1. A rod of length 1.50 m and diameter 0.12 m is mounted in a rigid wall A vertical bar of length 0.5 m is attached to the free end from the centroid of the rod. The rigid bar is loaded with a horizontal force of P= 50 kN at its free end. A torque T = -8 kN.m is also applied to the free end, as shown in Fig. 1. An axial test of the material of the rod shows that it has the following mechanical properties: E-210 GPa, o, - 280 MPa, and v=- (The origin of the coordinate system is at the wall). (a) Draw a free-body diagram of the structure in Fig. 1. (b) Use strength of materials to compute the stress components, and then (c) Write the stress tensor, as a matrix at a point on the bottom of the rod. (d) Determine the principal stresses at the same point as in (c). (e) Determine () the strain energy density (U.) of the rod; and () the total strain energy U stored in the rod requires vohume of the rod). (f) Determine the factor of safety if the rod is not to fail according to the maximum distortion energy criterion (von
1. A rod of length 1.50 m and diameter 0.12 m is mounted in a rigid wall A vertical bar of length 0.5 m is attached to the free end from the centroid of the rod. The rigid bar is loaded with a horizontal force of P= 50 kN at its free end. A torque T = -8 kN.m is also applied to the free end, as shown in Fig. 1. An axial test of the material of the rod shows that it has the following mechanical properties: E-210 GPa, o, - 280 MPa, and v=- (The origin of the coordinate system is at the wall). (a) Draw a free-body diagram of the structure in Fig. 1. (b) Use strength of materials to compute the stress components, and then (c) Write the stress tensor, as a matrix at a point on the bottom of the rod. (d) Determine the principal stresses at the same point as in (c). (e) Determine () the strain energy density (U.) of the rod; and () the total strain energy U stored in the rod requires vohume of the rod). (f) Determine the factor of safety if the rod is not to fail according to the maximum distortion energy criterion (von
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Parts d, e and f
Transcribed Image Text:1. A rod of length 1.50 m and diameter 0.12 m is mounted in a rigid wall A vertical bar of length 0.5 m is
attached to the free end from the centroid of the rod. The rigid bar is loaded with a horizontal force of P= 50 kN
at its free end. A torque T =-8 kN.m is also applied to the free end, as shown in Fig. 1. An axial test of the
material of the rod shows that it has the following mechanical properties: E=210 GPa, a, = 280 MPa, and v =:
(The origin of the coordinate system is at the wall).
(a) Draw a free-body diagram of the structure in Fig. 1.
(b) Use strength of materials to compute the stress components, and then
(c) Write the stress tensor, as a matrix at a point on the bottom of the rod.
(d) Determine the principal stresses at the same point as in (c).
(e) Determine () the strain energy density (U.) of the rod; and (î) the total strain energy U stored in the rod
(requires vohme of the rod).
(f) Determine the factor of safety if the rod is not to fail according to the maximum distortion energy criterion (von
Mises).
(Hints: 1. The axial load P will also give rise to a bending moment in the rod. 2. The bottom surface is in tension
while the top surface is in compression. 3. The given coordinate system, x. y. z implies 3D stress tensor).
y
1.5 m
0.12 m
0.5 m
Fig. 1
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