Question 1
A simply supported beam of span L = 4m is used to support an elevated stage at the local theatre. The expected loading on the beam is 4.8 kN/m. The stage manager thinks a simple wood beam, 60 mm by 120 mm, will do just fine. The consulting engineer however thinks it needs more support and recommends rigidly attaching a 4mm and 8mm thick steel plate on the top and bottom, respectively, as shown in Figure Q9.
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The Young’s modulus of the wood and steel are 10 GPa and 200 GPa, respectively. The allowable stress for the wood and steel are 50 MPa and 250 MPa, respectively. If the beam is only the wood, is the stage manager correct to think this is safe? Compute the maximum bending stress in the steel and wood for the two-material beam and check whether the consulting engineer’s recommendation to reinforce the beam with steel plates is correct.
Find the maximum vertical deflection of the composite beam assuming full composite action and check whether it exceeds L/360, the desired allowable deflection?
Hint: To calculate the deflection of a composite beam designed for full composite action, a transformed moment of inertia is calculated for the wood beam and steel plates. This moment of inertia is found by transforming the wood section into an equivalent steel section or vice versa. The transformed moment of inertia is used because it is assumed that the wood and steel will behave as a single unit, or plane sections remain plane, and there will not be any slip between the wood and steel.
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Question 2
(a) Determine the shear force and bending moment distributions in the beam shown in Figure Q10(a) and sketch them out. What are the maximum shear force and bending moment and where do they occur? Sketch approximately, the deflected shape of the beam.
(b) The dead-weight loading along the centerline of the airplane wing is shown Figure Q10(b). If the wing is fixed to the fuselage at A, determine the reactions at A, and then draw the shear force and bending moment diagram for the wing. What are the maximum shear force and bending moment and where do they occur? Assumptions: (1) The wing is modeled as a tapered cantilever beam. (2) The inertia loads acting on the wing are neglected.
Question 3
(a) The 1.8m long beam AB shown in Figure Q11(a) is supported by a pin at A and a cable BC. The beam carries a 45 kN load 0.45 m from end B. Determine the absolute value of the maximum normal stress at section D of the beam.
(b) A simply supported beam (see Figure Q11(b)) of length 3L carries a uniform load of intensity o q acting over one-third span of the beam near the right support and a concentrated load 2 o q L P = at a point distance L from support A. Determine the maximum deflection and the location where it occurs. The flexural rigidity of the beam is EI.
