Josephood7

A cantilever beam AB is loaded by a couple M₀ at its free end (see figure). The length of the beam is L = 2.0 m, and the longitudinal normal strain at the top surface is . The distance from the top surface of the beam to the neutral surface is c = 85 mm.

(a) Calculate the radius of curvature ρ, the curvature κ, and the vertical deflection δ at the end of the beam.

(b) If allowable strain what is the maximum acceptable depth of the beam? (Assume that the curvature is unchanged from Part(a)).

(c) If allowable strain and L = 4 m, what is deflection δ ?

A simply supported beam is subjected to a linearly varying distributed load q(x) = x/L q_0 with maximum intensity q_0 at B. The beam has a length L = 4 m and rectangular cross section with a width of 200 mm and height of 300 mm. Determine the maximum permissible value for the maximum intensity, q_0, if the allowable normal stresses in tension and compression are 120 MPa.

A freight-car axle AB is loaded approximately as shown in the figure, with the forces P representing the car loads (transmitted to the axle through the axle boxes) and the forces R representing the rail loads (transmitted to the axle through the wheels). The diameter of the axle is d = 82, the distance between centers of the rails is L, mm and the distance between the forces P and R is d = 220 mm.

A laminated wood beam on simple supports (figure part a) is built up by gluing together four 2 in. × 4 in. boards (actual dimensions) to form a solid beam 4 in. × 8 in. in cross section, as shown in the figure part b. The allowable shear stress in the glued joints is 62 psi, the allowable shear stress in the wood is 175 psi, and the allowable bending stress in the wood is 1650 psi.

(a) If the beam is 12 ft long, what is the allowable load P acting at the one-third point along the beam, as shown? (Include the effects of the beam’s own weight, assuming that the wood weighs 35 lb/ft³.)

(b) Repeat part (a) if the beam is assembled by gluing together two 3 in. × 4 in. boards and a 2 in. × 4 in. board (see figure part c).

A bridge girder AB on a simple span of length L = 14 m supports a distributed load of maximum intensity q at mid-span and minimum intensity q/2 at supports A and B that includes the weight of the girder (see figure). The girder is constructed of three plates welded to form the cross section shown.

Determine the maximum permissible load q based upon (a) an allowable bending stress

and (b) an allowable shear stress