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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 theassembly is suitably braced to prevent buckling. Use E st = 200 GPa, Eal = 70 GPa, and

Ebr = 83 GPa.

Solution 211 

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Based on allowable stresses: 

Steel:

Bronze:

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Aluminum:

Based on allowable deformation: ( steel and aluminum lengthens, bronze shortens)

Use the smallest value of P, P = 12.8 kN 

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materials/solution-to-problem-211-axial-deformation#sthash.UjzvOyuE.dpuf  

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.

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Solution 41 

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Member AB: 

By ratio and proportion:

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→ movement ofB

Member CD: 

Movement of D:

By ratio and proportion:

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  answer  

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materials/solution-to-problem-214-axial-deformation#sthash.POTaxR89.dpuf  

Problem 224 

For the block loaded triaxially as described in Prob. 223, find the uniformly distributed

load that must be added in the x direction to produce no deformation in the z direction.

Solution 224 

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Where

σx = 6.0 ksi (tension)

σy = 5.0 ksi (compression)

σz = 9.0 ksi (tension)

εz is positive, thus positive stress is needed in the x-direction to eliminate deformation in z-

direction.

The application of loads is still simultaneous:

( No deformation means zero strain)

Where

σy = 5.0 ksi (compression)

σσz = 9.0 ksi (tension)

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answer  

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materials/solution-to-problem-224-triaxial-deformation#sthash.Wo4cUEIK.dpuf