Q.No# An aluminum bar having a cross-sectional area of 0.5 in2 carries the axial loads applied at the positions shown in Fig. Compute the total change in length of the bar if E = 10 × 106 psi. Assume the bar is suitably braced to prevent lateral buckling.

1. Ghulam Mehdi 1 CMSID@23101
Faculty of Engineering
Departmentof MiningEngineering
MechanicsofMaterials
Instructor: Engr.NaseerKakar Date:21-04-2014
Submitted By:Ghulam Mehdi CMS ID# 23101
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Assignment No# 03
Q.No# An aluminum bar having a cross-sectional area of 0.5 in2 carries the axial
loads applied at the positions shown in Fig. Compute the total change in length of the
bar if E = 10 × 106 psi. Assume the bar is suitably braced to prevent lateral buckling.
Ans:
Given Data:
Area (A) =0.5 in2
Elasticity (E) = 10 × 106 psi.
Applied Force (P1) =4000 Ib Compression
Applied Force (P2) =11000 Ib Compression
Applied Force (P3) =6000 Ib Compression
Length (L1) =3 ft, 3*12=36 in
Length (L2) =5 ft, 5*12=60 in
Length (L3) =4 ft, 4*12=48 in
Sol:
As we know that:
δ =PL/AE
δT =-δ1 -δ2 -δ3
δT =-P1L1/AE- P2L2/AE- P3L3/AE
δT=- 4000(36)/AE- 11000(60)/AE- 6000(48)/AE
δT= (-144000-660000-288000)/AE
δT=-1092000/0.5(10 × 106)
δT=-0.2184 in
δT=-0.2184 in shortening……………….Ans.

2. Ghulam Mehdi 2 CMSID@23101