For a square cross-section bar affected by torsional moment at both ends, the streps components are shown as follows (opposite the figure): a) Find the principal directions for the zero principal stress? b) For the following special case, show that the stress vector on the lateral surface of the rod is zero: 4 = (xỉ - a?xx - a²) %3D c) Also the torsional moment at each of the two ends of the rod is equal to: M = 32 4 = f(x1, X2) %3D 013 ax2 %3D %3D 011 = 022 = 033 = 012 =0 X2

For a square cross-section bar affected by torsional moment at both ends, the streps components are shown as follows (opposite the figure): a) Find the principal directions for the zero principal stress? b) For the following special case, show that the stress vector on the lateral surface of the rod is zero: 4 = (xỉ - a?xx - a²) %3D c) Also the torsional moment at each of the two ends of the rod is equal to: M = 32 4 = f(x1, X2) %3D 013 ax2 %3D %3D 011 = 022 = 033 = 012 =0 X2

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Bars

In civil engineering, bars refer to steel reinforcement bars or rebars. These are structural members primarily used for reinforcement purposes in masonry works. A bar is characterized by its cross-sectional area, which is negligible compared to its length. Bars are usually manufactured by steel which is uniform throughout the length, or by meshing multiple steel wires. Other materials of the bar include carbon steel, glass fiber, carbon fiber, and basalt fiber. The reinforcing bars are coated with epoxy resins and other materials to enhance some of their properties including corrosion resistance.

Question

For a square cross-section bar affected by torsional moment at both ends, the stress components are
shown as follows (opposite the figure):
a) Find the principal directions for the zero principal stress?
b) For the following special case, show that the stress vector on the lateral surface of
the rod is zero:
4 = (xỉ – a?xx? - a²)
%3D
c) Also the torsional moment at each of the two ends of the rod is equal to:
M =
32
4 = f(x1, X2)
ax2
011 = 022= 033 = 012 = 0
X2
221 PM
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1/16/2022

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