Mechanics of Materials
9th Edition
ISBN: 9780133254426
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Chapter 1.2, Problem 1.30P
A differential element taken from a curved bar is shown in the figure. Show that dN/dθ = V, dV/dθ = −N, dM/dθ = −T, and dT/dθ = M.
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Forces of F1=15 kN in the z direction from the B point, F2=10 kN in the z direction from the C point and F3=10 kN in the y direction act on the arm in the figure. The lengths of the arm are also given as L1=0.15 m and L2=0.16 m. The radius r in the a-a section taken over the arm is r=0.2 m and it is desired to determine the stress state at point A. The shear modulus of the sleeve material is G=65 Gpa. According to this;
WRITE YOUR RESULTS IN THE BOXES WITHOUT THE UNITS IN kPa.
a) Find the shear stress due to the shear force at point A. Response
b) Find the shear stress due to the torsional moment at point A. Response
c) Find the total shear stress at point A. Response
d) Find the normal stress due to the normal force at point A. Response
e) Find the normal stress due to the bending moment at point A. Response
f) Find the total normal stress at point A. Response
Forces of F1=8 kN in the z direction from the B point, F2=5 kN in the z direction from the C point, and F3=10 kN in the y direction act on the arm in the figure. The lengths of the arm are also given as L1=0.15 m and L2=0.16 m. The radius r in the a-a section taken over the arm is r=0.2 m and it is desired to determine the stress state at point A. slip of sleeve material module is G=75 Gpa. Accordingly,
a) Find the shear stress due to the shear force at point A.
b) Find the shear stress due to the torsional moment at point A.
c) Find the total shear stress at point A.
d) Find the normal stress due to the normal force at point A.
e) Find the normal stress due to the bending moment at point A.
f) Find the total normal stress at point A.
The steel box wrench (E=29,000ksi, v=0.32) is
loaded with a 40-lb horizontal force and a 25-lb
vertical force. Find the following for an element
located at point B on Section a-a:
24 in.
1. The non-vanishing resultant internal moments
on section a-a are which of the following?
4 in.
a. (160 i- 600 j+960 k)in · Ib
b. (-160 i+600 j+960 k ) in · lb
c. (-960 i+160 j+600 k)in - lb
d. (-960 i -160 ј-600 k)in-lb
a
e. none of the above
2. The normal and shear force components on
section a-a are:
a. V, = 65lb;V, = 40lb; N¸ = 25lb
b. V, = 0;V, =40lb; N, = 25lb
c. V, = 64;V, = 25lb; N, = 40lb
d. V, =0;V, =-40lb; N¸ = -25lb
e. none of the above
3. The non-vanishing stress components at point B are:
0̟ =1.60; t =-4.89ksi;
а.
0, =-4.89; 7 =3.60ksi;
0, = 2.50ksi; T,
d. o, = 4.91ksi; t =-4.89ksi;
b.
с.
=-4.89ksi;
е.
none of the above
4. The principal stresses at point B from most tensile to most compressive are:
O1,02,0; =4.16,–0.8,–5.76
b. o,,0,,0, =5.76,0,–4.16
а.
O1,02,0; =1.9,-2.45,-6.8
с.
d.…
Chapter 1 Solutions
Mechanics of Materials
Ch. 1.2 - In each case, explain how to find the resultant...Ch. 1.2 - Determine the resultant internal normal force,...Ch. 1.2 - Determine the resultant internal normal force,...Ch. 1.2 - Determine the resultant internal normal force,...Ch. 1.2 - Determine the resultant internal normal force,...Ch. 1.2 - Determine the resultant internal normal force,...Ch. 1.2 - Determine the resultant internal normal force,...Ch. 1.2 - The shaft is supported by a smooth thrust bearing...Ch. 1.2 - Determine the resultant internal normal and shear...Ch. 1.2 - 1-3. The beam AB is fixed to the wall and has a...
Ch. 1.2 - The shaft is supported by a smooth thrust bearing...Ch. 1.2 - 1-5. Determine the resultant internal loadings in...Ch. 1.2 - 1-6. Determine the normal force, shear force, and...Ch. 1.2 - 1-7. The cable will fail when subjected to a...Ch. 1.2 - *1-8. Determine the resultant internal loadings on...Ch. 1.2 - 1-9. Determine the resultant internal loadings on...Ch. 1.2 - The boom DF of the jib crane and the column DE...Ch. 1.2 - 1-11. The forearm and biceps support the 2-kg load...Ch. 1.2 - *1-12. The serving tray T used on an airplane is...Ch. 1.2 - The blade of the hacksaw is subjected to a...Ch. 1.2 - The blade of the hacksaw is subjected to a...Ch. 1.2 - 1-15. A 150-lb bucket is suspended from a cable on...Ch. 1.2 - *1-16. A 150-lb bucket is suspended from a cable...Ch. 1.2 - 1-17. Determine resultant internal loadings acting...Ch. 1.2 - Prob. 1.18PCh. 1.2 - Prob. 1.19PCh. 1.2 - Prob. 1.20PCh. 1.2 - Prob. 1.21PCh. 1.2 - The metal stud punch is subjected to a force of...Ch. 1.2 - Determine the resultant internal loadings acting...Ch. 1.2 - Prob. 1.24PCh. 1.2 - 1-25. Determine the resultant internal loading...Ch. 1.2 - 1-26. The shaft is supported at its ends by two...Ch. 1.2 - 1-27. The pipe assembly is subjected to a force of...Ch. 1.2 - If the drill bit jams when the brace is subjected...Ch. 1.2 - 1-29. 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The joint is subjected to the axial member...Ch. 1.5 - Prob. 1.50PCh. 1.5 - Prob. 1.51PCh. 1.5 - Prob. 1.52PCh. 1.5 - Prob. 1.53PCh. 1.5 - Prob. 1.54PCh. 1.5 - The 2-Mg concrete pipe has a center of mass at...Ch. 1.5 - The 2-Mg concrete pipe has a center of mass at...Ch. 1.5 - Prob. 1.57PCh. 1.5 - Prob. 1.58PCh. 1.5 - 1-59. The jib crane is pinned at A and supports a...Ch. 1.5 - *1-60. If the shaft is subjected to an axial force...Ch. 1.5 - Prob. 1.61PCh. 1.5 - Prob. 1.62PCh. 1.5 - Prob. 1.63PCh. 1.5 - *1-64. A vertical force of P = 1500 N is applied...Ch. 1.5 - Prob. 1.65PCh. 1.5 - Determine the largest load P that can be applied...Ch. 1.5 - Prob. 1.67PCh. 1.5 - Prob. 1.68PCh. 1.7 - Rods AC and BC are used to suspend the 200-kg...Ch. 1.7 - If it is subjected to double shear, determine the...Ch. 1.7 - Determine the maximum average shear stress...Ch. 1.7 - If each of the three nails has a diameter of 4 mm...Ch. 1.7 - The strut is glued to the horizontal member at...Ch. 1.7 - Determine the maximum average shear stress...Ch. 1.7 - If the eyebolt is made of a material having a...Ch. 1.7 - If the bar assembly is made of a material having a...Ch. 1.7 - Determine the maximum force P that can be applied...Ch. 1.7 - The pin is made of a material having a failure...Ch. 1.7 - If the bolt head and the supporting bracket are...Ch. 1.7 - Six nails are used to hold the hanger at A against...Ch. 1.7 - If A and B are both made of wood and are 38 in....Ch. 1.7 - Prob. 1.70PCh. 1.7 - Prob. 1.71PCh. 1.7 - Prob. 1.72PCh. 1.7 - The steel swivel bushing in the elevator control...Ch. 1.7 - 1-74. 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