.8*I*P*x**3*exp(-1)", "rotation": "0.758567407695514*I*L**2*P - 4.8*I*L*P*x*exp(-1) + 2.4*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.95*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.75*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.25*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.45*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I need to figure out how to generate a question based on the setup provided. The setup describes a statically loaded beam with specific details. Let me break it down.\n\nFirst, the beam has a length of L. That's straightforward. The supports are a pin at x=0 and a roller at x=L. So, one end is fixed (pin) and the other is simply supported (roller). \n\nNext, there are four point loads applied at different positions along the beam. Each load is -2P, meaning they're downward. The positions are at 0.25L, 0.45L, 0.75L, and 0.95L. So, these are all along the length of the beam, closer to the center and towards the pin end.\n\nThe question needs to ask the reader to calculate the reaction forces at the supports. Since it's a statically loaded beam, the reactions can be found using static equilibrium equations. The key here is that the sum of moments about one support should equal zero, and the sum of forces in the vertical direction should also equal zero.\n\nI should make sure the question is self-contained and includes all necessary details: beam length, support locations and types, and load positions and magnitudes. It should be concise and clear so that someone can immediately understand what's being asked without extra information.\n\nPutting it all together, the question should state the beam's length, the support conditions (pin at one end, roller at the other), and list all the applied loads with their positions and magnitudes. Then, it should ask for the reaction forces at the supports.\n\nI think that covers everything. The question is straightforward and provides all the required information for someone to solve it using basic beam analysis principles.\n</think>\n\nTo determine the reaction forces at the supports of a statically loaded beam, consider a beam of length \\( L \\) with a pin support at \\( x = 0 \\) and a roller support at \\( x = L \\). The beam is subjected to four downward point loads of magnitude \\( -2P \\) at positions \\( x = 0.25L \\), \\( x = 0.45L \\), \\( x = 0.75L \\), and \\( x = 0.95L \\). Calculate the reaction forces at the supports."
] |
18
|
[
"0.55*L",
"0.35*L",
"0.05*L",
"0.25*L"
] |
{"L": "L", "E": "E", "I": "I", "P": {"P1": {"location": "0.55*L", "magnitude": "-2*P"}, "P2": {"location": "0.35*L", "magnitude": "-2*P"}, "P3": {"location": "0.05*L", "magnitude": "-2*P"}, "P4": {"location": "0.25*L", "magnitude": "-2*P"}}, "M": {}, "Q": {}, "R": {"R1": {"location": "0", "type": "pin"}, "R2": {"location": "L", "type": "roller"}}}
|
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] |
{"local_extrema": [], "null": [[0.35, 0]]}
|
{"local_extrema": [[0.0, 0.0], [0.35, 1.16], [1.0, 0.0]], "null": [[0.0, 0], [1.0, 0]]}
|
{"local_extrema": [[0.0, "0.141633584851005j"], [0.05, "0.1390584287628049j"], [0.35, "0.052238880646344785j"], [1.0, "-0.1195608183807188j"]], "null": [["(0.475112662285152+0j)", 0]]}
|
{"local_extrema": [[0.0, "0j"], [0.25, "0.03102449953879166j"], [0.4732323232323233, "0.041527121394225076j"], [1.0, "6.245004513516506e-17j"]], "null": [[0.0, 0], [1.0, 0]]}
|
{"header": "Beam points", "points": [{"coordinate": "0", "type": "Pinned Support", "load": "0", "moment": "0"}, {"coordinate": "0.05*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.25*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.35*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "0.55*L", "type": "Continuity point", "load": "-2*P", "moment": "0"}, {"coordinate": "L", "type": "Roller", "load": "0", "moment": "0"}]}
|
{"header": "Beam segments", "segments": [{"span": ["0", "0.05*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.05*L", "0.25*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.25*L", "0.35*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.35*L", "0.55*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.55*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
|
{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "5.6*P"}, {"point": "L", "type": "Force", "value": "2.4*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.05*L"], "shear_force": "-5.6*P", "bending_moment": "5.6*P*x"}, {"span": ["0.05*L", "0.25*L"], "shear_force": "-3.6*P", "bending_moment": "0.1*L*P + 3.6*P*x"}, {"span": ["0.25*L", "0.35*L"], "shear_force": "-1.6*P", "bending_moment": "0.6*L*P + 1.6*P*x"}, {"span": ["0.35*L", "0.55*L"], "shear_force": "0.4*P", "bending_moment": "1.3*L*P - 0.4*P*x"}, {"span": ["0.55*L", "L"], "shear_force": "2.4*P", "bending_moment": "2.4*L*P - 2.4*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.05*L"], "deflection": "0.141633584851005*I*L**2*P*x - 0.933333333333333*I*P*x**3*exp(-1)", "rotation": "0.141633584851005*I*L**2*P - 2.8*I*P*x**2*exp(-1)"}, {"span": ["0.05*L", "0.25*L"], "deflection": "-1.53283100488101e-5*I*L**3*P + 0.142553283453934*I*L**2*P*x - 0.05*I*L*P*x**2*exp(-1) - 0.6*I*P*x**3*exp(-1)", "rotation": "0.142553283453934*I*L**2*P - 0.1*I*L*P*x*exp(-1) - 1.8*I*P*x**2*exp(-1)"}, {"span": ["0.25*L", "0.35*L"], "deflection": "-0.00193136706615007*I*L**3*P + 0.165545748527149*I*L**2*P*x - 0.3*I*L*P*x**2*exp(-1) - 0.266666666666667*I*P*x**3*exp(-1)", "rotation": "0.165545748527149*I*L**2*P - 0.6*I*L*P*x*exp(-1) - 0.8*I*P*x**2*exp(-1)"}, {"span": ["0.35*L", "0.55*L"], "deflection": "-0.00718897741289194*I*L**3*P + 0.210610980070651*I*L**2*P*x - 0.65*I*L*P*x**2*exp(-1) + 0.0666666666666667*I*P*x**3*exp(-1)", "rotation": "0.210610980070651*I*L**2*P - 1.3*I*L*P*x*exp(-1) + 0.2*I*P*x**2*exp(-1)"}, {"span": ["0.55*L", "L"], "deflection": "-0.0275909580878581*I*L**3*P + 0.321894511025012*I*L**2*P*x - 1.2*I*L*P*x**2*exp(-1) + 0.4*I*P*x**3*exp(-1)", "rotation": "0.321894511025012*I*L**2*P - 2.4*I*L*P*x*exp(-1) + 1.2*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.55*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.35*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.05*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.25*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I need to generate a question based on the setup of a statically loaded beam. The user has provided a lot of specific details, so I should make sure to include all of them in the question. Let me go through each part step by step.\n\nFirst, the beam has a length of L. That's straightforward. The supports are a pin at x=0 and a roller at x=L. I should mention that in the question. Then there are four point loads, each with a magnitude of -2P applied at different positions: 0.05L, 0.25L, 0.35L, and 0.55L. All of these are downward, so I'll note the negative sign.\n\nThe question needs to ask for the reaction forces at the supports. Since it's a statics problem, I can use the equations of equilibrium to find these reactions. I should make sure the question is clear and concise, including all the necessary details without being too wordy.\n\nPutting it all together, I'll start with the beam's length and supports, then list each load with its position and magnitude. Finally, I'll ask for the reaction forces at the pin and roller supports. I think that covers everything the user provided.\n</think>\n\nGiven a beam of length L with a pin support at x=0 and a roller support at x=L, and four downward point loads of -2P each applied at x=0.05L, x=0.25L, x=0.35L, and x=0.55L, calculate the reaction forces at the supports. \n\n**Question:** \nCalculate the reaction forces at the pin and roller supports of a beam with length L, supported at x=0 and x=L, subjected to four downward point loads of -2P each at x=0.05L, x=0.25L, x=0.35L, and x=0.55L."
] |
19
|
[
"0.95*L",
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{"header": "Beam segments", "segments": [{"span": ["0", "0.15*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.15*L", "0.35*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.35*L", "0.65*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.65*L", "0.95*L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}, {"span": ["0.95*L", "L"], "young_modulus": "E", "inertia": "I", "distributed_load": "0"}]}
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{"header": "Exterior Reactions", "reactions": [{"point": "0", "type": "Force", "value": "3.8*P"}, {"point": "L", "type": "Force", "value": "4.2*P"}]}
|
{"header": "Internal Loads", "segments": [{"span": ["0", "0.15*L"], "shear_force": "-3.8*P", "bending_moment": "3.8*P*x"}, {"span": ["0.15*L", "0.35*L"], "shear_force": "-1.8*P", "bending_moment": "0.3*L*P + 1.8*P*x"}, {"span": ["0.35*L", "0.65*L"], "shear_force": "0.2*P", "bending_moment": "L*P - 0.2*P*x"}, {"span": ["0.65*L", "0.95*L"], "shear_force": "2.2*P", "bending_moment": "2.3*L*P - 2.2*P*x"}, {"span": ["0.95*L", "L"], "shear_force": "4.2*P", "bending_moment": "4.2*L*P - 4.2*P*x"}]}
|
{"header": "Rotation and deflection", "segments": [{"span": ["0", "0.15*L"], "deflection": "0.118733089638083*I*L**2*P*x - 0.633333333333333*I*P*x**3*exp(-1)", "rotation": "0.118733089638083*I*L**2*P - 1.9*I*P*x**2*exp(-1)"}, {"span": ["0.15*L", "0.35*L"], "deflection": "-0.000413864371317873*I*L**3*P + 0.12701037706444*I*L**2*P*x - 0.15*I*L*P*x**2*exp(-1) - 0.3*I*P*x**3*exp(-1)", "rotation": "0.12701037706444*I*L**2*P - 0.3*I*L*P*x*exp(-1) - 0.9*I*P*x**2*exp(-1)"}, {"span": ["0.35*L", "0.65*L"], "deflection": "-0.00567147471805974*I*L**3*P + 0.172075608607942*I*L**2*P*x - 0.5*I*L*P*x**2*exp(-1) + 0.0333333333333333*I*P*x**3*exp(-1)", "rotation": "0.172075608607942*I*L**2*P - 1.0*I*L*P*x*exp(-1) + 0.1*I*P*x**2*exp(-1)"}, {"span": ["0.65*L", "0.95*L"], "deflection": "-0.0393477718952956*I*L**3*P + 0.327504672502876*I*L**2*P*x - 1.15*I*L*P*x**2*exp(-1) + 0.366666666666667*I*P*x**3*exp(-1)", "rotation": "0.327504672502876*I*L**2*P - 2.3*I*L*P*x*exp(-1) + 1.1*I*P*x**2*exp(-1)"}, {"span": ["0.95*L", "L"], "deflection": "-0.144484650520084*I*L**3*P + 0.659515868160103*I*L**2*P*x - 2.1*I*L*P*x**2*exp(-1) + 0.7*I*P*x**3*exp(-1)", "rotation": "0.659515868160103*I*L**2*P - 4.2*I*L*P*x*exp(-1) + 2.1*I*P*x**2*exp(-1)"}]}
|
You are a question generation assistant. You will be given information about the setup of a statically loaded beam. Your task is to generate a question that asks the reader to calculate the reaction forces at the supports.
Generate a single, self-contained question that includes all the provided details from the setup below. All details are correct. The question should be short and concise. Use limited time reasoning.
The question needs to state the length of the beam, the location and typoe of the supports of the beam, and the location and magnitude of the loads applied to the beam.
Following the think tag concluding the reasoning section, return only the question and no other dialogue referencing the prompt or the setup.
The beam has a length of L.
The beam has a Young's modulus of E.
The beam has a moment of inertia of I.
There is an applied point load of -2*P at x=0.95*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.65*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.15*L.
A negative load means the load is applied downward.
There is an applied point load of -2*P at x=0.35*L.
A negative load means the load is applied downward.
The beam has a pin support at x=0 and a roller support at x=L.
<think>
|
[
"Okay, so I'm trying to figure out how to generate a question based on the given setup of a statically loaded beam. Let me start by reading through the details again to make sure I understand everything correctly.\n\nThe beam has a length of L. It's supported at two points: a pin support at x=0 and a roller support at x=L. There are four point loads applied to the beam, all downward (since they're negative) at specific locations: 0.15L, 0.35L, 0.65L, and 0.95L. Each of these loads is -2P. \n\nThe question I need to generate should ask the reader to calculate the reaction forces at the supports. To do this, the question should include all the necessary details: the length of the beam, the locations and types of the supports, and the positions and magnitudes of the applied loads.\n\nI should make sure the question is clear and concise, providing all the required information without being too lengthy. It should state that the beam is statically loaded and that it's supported at both ends with specific types of supports. Then, it should list the point loads and their positions.\n\nI think the key here is to include all the given data without making it too complicated. The user mentioned that the question should be self-contained, so it shouldn't rely on external information beyond what's provided. Also, it should be short and to the point, so the reader doesn't get overwhelmed.\n\nLet me structure this. The question should start by describing the beam and its supports, then mention the applied loads. I need to ensure that all the specifics are included: the number of supports, their positions, types of supports, and the location and magnitude of each load.\n\nI should also consider the terminology. Since it's a pin support at x=0, that's a fixed end, and the roller at x=L is a simply supported end. The loads are all downward, so that's an important detail to include.\n\nPutting it all together, the question should flow logically. It should first state the setup of the beam with supports, then describe the applied loads. This way, the reader can visualize the scenario and understand what needs to be calculated.\n\nI think I've covered all the necessary points. Now, I just need to make sure the question is clear and concise, without any unnecessary words. It should be straightforward so that the reader knows exactly what is being asked without confusion.\n\nSo, the final question should mention the beam's length, the supports at both ends with their types, and the four downward point loads at the specified positions. That should give the reader all the information needed to calculate the reaction forces.\n</think>\n\nGiven a beam of length L with a pin support at x=0 and a roller support at x=L, and four downward point loads of -2P each applied at x=0.15L, x=0.35L, x=0.65L, and x=0.95L, calculate the reaction forces at the supports."
] |
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