HW (7,9)

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In the name of GOD 
Homework #4 
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1. The gas storage tank is fabricated by bolting together two half cylindrical thin shells and two 
hemispherical shells as shown. If the tank is designed to withstand a pressure of 3 MPa, determine the 
required minimum thickness of the cylindrical and hemispherical shells and the minimum required number 
of longitudinal bolts per meter length at each side of the cylindrical shell. The tank and the 25 mm diameter 
bolts are made from material having an allowable normal stress of 150 MPa and 250 MPa, respectively. The 
tank has an inner diameter of 4 m. 
 
 
2. The state of stress at a point is shown on the element. Determine (a) the principal stress and (b) the 
maximum in-plane shear stress and average normal stress at the point. Specify the orientation of the element 
in each case. Show the results on each element. 
 
 
 
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3. For the cantilever beam and loading shown, determine (a) the equation of the elastic curve for portion AB 
of the beam, (b) the deflection at B, (c) the slope at B. 
 
4. For the beam and loading shown, determine (a) the equation of the elastic curve for portion AB of the 
beam, (b) the slope at A, (c) the slope at B. 
 
5. Knowing that beam AE is a W360 × 101 rolled shape and that MO=310 kN.m, L = 2.4 m, a = 0.5 m, and 
E = 200 GPa, determine (a) the equation of the elastic curve for portion BD, (b) the deflection at point C. 
 
6. Determine the equations of the elastic curve using the x1 and x2 coordinates. EI is constant. 
 
 
7. Determine the equations of the elastic curve for the beam using the x1 and x3 coordinates. Specify the 
beam’s maximum deflection. EI is constant.