Chapter 16, Problem 50RP

(a) Considering only buckling in the plane of the structure shown and using Euler’s formula, determine the value of θbetween 0 and 90° for which the allowable magnitude of the load P is maximum. (b) Determine the corresponding maximum value of P knowing that a factor of safety of 3.2 is required. Use E= 29 x 106 psi.

Two bars AD and DG are connected by a pin at D and by a spring AG . Knowing that the spring is 300 mm long when unstretched and that the constant of the spring is 5 kN/m, determine the value of x corresponding to equilibrium when a 900-N load is applied at E as shown.

A load P is supported as shown by a steel pin that has been inserted in a short wooden member hanging from the ceiling. The ultimate strength of the wood used is 60 MPa in tension and 7.5 MPa in shear,while the ultimate strength of the steel is 145 MPa in shear. Knowing that b = 40 mm, c = 55 mm, and d = 12 mm, determine the load P if an overall factor of safety of 3.2 is desired.

In the truss shown, members AC and AD consist of rods made of the same metal alloy. Knowing that AC is of 1-in. diameter and that the ultimate load for that rod is 75 kips, determine (a) the factor of safety for AC, (b) the required diameter of AD if it is desired that both rods have the same factor of safety.

Solve Prob. 4.133, assuming that cable GBH is replaced by a cable GB attached at G and B.(Reference to Problem 4.133):The frame ACD is supported by ball-and-socket joints at A and D and by a cable that passes through a ring at B and is attached to hooks at G and H . Knowing that the frame supports at point C a load of magnitude P = 268 N, determine the tension in the cable.

Knowing that the tension in cable AE of Prob. 2.123 is 75 lb, determine (a) the magnitude of the load P, (b) the tension in cables BAC and AD.(Reference to Problem 2.123):Cable BAC passes through a frictionless ring A and is attached to fixed supports at B and C , while cables AD and AE are both tied to the ring and are attached, respectively, to supports at D and E . Knowing that a 200-lb vertical load P is applied to ring A , determine the tension in each of the three cables.

A metal bar AB of a weight W is suspendedby a system of steel wires arranged as shown in thefigure. The diameter of the wires is 5/64 in., and theyield stress of the steel is 65 ksi.Determine the maximum permissible weightWmax for a factor of safety of 1.9 with respect toyielding.

Column ABC has a uniform rectangular cross section with b=12 mm and d=22 mm. The column is braced in the xz plane at its midpoint C and carries a centric load P of magnitude 3.8 kN. Knowing that a factor of safety of 3.2 is required, determine the largest allowable length L. Use E=200 GPa

The steel frame (E = 200 GPa) shown has a diagonal brace BD with an area of 1920 mm2. Determine the largest allowable load P if the change in length of member BD is not to exceed 1.9 mm.The largest allowable load P is