Axial Deformation

Problem 217
Solve Prob. 216 if rod AB is of steel, with E = 29 × 10⁶ psi. Assume α = 45° and θ = 30°; all other data remain unchanged.
 

Problem 216
As shown in Fig. P-216, two aluminum rods AB and BC, hinged to rigid supports, are pinned together at B to carry a vertical load P = 6000 lb. If each rod has a cross-sectional area of 0.60 in.² and E = 10 × 10⁶ psi, compute the elongation of each rod and the horizontal and vertical displacements of point B. Assume α = 30° and θ = 30°.
 

Problem 214
The rigid bars AB and CD shown in Fig. P-214 are supported by pins at A and C and the two rods. Determine the maximum force P that can be applied as shown if its vertical movement is limited to 5 mm. Neglect the weights of all members.
 

Problem 213
The rigid bar AB, attached to two vertical rods as shown in Fig. P-213, is horizontal before the load P is applied. Determine the vertical movement of P if its magnitude is 50 kN.
 

Problem 211
A bronze bar is fastened between a steel bar and an aluminum bar as shown in Fig. p-211. Axial loads are applied at the positions indicated. Find the largest value of P that will not exceed an overall deformation of 3.0 mm, or the following stresses: 140 MPa in the steel, 120 MPa in the bronze, and 80 MPa in the aluminum. Assume that the assembly is suitably braced to prevent buckling. Use E_st = 200 GPa, E_al = 70 GPa, and E_br = 83 GPa.
 

Problem 206
A steel rod having a cross-sectional area of 300 mm² and a length of 150 m is suspended vertically from one end. It supports a tensile load of 20 kN at the lower end. If the unit mass of steel is 7850 kg/m³ and E = 200 × 10³ MN/m², find the total elongation of the rod.
 

Problem 205
A uniform bar of length L, cross-sectional area A, and unit mass ρ is suspended vertically from one end. Show that its total elongation is δ = ρgL²/2E. If the total mass of the bar is M, show also that δ = MgL/2AE.