A steel beam, of lengths a= 6 m and b = 3 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 = 3.1 kN/m for AB span; and is constant with q=3.1 kN/m for BC span. The Young's modulus of steel is 200 GPa. y, v 9
A steel beam, of lengths a= 6 m and b = 3 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 = 3.1 kN/m for AB span; and is constant with q=3.1 kN/m for BC span. The Young's modulus of steel is 200 GPa. y, v 9
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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The two sub questions and question g as well :
Transcribed Image Text:Part
Perform double integration of the bending moment equations. You will obtain deflections in this form:
for 0 ≤ x ≤ a
vEI = F(x) + С₁x + С3
vEI = G(x) + C₂x + C4
for a ≤ x ≤a+b
Calculate:
e) the value of the integration constant C₂. Enter your answer in kNm² to three decimal places.
Answer:
Check
f) the value of the integration constant C4. Enter your answer in kNm² to three decimal places.
Transcribed Image Text:A steel beam, of lengths a= 6 m and b= 3 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 = 3.1
kN/m for AB span; and is constant with q= 3.1 kN/m for BC span. The Young's modulus of steel
is 200 GPa.
Part A
Calculate:
A
y, v
a
5 mm
200 mm
Figure Q.1
9
S B
300 mm
b
с
X
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Step 1: Introducing given data
VIEWStep 2: Calculate reactions
VIEWStep 3: Calculate moment for section in AB (0 < x< a)
VIEWStep 4: Calculate constants C1 & C3 for section in AB (0 < x< a)
VIEWStep 5: Calculate moment for section in BC (a < x < L)
VIEWStep 6: Calculate constants C2 & C4 for section in BC (a < x < L)
VIEWStep 7: Calculate deflection at C
VIEWStep 8: Calculate max deflection in span AB
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