A simply supported wood beam AB with span length L= 3.5 m carries a uniform load of intensity q = 6.4 kN/m as shown in the figure. Calculate the maximum bending stress due to the load q if the beam has a rectangular cross section with width b =140 mm and height h = 240 mm.

 

A simple beam of span length carries a uniform load of intensity , The cross section of the beam is a hollow box with wood flanges and steel side plates, as shown in the figure. The wood flanges are  in cross-section, and the steel plates are  deep.

What is the required thickness t of the steel plates if the allowable stresses are  for the steel and  for the wood? (Assume that the modull of elasticity for the stell and wood are  and , respectively, and disregard the weight of the beam.)

A timber beam AB of length L and rectangular cross-section carries a single concentrated load P at its midpoint C. (a) Show that the ratio τ m / σ m of the maximum values of the shearing and normal stresses in the beam is equal to 2h/L, where h and L are, respectively, the depth and the length of the beam, (b) Determine the depth h and the width b of the beam, knowing that L = 2 m, P = 40 kN, τm = 960 kPa, and σm = 12 MPa.

A machine of mass m= 500 kg is mounted on a simply supported steel beam of length l=2 m having a rectangular cross-section (depth = 0.1 m, width = 1.2m) and young's modulus E = 2.06 * 10^11 N/m^2. To reduce the vertical deflection of the beam, a spring of stiffness k is attached at mid-spam, as shown in fig. Determine the value of k needed to reduce the deflection of the beam by A) 25% of its original value. B) 50% of its original value. C) 75% of its original value.
Assume that the mass of the beam is negligible.