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 = 5 kN/m for AB span; and is constant with q = 5 kN/m for BC span. The Young’s modulus of steel is 200 GPa. Questions: 1. Calculate the vertical support reaction in support A. When sketching FBD, set the positive directions of both reactions in the positive direction of y axis. Enter your answer in kN to three decimal places. 2. Calculate the vertical support reaction in support B. Enter your answer in kN to two decimal places. 3. Calculate the value of the maximum bending moment in the beam. Enter your answer in kNm to three decimal places. Note: when deriving internal moment equations, use the following orientation of x coordinate: Segment AB: x changes from 0 at support A to a at support B. After making the cut, keep the part of the beam left from the cut. Segment BC: x changes from a at support B to L at point C, where L = a + b. After making the cut, keep the part of the beam right from the cut, i.e. distance from point C to the cut is equal L-x. 4. Calculate the maximum normal stress in the cross-section of the beam. Enter the positive value of the stress. Enter your answer in MPa to two decimal places. 5. Perform double integration of the bending moment equations. You will obtain deflections in this form: For 0≤x≤a0≤x≤a: vEI=F(x)+C₁x+C₃ For a≤x≤a+ba≤x≤a+b: vEI=G(x)+C2x+C₄ a. Calculate the value of the integration constant C2. Enter your answer in kNm2 to three decimal places. b. the value of the integration constant C4. Enter your answer in kNm2 to three decimal places. c. 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 of v axis.
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 = 5 kN/m for AB span; and is constant with q = 5 kN/m for BC span. The Young’s modulus of steel is 200 GPa.
Questions:
1. Calculate the vertical support reaction in support A. When sketching FBD, set the positive directions of both reactions in the positive direction of y axis. Enter your answer in kN to three decimal places.
2. Calculate the vertical support reaction in support B. Enter your answer in kN to two decimal places.
3. Calculate the value of the maximum bending moment in the beam. Enter your answer in kNm to three decimal places.
Note: when deriving internal moment equations, use the following orientation of x coordinate:
- Segment AB: x changes from 0 at support A to a at support B. After making the cut, keep the part of the beam left from the cut.
- Segment BC: x changes from a at support B to L at point C, where L = a + b. After making the cut, keep the part of the beam right from the cut, i.e. distance from point C to the cut is equal L-x.
4. Calculate the maximum normal stress in the cross-section of the beam. Enter the positive value of the stress. Enter your answer in MPa to two decimal places.
5. Perform double integration of the bending moment equations. You will obtain deflections in this form:
For 0≤x≤a0≤x≤a: vEI=F(x)+C₁x+C₃
For a≤x≤a+ba≤x≤a+b: vEI=G(x)+C2x+C₄
a. Calculate the value of the integration constant C2. Enter your answer in kNm2 to three decimal places.
b. the value of the integration constant C4. Enter your answer in kNm2 to three decimal places.
c. 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 of v axis.
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