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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Chapter 8.2, Problem 12P
(a)
To determine
The actual value of
(b)
To determine
The maximum value of principal stress
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A lightweight lever consists of a 0.8m solid bar rigidly mounted to a large structure and a 0.5m solid lever
welded to the solid bar. Using the loading indicated and assuming the material has a Young's Modulus of
200 GPa and a shear modulus of 86 GPa, calculate:
(a) the maximum stress at Point A on the Cross-section a-a,
(b) the vertical displacement of the knob when the load is applied relative to Cross-section a-a.
B
C
50 mm
Section ad
a 0.8 m
0.5 m
100 N
38 mm
Focus
b.
A draw bar between a tractor and a trailer is made from a length of steel
with a rectangular cross-section 100 mm by 12 mm. The load is transmitted
to the bar via a pin through a 25 mm diameter hole at each end as shown in
Fig. 5b.
x|
i.
ii.
of
100
O25
x|
Fig. 5b
CO
Y |
Y|
rum
beam
If the load P in the bar is 100 kN, determine the following:
The stress at the section X-X, shown in Fig. 5b.
The stress at the section Y-Y, shown in Fig. 5b. i ort ratelic
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Problem 1):
A circular pipe girder is constructed from 80mm external diameter and 60 mm internal diameter. Three such girders are mounted vertically one at equal angles of a circular horizontal platform which the girders support. The platform is 5 m above ground level and weighs (0.1*B) KN. The platform supports an additional central load of (0.2*B) KN. The weight of the girders may not be neglected. The density of the material from which the girders are constructed is (290*B) kg/m3. Assuming that each girder supports an equal share of the load, determine the compressive stresses set up in the material of each girder:1- At the lower point of the girder.2- At the middle point of the girder.3- At the upper point of the girder.
Discuss the above values when the weights of the girders are neglected.Note: B = 39
Problem 2):
A 20 mm diameter steel rod passes concentrically through a bronze tube (200+Q) mm long, 50 mm external diameter, and 40 mm internal diameter. The ends of the steel rod…
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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- A 20 mm diameter steel rod passes concentrically through a bronze tube (200+SN) mm long, 50 mm external diameter and 40 mm internal diameter. The ends of the steel rod are threaded and provided with nuts and washers which are adjusted initially so that there is no end play at 25°C.. 1. Assuming that there is no change in the thickness of the washers, if the stress produced in the steel is (200+SN) MN/m2 when one of the nuts is tightened, the pitch of the thread being 1 mm. Find the number of turns for the nut and stress in bronze tube.2. If the temperature of the steel and bronze is then raised to 4O°C find the changes that will occur in the stresses in both materials. The coefficient of linear expansion per C is 10 x10-6 for steel and 17 x10-6 for bronze. E for steel = 210 GN/m2. E %3D for bronze = 100 GN/m2.. Note: SN = %3D Student number Student Number =32arrow_forwardAn annular washer distributes the load P applied to a steel rod to a timber support. The rod's diameter is 22 mm, and the washer's inner diameter is 25 mm, which is larger than the hole's permissible outer diameter. Knowing that the axial normal stress in the steel rod is 35 MPa and the average bearing stress between the washer and the timber must not exceed 5 MPa, examine the smallest allowed outer diameter, d, of the washer. %3D %3D +22 mm P Figure 4arrow_forwardEach of the three rolled-steel beams shown (numbered 1, 2, and 3) is to carry a 64-kip load uniformly distributed over the beam. Each of these beams has a 12-ft span and is to be supported by the two 24-ft rolled-steel girders AC and BD. The allowable normal stress for the steel used is 22.5 ksi. Determine the section modulus for each girder and select the most economical W shape for the two girders using the table given below. (Round the final answer to one decimal place.)arrow_forward
- Problem Steel block with triaxial loading as shown, y 2" 3" For Steel, E = 29 x 106 Psi y = 0.3 Loads: (Original Loading – Load are Uniformly Distributed Along Their Axis) F; = 48 Kips (T) Fy 60 Kips (C) F2 54 Kips (T) Required: Determine the magnitude F,'of the single uniformly distributed load in the x- direction that would produce the same deformation in the y-direction as the original loading. F + F2 Fyarrow_forward|This problem is just like the example problem, but dimension changed so centroid and moment of inertia change, AND the applied load is up and not down. - 3". - 3"-| A vertical force P of magnitude 20 kips is applied at point C located on the axis of symmetry of the cross section of a short column. Knowing that y = 11" determine at the top of column B 2" 6" the stress @ pt A @ pt b @ pt C @ the N.A. A 4" 2" Y' 2" 1/2"arrow_forwardA draw bar between a tractor and a trailer is made from a length of steel with a rectangular cross-section 100 mm by 12 mm. The load is transmitted to the bar via a pin through a 25 mm diameter hole at each end as shown in Fig. 4c. for 100 Fig. 4c If the load P in the bar is 100 kN, determine the following: The stress at the section X-X, shown in Fig. 4c. i (6 marks) ii The stress at the section Y-Y, shown in Fig. 4c. (5 marks)arrow_forward
- PROBLEM NO. 2 A flanged bolt coupling connects two shafts. The bolt circle diameter is 250 mm in which there are 12 bolts. The allowable shear stress is 50 MPa in the shafts and 23 MPa in the bolts. One shaft is hollow with outside diameter of 100 mm, while the other one is solid of diameter 50 mm. Determine the ratio of the outside and inside diameter of the hollow shaft and the bolt diameter so that both shafts and the flanged bolt coupling are having the same strength in torsion.arrow_forward1. A cantilever of square cross section as shown was made of mild carbon steel SAE 1020, as rolled, and was designed to support a static load W = 15 lb. After the beam was installed, it was discovered that the weight W was not static but vibrated, so that actually the beam was subjected to a repeated load. Measurement showed that the weight rose and fell a distance h equal to 0.05 inch. Shortly thereafter the beam fractured at the fillet which had a machined radius of 1/32 in. (a) Make calculations to show and state your conclusion whether or not the beam should have been expected to fail. (b) for the same data, design a new cantilever with the same dimensions except with a fillet radius r= 1/8 in. Determine whether a carbon steel would be necessary, and if so, its SAE or AISI no. 1/2" 3/4". 6"arrow_forwardProblem !. , The steel tie bar shown is to be designed to carry a tension force of magnitude P = 130KN when bolted between double brackets at A and B. The bar will be fabricated from 25-mm-thick plate stock. For the grade of steel to be used, the maximum allowable stresses are: o = 170 MPa, t = 110 MPa, op = 370 MPa. Design the tie bar by determining the required values of: a. the diameter d of the bolt, b. the dimension b at each end of the bar, c. the dimensionh of the bar.arrow_forward
- 2. (a) A steel cylinder of 60 mm inner radius and 80 mm outer radius is subjected to an internal pressure of 30 MNm ². Determine the resulting hoop stress values at the inner and outer surfaces and graphically represent (sketch) the general form of hoop stress variation through the thickness of the cylinder wall. (b) (c) The cylinder in (a) is to be used as a shrink-fitted sleeve to strengthen a hydraulic cylinder manufactured of the same steel. The cylinder bore radius is 40 mm. When the hydraulic cylinder is not subjected to internal pressure, the interference pressure generated due to the shrink fit alone is 30 MNm2. Note: This is the same value of pressure as in the problem analysed in part (a). Determine the resulting hoop stress values at the inner and outer walls of the inner cylinder. Graphically represent the general form of hoop stress variation through the wall thickness in the combination indicating the key values as calculated in parts (a) and (b). (d) If the Young's…arrow_forwardа) An annular washer distributes the load P applied to a steel rod to a timber support. The rod's diameter is 22 mm, and the washer's inner diameter is 25 mm, which is larger than the hole's permissible outer diameter. Knowing that the axial normal stress in the steel rod is 35 MPa and the average bearing stress between the washer and the timber must not exceed 5 MPa, examine the smallest allowed outer diameter, d, of the washer. - 22 mm Figure 4arrow_forwardProblem 6.1 A cantilever beam is subject to an end force of 15 kN inclined at 15° to the horizontal axis of the beam. The beam is 150 mm long with a rectangular section 50 mm wide x 25 mm deep. Determine the net stress distribution across the fixed end section.arrow_forward
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