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 0.5 kN 4.5 kN 4.5 kN Im+1m -2 m- (a) (b) Figure.1: (a) Bridge element modelled as simply supported beam (b) Beam section For the beam section in Figure.1(b), use the method of superposition to evaluate the deflection equation. (P5) For section A – A, calculate the maximum shear stress if the beam's cross section is shown in Figure.2(a). (D1) If the stress element in Figure.2(b) has the following normal stress values: (0x, Gy, 2) = (-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 сm 15 cm 5 cm 15 cm Figure.2(a): The beam’s cross-section. Figure.2(b): 3D stress element from the simply supported beam.

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 0.5 kN 4.5 kN 4.5 kN Im+1m -2 m- (a) (b) Figure.1: (a) Bridge element modelled as simply supported beam (b) Beam section For the beam section in Figure.1(b), use the method of superposition to evaluate the deflection equation. (P5) For section A – A, calculate the maximum shear stress if the beam's cross section is shown in Figure.2(a). (D1) If the stress element in Figure.2(b) has the following normal stress values: (0x, Gy, 2) = (-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 сm 15 cm 5 cm 15 cm Figure.2(a): The beam’s cross-section. Figure.2(b): 3D stress element from the simply supported beam.

Materials Science And Engineering Properties

1st Edition

ISBN:9781111988609

Author:Charles Gilmore

Publisher:Charles Gilmore

Chapter9: Time, Temperature, And Mechanical Properties

Section: Chapter Questions

Problem 9.3P

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Solid Mechanics

Engineering mechanics is a branch of science that deals with forces causing bulk motion in bodies and the effect that these forces cause on the bodies. Engineering mechanics does not deal with the internal changes that occur on account of these external forces. The internal effects in a body or a material under the action of external forces are studied in a new branch of science called solid mechanics, the strength of materials, or the mechanical behavior of engineering materials.

Question

Problem 1: (P1, P4, P5, M1, D1, D3)
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
0.5 kN
2 m-
4.5 kN
4.5 kN
Im+1m
2 m
(a)
(b)
Figure.1: (a) Bridge element modelled as simply supported beam (b) Beam section
For the beam section in Figure.1(b), use the method of superposition to evaluate the deflection
equation. (P5)
For section A – A, calculate the maximum shear stress if the beam's cross section is shown in
Figure.2(a). (D1)
If the stress element in Figure.2(b) has the following normal stress values: (0,, 0y, 02) = (-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 ст
15 cm
5 cm
15 cm
Figure.2(a): The beam's cross-section. Figure.2(b): 3D stress element from the simply supported beam.

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