Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal andvertical planes at the point are S-12 ksi, Sy-37 ksi, and Sy-23 ksi.(a) Determine the principal stresses (op) > o2) and the maximum in-plane shear stress max acting at the point.(b) Find the smallest rotation angle 6, (counterclockwise is positive, clockwise is negative) that will rotate to principal directions. Thenshow these stresses in an appropriate sketch (eg, see Figure 12.15 or Figure 12.16)Answers:ksi.Opl =ksi.Op2 =ksi.Tmax =0, =

Answered: Image /qna-images/answer/085f37c2-3502-4754-8e01-6b4a9e1cce49.jpg

Answered: vertical planes at the point are S-12…

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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Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 6 ksi, Sy = 17 ksi, and Sxy = 13 ksi. (a) Determine the principal stresses (σp1>σp2σp1>σp2) and the maximum in-plane shear stress τmaxτmax acting at the point. (b) Find the smallest rotation angle θpθp (counterclockwise is positive, clockwise is negative) that will rotate to principal directions. Then show these stresses in an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16)
Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 17 ksi, Sy = 11 ksi, and Sxy = 17 ksi. (a) Draw Mohr’s circle for this state of stress. (b) Determine the principal stresses (σp1>σp2) and the maximum in-plane shear stress τmax acting at the point. (c) Find the smallest rotation angle θp (counterclockwise is positive, clockwise is negative) that will rotate to principal directions. Then show these stresses in an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16)
Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 19 ksi, Sy = 25 ksi, and Sxy = 19 ksi. (a) Determine the principal stresses (σp1>σp2) and the maximum in-plane shear stress τmax acting at the point. (b) Find the smallest rotation angle θp (counterclockwise is positive, clockwise is negative) that will rotate to principal directions. Then show these stresses in an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16)
The solid shaft is fixed to the support at C and subjected to the torsional loadings and axial load P as shown. a. Determine the torsional shear stress at Point A (50mm from the center) and Point B (on the Surface) b. Determine the absolute maximum torsional shear stress in the shaft. c. sketch the state of stress at point A and draw its corresponding Mohr’s Circle of stress. compute the principal stresses and maximum in-plane stress. T=10.38kN-m
Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 12 ksi, Sy = 35 ksi, and Sxy = 12 ksi. (a) Determine the principal stresses (σp1>σp2) and the maximum in-plane shear stress τmax acting at the point. (b) Find the smallest rotation angle θp (counterclockwise is positive, clockwise is negative) that will rotate to principal directions. Then show these stresses in an appropriate sketch
Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 17 ksi, Sy = 24 ksi, and Sxy = 16 ksi. (a) Determine the principal stresses (0p1 > 0p2) and the maximum in-plane shear stress max acting at the point. (b) Find the smallest rotation angle Op (counterclockwise is positive, clockwise is negative) that will rotate to principal directions. Then show these stresses in an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16)
For the state of stress shown in the figure. a. Determine the maximum and minimum principal stresses.b. Describe the location of the maximum principal stress from side BC.c. Describe the location of the maximum principal stress from side BD.d. Determine the maximum shear stress.e. Determine the normal and shear stresses at plane AB. A = 30 ,B = 50 , C = 10 ,D = 37
Determine the magnitude of the maximum in-plane shear stress at point A (in MPa).
The 60-mm-diameter solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the absolute maximum and minimum shear stresses on the shaft’s surface and specifies their locations, measured from the free end.
The column is subjected to an axial force of 8 kN, which is applied through the centroid of the cross-sectional area. Determine the average normal stress acting at section a-a. Show this distribution of stress acting over the area’s cross section.
5.2.2 The thin-walled tube is used as a beam to support the uniformly distributed load of intensity w0. (a) Find the largest allowable value of w0 based on the allowable stress in bending of 100 MPa. (b) Compute the corresponding maximum shear stress in the beam.
A thin walled tube of thickness (t) 5mm and diameter (d) 200mm with closed ends is subjected to an internal pressure (p) 7.0 MN/m2, producing an axial and circumferential direct stresses given by pd/4t and pd/2t respectively. A torque T = 15.0 kNm is also applied which sets up a shear stress ? = ?/2??2? where r is the radius. (a) Determine the magnitude and direction of the principal stresses. (b) Calculate the overall maximum shear stress.

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