Math Problem Statement
Solution
The diagram you uploaded represents a beam with multiple loads. Let me summarize the details:
-
Beam supports:
- Support at point is a pin (hinged) support.
- Support at point is a roller support.
-
Loads applied on the beam:
- A point load of 60 kN is applied 1 m from the left support .
- A uniformly distributed load (UDL) of 30 kN/m extends over a 6-meter section from 3 m to 9 m of the beam.
- A moment of 120 kN·m is applied at the far-right end, 12 m from point .
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Beam segments:
- The total length of the beam is 12 meters, divided as follows:
- 1 m from to the first load.
- 2 m to the start of the UDL at point .
- 6 m length of UDL.
- 2 m to point .
- 1 m from to the moment.
- The total length of the beam is 12 meters, divided as follows:
Next Steps for Analysis:
-
Calculate reactions at the supports:
- Since the beam has both vertical loads and a moment, we can use static equilibrium conditions to solve for reactions at supports and .
- The three equations of equilibrium are:
- (Sum of vertical forces)
- (Sum of moments about point )
- (Sum of moments about point )
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Determine shear forces and bending moments:
- Once reactions are known, shear force and bending moment diagrams can be created.
Shall we proceed with the calculation of the reactions at the supports?
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Math Problem Analysis
Mathematical Concepts
Statics
Equilibrium of forces and moments
Shear forces
Bending moments
Formulas
ΣF_y = 0 (Sum of vertical forces = 0)
ΣM_A = 0 (Sum of moments about point A = 0)
ΣM_B = 0 (Sum of moments about point B = 0)
Theorems
Equilibrium equations
Moment distribution method
Shear force and bending moment relationship
Suitable Grade Level
Undergraduate Engineering
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