Bridges are usually modeled as simply supported beams. Your role in a building and construct company is to analyse and design the bridge based on simply supported beam theory. Your mana asked you to perform a stress analysis for bridge element modelled as simply supported beam show the Figure. 1(a), this task is best achieved by performing the following required steps:

Elements Of Electromagnetics
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Bridges are usually modeled as simply supported beams. Your role in a building and construction
company is to analyse and design the bridge based on simply supported beam theory. Your manager
asked you to perform a stress analysis for bridge element modelled as simply supported beam shown in
the Figure.1(a), this task is best achieved by performing the following required steps:
2 kN
3 kN/m
3 kN/m
3kN.m
A
0.5 kN
4.5 kN
kN
2 m
1 т+1m-
2 m
R|
-2 m
(а)
(b)
Figure.1: (a) Bridge element modelled as simply supported beam (b) Beam section
Transcribed Image Text:Bridges are usually modeled as simply supported beams. Your role in a building and construction company is to analyse and design the bridge based on simply supported beam theory. Your manager asked you to perform a stress analysis for bridge element modelled as simply supported beam shown in the Figure.1(a), this task is best achieved by performing the following required steps: 2 kN 3 kN/m 3 kN/m 3kN.m A 0.5 kN 4.5 kN kN 2 m 1 т+1m- 2 m R| -2 m (а) (b) Figure.1: (a) Bridge element modelled as simply supported beam (b) Beam section
1. By hand, construct diagrams for the shear force and bending moment distributions. (P1)
2. Construct the equations for shear force and bending moment and deflection in the beam using
singularity functions. (M1, D3)
3. For the beam section in Figure.1(b), determine the equations (in terms of the variable x, after
evaluating the internal shear force R) for the slope and deflection using the analytical solution. (P4)
4. For the beam section in Figure.1(b), use the method of superposition to evaluate the deflection
equation. (P5)
5. For section A - A, calculate the maximum shear stress if the beam's cross section is shown in
Figure.2(a). (D1)
6. If the stress element in Figure.2(b) has the following normal stress values: (ox, 0y, Oz)=(-2, 1, 1.5)
kN, and the following shear stress values: (txy, Txz, Tyz)= (0.5, 0, 0) kN.m. Find the principal
stresses for all 3 dimensions and draw the Mohr's circle for this 3D element. (P1)
5 cm
15 cm
5 cm
15 cm
Figure.2(a): The beam's cross-section.
zx
Figure.2(b): 3D stress element from the simply supported beam.
Transcribed Image Text:1. By hand, construct diagrams for the shear force and bending moment distributions. (P1) 2. Construct the equations for shear force and bending moment and deflection in the beam using singularity functions. (M1, D3) 3. For the beam section in Figure.1(b), determine the equations (in terms of the variable x, after evaluating the internal shear force R) for the slope and deflection using the analytical solution. (P4) 4. For the beam section in Figure.1(b), use the method of superposition to evaluate the deflection equation. (P5) 5. For section A - A, calculate the maximum shear stress if the beam's cross section is shown in Figure.2(a). (D1) 6. If the stress element in Figure.2(b) has the following normal stress values: (ox, 0y, Oz)=(-2, 1, 1.5) kN, and the following shear stress values: (txy, Txz, Tyz)= (0.5, 0, 0) kN.m. Find the principal stresses for all 3 dimensions and draw the Mohr's circle for this 3D element. (P1) 5 cm 15 cm 5 cm 15 cm Figure.2(a): The beam's cross-section. zx Figure.2(b): 3D stress element from the simply supported beam.
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