# Axial Deformation

## Solution to Problem 217 Axial Deformation

## 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 × 10^{6} psi, compute the elongation of each rod and the horizontal and vertical displacements of point B. Assume α = 30° and θ = 30°.

## 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.

**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.

## 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.

## 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.

## 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 E_{st} = 200 GPa, E_{al} = 70 GPa, and E_{br} = 83 GPa.

## Solution to Problem 209 Axial Deformation

**Problem 209**

An aluminum bar having a cross-sectional area of 0.5 in^{2} 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 × 10^{6} psi. Assume the bar is suitably braced to prevent lateral buckling.

## Solution to Problem 206 Axial Deformation

**Problem 206**

A steel rod having a cross-sectional area of 300 mm^{2} 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/m^{3} and E = 200 × 10^{3} MN/m^{2}, 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 = ρgL^{2}/2E. If the total mass of the bar is M, show also that δ = MgL/2AE.

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