D 2 ft -2 ft

. A composite beam, made of aluminum (Al) and magnesium (Mg), has the cross section shown below. The moduli of elasticity for aluminum and magnesium are EAI = 70 GPa and EMg = 45 GPa, respectively. If the allowable flexural stresses (in tension and com- pression) are All 135 MPa for the aluminum and Mg 120 MPa for the magnesium, determine the maximum allowable bending moment for the beam. all - 0.2 m 0.2 m Al 0.2 m Mg C

A solid rod has a diameter of e = 55 mm and is subjected to the loading shown. Let a = 200 mm , b = 210 mm , c = 310 mm , d = 250 mm , and P = 3.0 kN. Take point A to be at the top of the circular cross-section. (Figure 1) a. As shown (Figure 2), a cut was made at A to determine the resultant internal loadings. Determine the moment about the x-axis, Mx. b. To find the state of stress at A, the principle of superposition must be used. If the rod has a diameter of 55 mm, find the stress σA due to the normal force. c. To find the state of stress at A, the principle of superposition must be used. If the rod has a diameter of 55 mm,  find the stress σA due to the bending moment about the x-axis. d. To find the state of stress at A, the principle of superposition must be used. Find the stress σA due to all of the loadings on the rod.

Determine the reactions at the supports of the built-in beam shown below. Note: Express your answers following the standard sign convention for the coordinate system shown. Report counterclockwise moments as positive (+) and clockwise moments as negative (-). y Given: A • L₁ • F Ay= By = MRA MRB 18 = = L2 = 9 ft F = 22 kip = L₂ = 15 ft L₁ F number (rtol=0.01, a number (rtol=0.01, a number (rtol= number (rtol= B kip ? kip kip. ft kip. ft ? ? ?