Axial Deformation

Solution to Problem 217 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.

Solution to Problem 216 Axial Deformation

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°.

Figure P-216 and P-217


Solution to Problem 215 Axial Deformation

Problem 215
A uniform concrete slab of total weight W is to be attached, as shown in Fig. P-215, to two rods whose lower ends are on the same level. Determine the ratio of the areas of the rods so that the slab will remain level.

Figure P-215


Solution 215

Solution to Problem 214 Axial Deformation

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.

Figure P-214


Solution to Problem 213 Axial Deformation

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.

Figure P-213


Solution to Problem 212 Axial Deformation

Problem 212
The rigid bar ABC shown in Fig. P-212 is hinged at A and supported by a steel rod at B. Determine the largest load P that can be applied at C if the stress in the steel rod is limited to 30 ksi and the vertical movement of end C must not exceed 0.10 in.

Figure P-212


Solution to Problem 211 Axial Deformation

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 Est = 200 GPa, Eal = 70 GPa, and Ebr = 83 GPa.

Figure P-211


Solution to Problem 209 Axial Deformation

Problem 209
An aluminum bar having a cross-sectional area of 0.5 in2 carries the axial loads applied at the positions shown in Fig. P-209. Compute the total change in length of the bar if E = 10 × 106 psi. Assume the bar is suitably braced to prevent lateral buckling.

Aluminum bar loaded as indicated


Solution to Problem 206 Axial Deformation

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.

Solution to Problem 205 Axial Deformation

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.


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