Math Problem Statement

The diagram submitted by the user shows a beam with multiple loads, including point loads, a uniformly distributed load, and a moment, as depicted in the image.

Solution

The diagram you uploaded represents a beam with multiple loads. Let me summarize the details:

  1. Beam supports:

    • Support at point AA is a pin (hinged) support.
    • Support at point BB is a roller support.
  2. Loads applied on the beam:

    • A point load of 60 kN is applied 1 m from the left support AA.
    • 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 AA.
  3. Beam segments:

    • The total length of the beam is 12 meters, divided as follows:
      • 1 m from AA to the first load.
      • 2 m to the start of the UDL at point CC.
      • 6 m length of UDL.
      • 2 m to point BB.
      • 1 m from BB to the moment.

Next Steps for Analysis:

  1. 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 AA and BB.
    • The three equations of equilibrium are:
      • ΣFy=0\Sigma F_y = 0 (Sum of vertical forces)
      • ΣMA=0\Sigma M_A = 0 (Sum of moments about point AA)
      • ΣMB=0\Sigma M_B = 0 (Sum of moments about point BB)
  2. 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