February 2009

Problem 507
In a laboratory test of a beam loaded by end couples, the fibers at layer AB in Fig. P-507 are found to increase 60 × 10^-3 mm whereas those at CD decrease 100 × 10^-3 mm in the 200-mm-gage length. Using E = 70 GPa, determine the flexural stress in the top and bottom fibers.
 

Problem 506
A flat steel bar, 1 inch wide by ¼ inch thick and 40 inches long, is bent by couples applied at the ends so that the midpoint deflection is 1.0 inch. Compute the stress in the bar and the magnitude of the couples. Use E = 29 × 10⁶ psi.
 

Problem 503
A cantilever beam, 50 mm wide by 150 mm high and 6 m long, carries a load that varies uniformly from zero at the free end to 1000 N/m at the wall. (a) Compute the magnitude and location of the maximum flexural stress. (b) Determine the type and magnitude of the stress in a fiber 20 mm from the top of the beam at a section 2 m from the free end.
 

Problem 457
A truck and trailer combination crossing a 12-m span has axle loads of 10, 20, and 30 kN separated respectively by distances of 3 and 5 m. Compute the maximum moment and maximum shear developed in the span.
 

Problem 456
Three wheel loads roll as a unit across a 44-ft span. The loads are P₁ = 4000 lb and P₂ = 8000 lb separated by 9 ft, and P₃ = 6000 lb at 18 ft from P₂. Determine the maximum moment and maximum shear in the simply supported span.
 

Problem 455
A tractor weighing 3000 lb, with a wheel base of 9 ft, carries 1800 lb of its load on the rear wheels. Compute the maximum moment and maximum shear when crossing a 14 ft-span.
 

Problem 454
Repeat Prob. 453 using axle loads of 30 kN and 50 kN on a wheel base of 4 m crossing an 8-m span.
 

Problem 453
A truck with axle loads of 40 kN and 60 kN on a wheel base of 5 m rolls across a 10-m span. Compute the maximum bending moment and the maximum shearing force.