A steel beam, of lengths a=5 m and b=2 m and a hollow box cross section, is supported by a hinge support A and roller support B, see Figure Q.1. The width and height of the cross section are 200 mm and 300 mm, respectively, and the wall thi of the cross section is 5 mm. The beam is under a distributed load of the intensity that linearly varies from q = 0 kN/m to q= kN/m for AB span; and is constant with q=3.2 kN/m for BC span. The Young's modulus of steel is 200 GPa. YA q X 78

A steel beam, of lengths a=5 m and b=2 m and a hollow box cross section, is supported by a hinge support A and roller support B, see Figure Q.1. The width and height of the cross section are 200 mm and 300 mm, respectively, and the wall thi of the cross section is 5 mm. The beam is under a distributed load of the intensity that linearly varies from q = 0 kN/m to q= kN/m for AB span; and is constant with q=3.2 kN/m for BC span. The Young's modulus of steel is 200 GPa. YA q X 78

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

Calculate the value of integration constant C₂

Calculate the value of integration constant C₄

the value of the deflection at point C

Perform double integration of the bending moment equations. You will obtain deflections in this form:
VEI= F(x) + C₁x + C3
for 0 ≤ x ≤ a
VEI = G(x) + C₂x + C4
for a ≤ x ≤a+b

A steel beam, of lengths a=5 m and b=2 m and a hollow box cross section, is supported by a hinge support A and roller
support B, see Figure Q.1. The width and height of the cross section are 200 mm and 300 mm, respectively, and the wall thickness
of the cross section is 5 mm. The beam is under a distributed load of the intensity that linearly varies from q=0 kN/m to q= 3.2
kN/m for AB span; and is constant with q=3.2 kN/m for BC span. The Young's modulus of steel is 200 GPa.
YA
q
Part A
A
a
5 mm
200 mm
Figure Q.1
Дв
300 mm
b
C
X

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