Question 1:

For a uniformly loaded beam as shown in Figure, the strength of materials theory gives the maximum deflection as

V_max = - 5qL⁴/384El_z

at x = 1./2. Treat this beam as a single finite element and compute the maximum deflection. How do the values compare?

Question 2:

Consider the beam shown in Figure P4.8. What is the minimum number of elements that can be used to model this problem? Construct the global nodal load vector corresponding to your answer.

Question 3:

compute the deflection at the element nodes. The modulus of elasticity is E = 10 x 10⁶ psi and the cross section is as shown in each figure. Also compute the maximum bending stress. Use the finite element method with the minimum number of elements for each case.

Question 4:

compute the deflection at the element nodes. The modulus of elasticity is E = 10 x 10⁶ psi and the cross section is as shown in each figure. Also compute the maximum bending stress. Use the finite element method with the minimum number of elements for each case.