Mechanics of Materials, 7th Edition
7th Edition
ISBN: 9780073398235
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 8.3, Problem 45P
Three forces are applied to the bar shown. Determine the normal and shearing stresses at (a) point a, (b) point b, (c) point c.
Fig. P8.45
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Students have asked these similar questions
PROBLEM 8.40
A thin strap is wrapped around a solid rod of radius c= 20 mm as shown.
Knowing that I = 100 mm and F = 5 kN, determine the normal and
shearing stresses at (a) point H, (b) point K.
o = 79.6 MPa
T=7.96 MPa
O =0
T=13.26 MPa
Problem 2. Three loads are applied to the short rectangular post shown In Fig. 2(a). The cross-
sectional dimensions of the post are shown in Fig. 2(b). Determine:
Me
(a) The normal and shear stresses and points H and K;
(b) The principal stresses and maximum in-plane shear stress at point H, and show the
orientation of theses stresses in an appropriate sketch.
No.
M2
y
50 mm
210 kN
%3D
120 mm
(Naー
75 mm
K
65 kN
30 mm
95 kN
160 mm
150 mm
30 mm
Y-axis is the w
to the sectin
paimt Hond E
امقره
Fig. 2(b)
文
Section Proputics
A= 120 X160=19200 mm Lx=160 - 40960000 mm-4094r
L= 160x128
5KNス50 m-)
%3D
%3D
= 23040000mm'= 23; 40Xlʻmm7
Int Faices
PROBLEM 7.26
0.2 m
The axle of an automobile is acted upon by the forces and couple
shown. Knowing that the diameter of the solid axle is 32 mm,
determine (a) the principal planes and principal stresses at point H
located on top of the axle, (b) the maximum shearing stress at the
same point.
3 kN
350 N- m
3 kN
Omax = 18.67 MPa
= -158,5 MPa
O min
Chapter 8 Solutions
Mechanics of Materials, 7th Edition
Ch. 8.2 - A W10 = 39 rolled-steel beam supports a load P as...Ch. 8.2 - Solve Prob. 8.1, assuming that P = 22.5 kips and a...Ch. 8.2 - An overhanging W920 449 rolled-steel beam...Ch. 8.2 - Solve Prob. 8.3, assuming that P = 850 kN and a =...Ch. 8.2 - 8.5 and 8.6 (a) Knowing that all = 160 MPa and all...Ch. 8.2 - 8.5 and 8.6 (a) Knowing that all = 160 MPa and all...Ch. 8.2 - 8.7 and 8.8 (a) Knowing that all = 24 ksi and all...Ch. 8.2 - 8.7 and 8.8 (a) Knowing that all = 24 ksi and all...Ch. 8.2 - 8.9 through 8.14 Each of the following problems...Ch. 8.2 - 8.9 through 8.14 Each of the following problems...
Ch. 8.2 - 8.9 through 8.14 Each of the following problems...Ch. 8.2 - Prob. 12PCh. 8.2 - 8.9 through 8.14 Each of the following problems...Ch. 8.2 - 8.9 through 8.14 Each of the following problems...Ch. 8.2 - Determine the smallest allowable diameter of the...Ch. 8.2 - Determine the smallest allowable diameter of the...Ch. 8.2 - Using the notation of Sec. 8.2 and neglecting the...Ch. 8.2 - The 4-kN force is parallel to the x axis, and the...Ch. 8.2 - The vertical force P1 and the horizontal force P2...Ch. 8.2 - The two 500-lb forces are vertical and the force P...Ch. 8.2 - Prob. 21PCh. 8.2 - Prob. 22PCh. 8.2 - The solid shaft AB rotates at 600 rpm and...Ch. 8.2 - The solid shaft AB rotates at 600 rpm and...Ch. 8.2 - The solid shafts ABC and DEF and the gears shown...Ch. 8.2 - Prob. 26PCh. 8.2 - Prob. 27PCh. 8.2 - Prob. 28PCh. 8.2 - The solid shaft AE rotates at 600 rpm and...Ch. 8.2 - The solid shaft AE rotates at 600 rpm and...Ch. 8.3 - Two 1.2-kip forces are applied to an L-shaped...Ch. 8.3 - Two 1.2-kip forces are applied to an L-shaped...Ch. 8.3 - The cantilever beam AB has a rectangular cross...Ch. 8.3 - 8.34 through 8.36 Member AB has a uniform...Ch. 8.3 - 8.34 through 8.36 Member AB has a uniform...Ch. 8.3 - 8.34 through 8.36 Member AB has a uniform...Ch. 8.3 - Prob. 37PCh. 8.3 - Two forces are applied to the pipe AB as shown....Ch. 8.3 - Several forces are applied to the pipe assembly...Ch. 8.3 - The steel pile AB has a 100-mm outer diameter and...Ch. 8.3 - Three forces are applied to a 4-in.-diameter plate...Ch. 8.3 - The steel pipe AB has a 72-mm outer diameter and a...Ch. 8.3 - A 13-kN force is applied as shown to the...Ch. 8.3 - A vertical force P of magnitude 60 lb is applied...Ch. 8.3 - Three forces are applied to the bar shown....Ch. 8.3 - Prob. 46PCh. 8.3 - Three forces are applied to the bar shown....Ch. 8.3 - Three forces are applied to the bar shown....Ch. 8.3 - Two forces are applied to the small post BD as...Ch. 8.3 - Two forces are applied to the small post BD as...Ch. 8.3 - Three forces are applied to the machine component...Ch. 8.3 - Prob. 52PCh. 8.3 - Three steel plates, each 13 mm thick, are welded...Ch. 8.3 - Three steel plates, each 13 mm thick, are welded...Ch. 8.3 - Two forces P1 and P2 are applied as shown in...Ch. 8.3 - Two forces P1 and P2 are applied as shown in...Ch. 8.3 - Prob. 57PCh. 8.3 - Four forces are applied to a W8 28 rolled-steel...Ch. 8.3 - A force P is applied to a cantilever beam by means...Ch. 8.3 - Prob. 60PCh. 8.3 - A 5-kN force P is applied to a wire that is...Ch. 8.3 - Knowing that the structural tube shown has a...Ch. 8.3 - The structural tube shown has a uniform wall...Ch. 8.3 - The structural tube shown has a uniform wall...Ch. 8 - (a) Knowing that all = 24 ksi and all = 14.5 ksi,...Ch. 8 - Neglecting the effect of fillets and of stress...Ch. 8 - Knowing that rods BC and CD are of diameter 24 mm...Ch. 8 - The solid shaft AB rotates at 450 rpm and...Ch. 8 - A 6-kip force is applied to the machine element AB...Ch. 8 - A thin strap is wrapped around a solid rod of...Ch. 8 - A close-coiled spring is made of a circular wire...Ch. 8 - Forces are applied at points A and B of the solid...Ch. 8 - Knowing that the bracket AB has a uniform...Ch. 8 - For the post and loading shown, determine the...Ch. 8 - Knowing that the structural tube shown has a...Ch. 8 - The cantilever beam AB will be installed so that...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Problem 8.12 A bar of rectangular cross-section, with a width of 60 mm and a thickness of 40 mm, is bent in the shape of a horse shoe having a mean radius of 70 mm. Two equal and opposite forces of 10 kN each are applied at a distance of 12 cm from the centre line of the middle section so that they tend to straighten the rod. Find the maximum ten- sile and compressive stresses and construct a diagram showing the vari- ation of the normal stresses over the central section.arrow_forwardProblem 8.5 A circular ring is subjected to a pull of 15 kN. The ring is of T-section as shown in Fig. 8.12 and the internal radius is 10 cm. Determine the maximum and minimum stresses in the ring. 2cm 12cm 10cm 2 cm Fig. 8.12arrow_forwardFor the state of stress shown, Using Mohr's circle. determine (a) the principal stresses; and (b) the maximum in-plane shear stress. Show the results on properly oriented elements. 8 ksi 6 ksi 4 ksi FIG. P8.58arrow_forward
- 7. Knowing that 0=40° and P=9 kN, determine (a) the smallest allowable diameter of the pin at Bif the average shearing stress in the pin is not exceed 120 MPa, (b) the corresponding average bearing stress in the member AB at B, (c) the corresponding average bearing stress in each of the support brackets at B. P 16 mm 750 mm 750 mm 50 mm- 12 inmarrow_forwardA steel pipe of 300-mm outer diameter is fabricated from an 8-mm-thick plate by welding along a helix that forms an angle of 20° with a plane perpendicular to the axis of the pipe. Knowing that a 250-kN axial force P and a 12-kN-m torque T. each directed as shown, are applied to the pipe, determine the normal and in-plane shearing stresses in directions, respectively, normal and tangential to the weld. T The normal stress is - The shear stress is- Weld 20⁰ 8 mm MPa MPa.arrow_forward60 MPa PROBLEM 7.3 45 MPa For the given state of stress, determine the normal and shearing stresses exerted on the oblique face of the shaded triangular element shown. Use a method of 120 MPA analysis based on the equilibrium of that element, as was done in the 70° derivations of Sec. 7.2. O=14.19 MPa T = 15.19 MPaarrow_forward
- Prob.6: [2.53] A rod consisting of two cylindrical portions AB and BC is restrained at both ends. Portion AB is made of brass (Es =105 GPa , ab= 20.9 x 106 /"C) and portion AB is made of aluminum (Ea =72 GPa , a.= 23.9 x 10-6 /C). Knowing that the rod is initially unstressed, determine (a) the normal stresses induced in portions AB and BC by a temperature rise of 42°C, (b) the corresponding deflection of point B. A 60-mm diameter 1.1 m - 40-mm diameter 1.3 m Carrow_forwardProblem 4 The steel pipe AB has a 102-mam outer diameter and a 6-mm wall thickness. Knowing that arm CD is rigidly attached to the pipe, determine the principal stresses and the maximum shearing stress at point K. And then show stress on Mohr's circle. 200 mm 6 mm B H D 51 mm 150 mm xarrow_forwardFig. 2 4. A steel shaft of diameter 50 mm and length 1.2 m (E = 210 GPa and v = 0.3) is loaded with multiple force system. At a point in the shaft, the state of stress relative to the x, y, z coordinate system was found to be: [600 0 T = 0 320 MPa -480 (a) Draw a cube element showing the stress components on each coordinate face (Hint: No vector lines for zero stresses; Warning: A stress element without reference axes will receive zero point). (b) From the given stress tensor, determine the values of (i) octahedral normal stress (Goct) and (ii) octahedral shear stress (toct). (c) From your answer in (b), determine (i) dilatational strain energy Udilat '); and (ii) deviatoric strain energy (Udist). (d) Find the total strain energy at the point.arrow_forward
- 7.25 The steel pipe AB has a 102-mm outer diameter and a 6-mm wall thickness. Knowing that arm CD is rigidly attached to the pipe, determine the principal stresses and the maximum shearing stress at point K. 10 kN 200 mm C Fig. P7.25 22 6 mm B H D 51 mm 150 mmarrow_forwardQue 5.6. A crane hook trapezoidal horizontal cross-section is 50 mm wide inside and 30 mm wide outside. Thickness of the section is 60 mm. The crane hook carries a vertical load of 20 kN whose line of action is 50 mm from the inside edge of the section. The center of curvature is 60 mm from the inside edge. Determine the maximum tensile and compressive stresses in the section.arrow_forwardProb.4: [2.37] The 1.5 m concrete post is reinforced with six steel bars, each with 28 mm diameter. Knowing the E, = 200 GPa and Ec = 200 GPa, determine the normal stresses in the steel and concrete when a 1550 kN axial centric force P is applied to the post. 450 mm 1.5 marrow_forward
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