A steel beam, of lengths a=4 m and b=4 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=4.4 kN/m for AB span; and is constant with q= 4.4 kN/m for BC span. The Young's modulus of steel is 200 GPa. y, v A a 9 mium ÅB C b 5 mm 200 mm Figure Q.1 300 mm X

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
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A steel beam, of lengths a=4 m and b=4 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=4.4 kN/m for AB span; and is constant with q= 4.4 kN/m for BC span. The Young's modulus of steel is 200 GPa.
y, v
A
a
9
mium
Дв
5 mm
200 mm
Figure Q.1
300 mm
b
C
Transcribed Image Text:A steel beam, of lengths a=4 m and b=4 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=4.4 kN/m for AB span; and is constant with q= 4.4 kN/m for BC span. The Young's modulus of steel is 200 GPa. y, v A a 9 mium Дв 5 mm 200 mm Figure Q.1 300 mm b C
Part B
Perform double integration
VEI = F(x) + C₁x + C3
UEI = G(x) + C₂x + C4
Calculate:
of the bending moment equations. You will obtain deflections in this form:
for 0≤x≤a
for a ≤ x ≤a+b
e) the value of the integration constant C₂. Enter your answer in kNm² to three decimal places.
f) the value of the integration constant C4. Enter your answer in kNm² to three decimal places.
g) the value of the deflection at point C. Enter your answer in mm to three decimal places. Assume the positive direction of deflection in the positive direction
v axis.
Transcribed Image Text:Part B Perform double integration VEI = F(x) + C₁x + C3 UEI = G(x) + C₂x + C4 Calculate: of the bending moment equations. You will obtain deflections in this form: for 0≤x≤a for a ≤ x ≤a+b e) the value of the integration constant C₂. Enter your answer in kNm² to three decimal places. f) the value of the integration constant C4. Enter your answer in kNm² to three decimal places. g) the value of the deflection at point C. Enter your answer in mm to three decimal places. Assume the positive direction of deflection in the positive direction v axis.
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