Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Textbook Question
Chapter 8.2, Problem 8.73P
Determine the state of stress at point B at section a–a. The cross section has a diameter of 0.5 in. Use the curved-beam formula to calculate the bending stress.
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Find the second moment of area, the location of the neutral axis, and the distances from the neutral axis to the top and
bottom surfaces. Consider that the section is transmitting a positive bending moment about the z axis, Mz, where M₂ = 10
kip-in if the dimensions of the section are given in ips units, or M₂ = 1.13 kN·m if the dimensions are in Sl units. Determine
the resulting stresses at the top and bottom surfaces and at every abrupt change in the cross section.
From the figure
Z
1 in
112
in
y
in → ← ¹ in
12
in
D
C
B
A
++
in
The area is determined to be 2.0625 in².
The distances from the neutral axis to the top and bottom surfaces are determined to be 0.858 x in and
The second moment of area is determined to be 0.447 in 4.
1.017
xin.
Find the second moment of area, the location of the neutral axis, and the distances from the neutral axis to the top and
bottom surfaces. Consider that the section is transmitting a positive bending moment about the z axis, Mz, where M₂ = 10
kip-in if the dimensions of the section are given in ips units, or M₂ = 1.13 kN·m if the dimensions are in Sl units. Determine
the resulting stresses at the top and bottom surfaces and at every abrupt change in the cross section.
From the figure,
с
- 12.5
B
A
y
I
50
100
75
12.5-
12.5
25
D
100
The area is determined to be 3750 mm²
The distances from the neutral axis to the top and bottom surfaces are determined to be 57.292
The second moment of area is determined to be 4.293
x 106 mm4.
mm and 42.708 ✪ mm.
Determine the moment M that must be applied to the beam in order to create amaximum stress of 90 MPa. Also sketch the stress distribution acting over the cross section.
Chapter 8 Solutions
Mechanics of Materials (10th Edition)
Ch. 8.1 - If it is subjected to an internal pressure of p =...Ch. 8.1 - If it is subjected to an internal pressure of p =...Ch. 8.1 - The thin-walled cylinder can be supported in one...Ch. 8.1 - If the inner diameter of the tank is 22 in., and...Ch. 8.1 - Air pressure in the cylinder is increased by...Ch. 8.1 - Determine the maximum force P that can be exerted...Ch. 8.1 - A boiler is constructed of 8-mm-thick steel plates...Ch. 8.1 - 88. The steel water pipe has an inner diameter of...Ch. 8.1 - The steel water pipe has an inner diameter of 12...Ch. 8.1 - The A-36-steel band is 2 in. wide and is secured...
Ch. 8.1 - The gas pipe line is supported every 20 ft by...Ch. 8.1 - A pressure-vessel head is fabricated by welding...Ch. 8.1 - An A-36-steel hoop has an inner diameter of 23.99...Ch. 8.1 - The ring, having the dimensions shown, is placed...Ch. 8.1 - The inner ring A has an inner radius r1 and outer...Ch. 8.1 - Two hemispheres having an inner radius of 2 ft and...Ch. 8.1 - In order to increase the strength of the pressure...Ch. 8.2 - Show the results on the left segment.Ch. 8.2 - Show the stress that each of these loads produce...Ch. 8.2 - Fundamental Problems F81. Determine the normal...Ch. 8.2 - Show the results in a differential element at the...Ch. 8.2 - Determine the state of stress at point A on the...Ch. 8.2 - Determine the magnitude of the load P that will...Ch. 8.2 - Determine the state of stress at point B. Show the...Ch. 8.2 - Determine the state of stress at point A on the...Ch. 8.2 - Determine the state of stress at point A on the...Ch. 8.2 - Show the results in a differential element at the...Ch. 8.2 - Determine the shortest distance d to the edge of...Ch. 8.2 - The plate has a thickness of 20 mm and P acts...Ch. 8.2 - Plot the distribution of normal stress acting...Ch. 8.2 - Also, plot the normal-stress distribution over the...Ch. 8.2 - If the allowable normal stress for the steel is...Ch. 8.2 - If the applied force P = 1.50 kip, determine the...Ch. 8.2 - Determine the maximum normal stress on the cross...Ch. 8.2 - If the wood has an allowable normal stress of...Ch. 8.2 - Determine the maximum normal stress along section...Ch. 8.2 - Sketch the stress distribution along section aa of...Ch. 8.2 - Sketch the normal-stress distribution acting over...Ch. 8.2 - Determine the state of stress at points A and B,...Ch. 8.2 - If the force of 100 N is applied to the handles,...Ch. 8.2 - Determine the stress components at point A on the...Ch. 8.2 - Determine the stress components at point B on the...Ch. 8.2 - Determine the normal stress developed at points A...Ch. 8.2 - Sketch the normal-stress distribution acting over...Ch. 8.2 - Determine the state of stress at points A and B,...Ch. 8.2 - Determine the state of stress at point A on the...Ch. 8.2 - Determine the state of stress at point B on the...Ch. 8.2 - Determine the state of stress acting at point D....Ch. 8.2 - Determine the state of stress acting at point E....Ch. 8.2 - If it is subjected to the force system shown,...Ch. 8.2 - Solve Prob.840 for point B.Ch. 8.2 - Determine the stress components acting on the...Ch. 8.2 - Determine the stress components acting on the...Ch. 8.2 - Neglect the weight of the block.Ch. 8.2 - Neglect the weight of the block.Ch. 8.2 - He is supported uniformly by two bars, each having...Ch. 8.2 - Determine the state of stress at point A, and show...Ch. 8.2 - Determine the state of stress at point B, and show...Ch. 8.2 - Determine the state of stress at point C, and show...Ch. 8.2 - Determine the maximum radius e at which the load P...Ch. 8.2 - Specify the region to which this load can be...Ch. 8.2 - Determine the smallest force P that can be applied...Ch. 8.2 - The coiled spring is subjected to a force P. If we...Ch. 8.2 - The pins at C and D are at the same location as...Ch. 8.2 - Determine the state of stress at point A, and show...Ch. 8.2 - Determine the state of stress at point B, and show...Ch. 8.2 - Determine the stress components at points A and B...Ch. 8.2 - Determine the stress components at points C and D...Ch. 8.2 - Determine the stress components in the support...Ch. 8.2 - Determine the stress components in the support...Ch. 8.2 - If the force at the ram on the clamp at D is P= 8...Ch. 8.2 - Determine the maximum ram force P that can be...Ch. 8.2 - and an outer radius of 3.00 in. If the face of the...Ch. 8.2 - for points E and F.Ch. 8.2 - Determine the stress components at points A and B...Ch. 8.2 - Solve Prob.8-65 for points C and D.Ch. 8.2 - Due to internal gearing, this causes the block to...Ch. 8.2 - Determine the state of stress at point A and show...Ch. 8.2 - Solve Prob.868 for point B.Ch. 8.2 - Determine the stress components at point A. Sketch...Ch. 8.2 - for the stress components at point B.Ch. 8.2 - Determine the state of stress at point A at...Ch. 8.2 - Determine the state of stress at point B at...Ch. 8 - If it supports a cable loading of 800 lb,...Ch. 8 - Determine the state of stress at point E on the...Ch. 8 - Determine the state of stress at point F on the...Ch. 8 - The suspender arm AE has a square cross-sectional...Ch. 8 - If the cross section of the femur at section aa...Ch. 8 - If it has a mass of 5 kg/m, determine the largest...Ch. 8 - and is used to support the vertical reactions of...Ch. 8 - and is used to support the vertical reactions of...
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- The aluminium machine part shown below is subjected to a moment of M = 75 N.m. Determine the bending stress created at points B and A on the cross section. Sketch the results on a volume element located at each of these points. A- 50mm 50mm 100mm 100mm 20mm B- M=8kN-m 20mmarrow_forwardA member having the dimensions shown is used to resist an internal bending moment of M kNm. Determine the maximum stress in the member if the moment is applied (a) about the z axis (as shown) (b) about the y axis. Sketch the stress distribution for each case. Take: M= 90 kNm A mm A= 200 mm B= 150 mm B mm Solution: The moment of inertia of the cross-section about z and y axes are I;-4 1 - AB³ 12 (10) m* I BA = (10) m*arrow_forward4arrow_forward
- The curved beam is subjected to a moment of M = 40 lb # ft. Determine the maximum bending stress in the beam. Also, sketch a two-dimensional view of the stress distribution acting on section a–a.arrow_forwardIf the internal moment acting on the cross-section is 800 N.m, determine the maximum tensile and compressive bending stresses acting in the beam. Sketch the stress-distribution acting on the cross-section.arrow_forwardQuestion 1: A member having the dimensions shown is used to resist an internal bending moment of M kNm. Determine the maximum stress in the member if the moment is applied (a) about the z axis (as shown) (b) about the y axis. Sketch the stress distribution for each case. Take: M= 98 kNm mm A= 208 mm B= 158 mm B mm Solution: The moment of inertia of the cross-section about z and y axes are 1 AB³ 12 |(10-) m* 1 ВАЗ — 12 I, |(10) m* = For the bending about z axis, c = m Mc O pax MPа Iz For the bending about y axis, c = m Mc MPа Iy max z MPa KN=M Omax Y MPa. M KN-M MPa O max Z Omax Y MPaarrow_forward
- Determine the bending stress at point B and Carrow_forward2. If the bending stress at section 2 =20 MPa. What are the bending stresses at sections 1, 3, and 4. 12 mm 12 mm 12 mm 276 mm N.A.- 12 mm 150 mmarrow_forwardProblem 2. Consider a rod with radius c, subject to shear force V. Clearly show the Neutral Axis on the cross-sectional area. Determine the maximum shear stress from the shear formula t=VQ/(It) and identify where these maximum shear stresses occur; write magnitude in terms of V and c. Identify the section area and section area centroid used to calculate the maximum first area moment max What is the shear stress at points A У А where t=t, max and B? What is the shear stress at the centroid? What is the shear stress at points F and E at the top and bottom? By what factor is the maximum shear stress greater than the average shear stress acting over the cross-section.arrow_forward
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