Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Textbook Question
Chapter 11.2, Problem 11.16P
The beam has an allowable normal stress of σallow. =150 MPa and an allowable shear stress of τallow = 85 MPa.
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A beam carries a uniform distributed load of intensity w in N/m. It was determined that Vmax = 3.75w N, (++)Mmax = 2.53w N-m, (−−)Mmax = 4.5w N-m. From the given cross section shown, ytop = 100mm, ybot = 150mm, and INA = 72.92 x 10 6 mm4. The allowable stresses are as follows: σfT = 40 MPa, σfC = 70 MPa, and τ = 10 MPa.
(a) The safe uniform load considering tensile flexural stress is _____ N/m.
(b) The safe uniform load considering compressive flexural stress is _____ N/m.
(c) The moment of the area about the neutral axis is _____ mm3.
(d) The safe uniform load considering maximum shear force is _____ N/m.
(e) Based on your analysis, the safe uniform load to recommend is _____ N/m
The wood has an allowable normal stress of σallow = 15 MPa and an allowable shear stress ofτallowt = 1.33 MPa .
Part A
Determine the minimum dimension hh of the beam's cross section to safely support the load.
Determine the average shear stress developed in
the nails within region AB of the beam. The nails are
located on each side of the beam and are space 100
mm apart. Each nail has a diameter of 4 mm. Take P
= 2kN.
=
Hint: Think carefully about the number of nails
transferring shear stress from board-to-board.
2 kN/m
A
B
-1.5 m
1.5 m
100 mm
+
20 mm
40 mm
200 mm 20 mm
200 mm
Chapter 11 Solutions
Mechanics of Materials (10th Edition)
Ch. 11.2 - Determine the minimum dimension a to the nearest...Ch. 11.2 - of the rod to safely support the load. The rod is...Ch. 11.2 - The wood has an allowable normal stress of allow =...Ch. 11.2 - of the beam's cross section to safely support the...Ch. 11.2 - Determine the minimum dimension b to the nearest...Ch. 11.2 - The beam is made of steel having an allowable...Ch. 11.2 - Determine its dimensions if it is to be...Ch. 11.2 - Determine the minimum width of the beam to the...Ch. 11.2 - if P=10 kip.Ch. 11.2 - If the allowable bending stress is allow = 22 ksi...
Ch. 11.2 - The allowable bending stress is allow = 24 ksi and...Ch. 11.2 - The allowable bending stress is allow = 22 ksi and...Ch. 11.2 - The allowable bending stress is allow = 24 ksi and...Ch. 11.2 - Select the lightest-weight wide-flange beam from...Ch. 11.2 - The beam has an allowable normal stress of allow =...Ch. 11.2 - The beam has an allowable normal stress of allow...Ch. 11.2 - If each nail can support a shear force of 200 lb....Ch. 11.2 - If each beam is to be designed to carry 90 lb/ft...Ch. 11.2 - Determine its height h so that it simultaneously...Ch. 11.2 - The beam is constructed from four boards. If each...Ch. 11.2 - Prob. 11.15PCh. 11.2 - The beam has an allowable normal stress of allow....Ch. 11.2 - Determine the maximum cable force P that can...Ch. 11.2 - to safely support the load. The wood has an...Ch. 11.2 - and the wood has an allowable normal stress of...Ch. 11.2 - If the glue can support a shear stress of allow, =...Ch. 11.2 - If the allowable bending stress is allow = 6 MPa,...Ch. 11.2 - Determine the width b if the height h=2b.Ch. 11.2 - The allowable bending stress is allow = 24 ksi and...Ch. 11.2 - if allow = 30 ksi and allow = 15 ksi. The journal...Ch. 11.2 - if allow = 30 ksi and allow = 15 ksi. The journal...Ch. 11.2 - Select the lightest-weight wide-flange beam from...Ch. 11.2 - The allowable bending stress is allow = 30 ksi and...Ch. 11.2 - The allowable bending stress is allow = 30 ksi and...Ch. 11.2 - If the maximum bending stress is not to exceed...Ch. 11.2 - Determine the maximum load that can safely be...Ch. 11.4 - Determine the variation in the width was a...Ch. 11.4 - The tapered beam supports a uniform distributed...Ch. 11.4 - The tapered beam supports the concentrated force P...Ch. 11.4 - The beam is made from a plate that has a constant...Ch. 11.4 - Determine the variation in the depth d of a...Ch. 11.4 - Determine the variation of the radius r of the...Ch. 11.4 - Prob. 11.37PCh. 11.4 - Determine the variation in the width b as a...Ch. 11.4 - The tubular shaft has an inner diameter of 15 mm....Ch. 11.4 - Prob. 11.40PCh. 11.4 - Prob. 11.41PCh. 11.4 - The pulleys fixed to the shaft are loaded as...Ch. 11.4 - Prob. 11.43PCh. 11.4 - Prob. 11.44PCh. 11.4 - Prob. 11.45PCh. 11 - The cantilevered beam has a circular cross...Ch. 11 - Select the lightest-weight wide-flange overhanging...Ch. 11 - Prob. 11.3RPCh. 11 - Determine the shaft's diameter to the nearest...Ch. 11 - Select the lightest-weight wide-flange beam from...Ch. 11 - The simply supported joist is used in the...Ch. 11 - The simply supported joist is used in the...Ch. 11 - by 4-in. pieces of wood braced as shown. If the...
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- 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.arrow_forwardFIl-1. Determine the minimum dimension a to the nearest FII-4. Determine the minimum dimension h to the nearest mm of the beam's cross section to safely support the load. The wood has an allowable normal stress of atow- 10 MPa and an allowable shear stress of Talow -1 MPa. in. of the beam's cross section to safely support the koad. The wood has an allowable normal stress of ale 2 ksi and an allowable shear stress of Tatow - 200 psi. 1.5 kip/ft 6kN 6kN 2a FIl-1 FII-4 FIl-2. Determine the minimum diameter d to the nearest in. of the rod to safely support the load. The rod is made of a material having an allowable normal stress of o- 20 ksi and an allowable shear stress of rh - 10 ksi. F1l-5. Determine the minimum dimension b to the nearest mm of the beam's cross section to safely support the load. The wood has an allowable normal stress of oow- 12 MPa and an allowable shear stress of Tlow - 1.5 MPa. 3 kip ft 50 kN 5 kN-m 5 kN-m -15 ft -1.5 ft 3kip m- -1 m FII-2 FIl-3. Determine the…arrow_forwardB10arrow_forward
- Determine the shear stress (in Mpa) in the 28.54-mm-diameter pin at B that support the beam if P = 35.79 kN, a = 2.76 m, and b = 5.95 m.arrow_forwardThe simply supported joist is used in the construction of a floor for a building. In order to keep the floor low with respect to the sill beams C and D, the ends of the joists are notched as shown. If the allowable shear stress is tallow = 350 psi and the allowable bending stress is sallow = 1500 psi, determine the height h that will cause the beam to reach both allowable stresses at the same time. Also, what load P causes this to happen? Neglect the stressconcentration at the notch.arrow_forwardNEED ASAP THANK YOUarrow_forward
- Calculate the maximum stresses due to the Pload = 2000 N over the cross section. Also draw the stress distribution over the cross section.arrow_forwardConsider that the section is transmitting a positive bending moment about the z axis,Mz, where Mz=10 kip*in if the dimensions of the section are given in ips units, or Mz=1.13kN*m if the dimensions are in SI units. Determine the resulting stresses at the top and bottom surfaces and at every abrupt change in the cross section. 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.arrow_forwardSolve for the largest shraring stress in that section. Please show all values and where you got the numbers from when solving for moment of inertia, thank you.arrow_forward
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