Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 6.4, Problem 65P
A shaft is made of a polymer having an elliptical cross section. If it resists an internal moment of M = 50 N · m, determine the maximum bending stress in the material (a) using the flexure formula, where lz =
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Answer the following:
A composite beam is made of two brass [E = 98 GPa] plates bonded to an aluminum [E = 60 GPa] bar, as shown. The beam is subjected
to a bending moment of 2270 N-m acting about the z axis. Assume b=44 mm, d₁=25 mm, d₂-8 mm. Determine:
(a) the maximum bending stresses Obr, Gal in the brass plates and the aluminum bar.
(b) the stress in the brass brj at the joints where the two materials are bonded together.
Z
Brass (2)
Aluminum (1)
Brass (2)
Answers:
(a) Obr =
(b) Obrj
=
i
i
b
d₂
d₁
d₂
MPa, Gal =
MPa.
i
MPa.
The aluminum machine part is subjected to a moment of M = 75 N.m. (i) Determinethe bending stress created at points B and C on the cross section; (ii) Determine the maximumtensile and compressive bending stresses in the part.
Chapter 6 Solutions
Mechanics of Materials
Ch. 6.2 - and then draw the shear and moment diagrams for...Ch. 6.2 - In each case, express the shear and moment...Ch. 6.2 - In each case, express the shear and moment...Ch. 6.2 - In each case, express the shear and moment...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - Prob. 1PCh. 6.2 - Prob. 2P
Ch. 6.2 - Prob. 3PCh. 6.2 - Express the shear and moment in terms of x for 0 ...Ch. 6.2 - Express the internal shear and moment in the...Ch. 6.2 - Draw the shear and moment diagrams for the shaft....Ch. 6.2 - Determine the shear and moment as functions of x,...Ch. 6.2 - Determine the shear and moment as functions of x,...Ch. 6.2 - Determine the shear and moment as functions of x,...Ch. 6.2 - Determine the shear and moment in the double...Ch. 6.2 - Draw the shear and moment diagrams for the...Ch. 6.2 - Draw the shear and moment diagrams for the shaft....Ch. 6.2 - Draw the shear and moment diagrams for the...Ch. 6.2 - Draw the shear and moment diagrams for the...Ch. 6.2 - Draw the shear and moment diagrams for the...Ch. 6.2 - Prob. 16PCh. 6.2 - Draw the shear and moment diagrams for the simply...Ch. 6.2 - Prob. 19PCh. 6.2 - Draw the shear and moment diagrams for the beam.Ch. 6.2 - Draw the shear and moment diagrams for the...Ch. 6.2 - The 150-lb man sits in the center of the boat,...Ch. 6.2 - Prob. 24PCh. 6.2 - Draw the shear and moment diagrams for the beam.Ch. 6.2 - Prob. 26PCh. 6.2 - Draw the shear and moment diagrams for the beam....Ch. 6.2 - Prob. 29PCh. 6.2 - Prob. 30PCh. 6.2 - Prob. 31PCh. 6.2 - Prob. 34PCh. 6.2 - Prob. 35PCh. 6.2 - The beam is used to support a uniform load along...Ch. 6.2 - Prob. 39PCh. 6.2 - Prob. 42PCh. 6.2 - Prob. 43PCh. 6.2 - Prob. 44PCh. 6.2 - Prob. 45PCh. 6.2 - The truck is to be used to transport the concrete...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - Determine the moment M that will produce a maximum...Ch. 6.4 - Determine the maximum tensile and compressive...Ch. 6.4 - The beam is constructed from four pieces of wood,...Ch. 6.4 - The beam is constructed from four pieces of wood,...Ch. 6.4 - The beam is made from three boards nailed together...Ch. 6.4 - The beam is made from three boards nailed together...Ch. 6.4 - Prob. 54PCh. 6.4 - The tubular shaft is supported by a smooth thrust...Ch. 6.4 - Prob. 57PCh. 6.4 - If the beam is subjected to an internal moment or...Ch. 6.4 - If the beam is made of material having an...Ch. 6.4 - Prob. 60PCh. 6.4 - Prob. 61PCh. 6.4 - The beam is subjected to a moment of M = 40 kN m....Ch. 6.4 - The steel shaft has a diameter of 2 in. It is...Ch. 6.4 - Determine the dimension a of a beam having a...Ch. 6.4 - A shaft is made of a polymer having an elliptical...Ch. 6.4 - Solve Prob. 6-65 if the moment M = 50 N m is...Ch. 6.4 - Prob. 67PCh. 6.4 - If M=4kipft , determine the resultant force the...Ch. 6.4 - The strut on the utility pole supports the cable...Ch. 6.4 - The pin is used to connect the three links...Ch. 6.4 - Prob. 75PCh. 6.4 - A timber beam has a cross section which is...Ch. 6.4 - If the beam is subjected to an internal moment of...Ch. 6.4 - If the allowable tensile and compressive stress...Ch. 6.4 - If the beam is subjected to an internal moment of...Ch. 6.4 - Prob. 80PCh. 6.4 - Prob. 81PCh. 6.4 - Prob. 82PCh. 6.4 - Prob. 83PCh. 6.4 - If the intensity of the load w=15kN/m , determine...Ch. 6.4 - Prob. 85PCh. 6.4 - Determine the absolute maximum bending stress in...Ch. 6.4 - Prob. 87PCh. 6.4 - Prob. 88PCh. 6.4 - If the compound beam in Prob. 642 has a square...Ch. 6.4 - If the beam in Prob. 628 has a rectangular cross...Ch. 6.4 - Determine the absolute maximum bending stress in...Ch. 6.4 - Determine, to the nearest millimeter, the smallest...Ch. 6.4 - If the beam in Prob.63 has a rectangular cross...Ch. 6.4 - The simply supported truss is subjected to the...Ch. 6.4 - If d = 450 mm, determine the absolute maximum...Ch. 6.4 - If the allowable bending stress is allow = 6 MPa,...Ch. 6.4 - Prob. 102PCh. 6.4 - Prob. 103PCh. 6.5 - Determine the bending stress at corners A and B....Ch. 6.5 - Determine the maximum bending stress in the beams...Ch. 6.5 - The member has a square cross section and is...Ch. 6.5 - The member has a square cross section and is...Ch. 6.5 - Consider the general case of a prismatic beam...Ch. 6.5 - The steel shaft is subjected to the two loads. If...Ch. 6.5 - The 65-mm-diameter steel shaft is subjected to the...Ch. 6.5 - For the section, lz = 31.7(10-5) m4, lY =...Ch. 6.5 - For the section, lz, = 31.7(10-5) m4, lY =...Ch. 6.9 - The composite beam is made of steel (A) bonded to...Ch. 6.9 - The composite beam is made of steel (A) bonded to...Ch. 6.9 - Segment A of the composite beam is made from...Ch. 6.9 - Segment A of the composite beam is made from...Ch. 6.9 - A wood beam is reinforced with steel straps at its...Ch. 6.9 - The composite beam is made of A-36 steel (A)...Ch. 6.9 - The composite beam is made of A-36 steel (A)...Ch. 6.9 - If the beam is subjected to a moment of M = 45 kN...Ch. 6.9 - The Douglas Fir beam is reinforced with A-36 steel...Ch. 6.9 - For the curved beam in Fig. 640a, show that when...Ch. 6.9 - The curved member is subjected to the moment of M...Ch. 6.9 - The curved member is made from material having an...Ch. 6.9 - If P = 3 kN, determine the bending stress at...Ch. 6.9 - If the maximum bending stress at section a-a is...Ch. 6.9 - The elbow of the pipe has an outer radius of 0.75...Ch. 6.9 - The curved bar used on a machine has a rectangular...Ch. 6.9 - The steel rod has a circular cross section. If it...Ch. 6.9 - Prob. 150PCh. 6.9 - Prob. 151PCh. 6.9 - The bar has a thickness of 1 in. and the allowable...Ch. 6.9 - The bar has a thickness of 1 in. and is subjected...Ch. 6.9 - Prob. 154PCh. 6.9 - The bar is subjected to a moment of M=17.5Nm If...Ch. 6.9 - Prob. 156PCh. 6.9 - Prob. 157PCh. 6.10 - The beam is made of an elastic plastic material...Ch. 6.10 - The wide-flange member is made from an elastic...Ch. 6.10 - The rod has a circular cross section. If it is...Ch. 6.10 - The rod has a circular cross section. If it is...Ch. 6.10 - The beam is made of an elastic perfectly plastic...Ch. 6.10 - Determine the plastic moment Mp that can be...Ch. 6.10 - Prob. 164PCh. 6.10 - Prob. 166PCh. 6.10 - Prob. 170PCh. 6.10 - Prob. 171PCh. 6.10 - The box beam is made of an elastic perfectly...Ch. 6.10 - The plexiglass bar has a stress-strain curve that...Ch. 6 - Determine the shape factor for the wide-flange...Ch. 6 - The compound beam consists of two segments that...Ch. 6 - The composite beam consists of a wood core and two...Ch. 6 - If it resists a moment of M = 125 N m, determine...Ch. 6 - Determine the maximum bending stress in the handle...Ch. 6 - The curved beam is subjected to a bending moment...Ch. 6 - Determine the shear and moment in the beam as...Ch. 6 - A wooden beam has a square cross section as shown...Ch. 6 - Draw the shear and moment diagrams for the shaft...Ch. 6 - The strut has a square cross section a by a and is...
Knowledge Booster
Learn more about
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
- A thin-walled rectangular tube has uniform thickness t and dimensions a x b to the median line of the cross section (see figure). How does the shear stress in the tube vary with the ratio = a/b if the total length Lmof the median line of the cross section and the torque T remain constant? From your results, show that the shear stress is smallest when the tube is square (ß = 1).arrow_forwardA 4.75-in, outside diameter polyethylene pipe designed to carry chemical waste is placed in a trench and bent around a quarter-circular 90° bend (see figure). The bent section of the pipe is 52 ft long. Determine the maximum compressive strain If the normal strain cannot exceed 6.1 × 10-3 , what is the maximum diameter of the pipe? If d = 4.75 in., what is the minimum acceptable length of the bent section of the pipe?arrow_forwardThe Z-section of Example D-7 is subjected to M = 5 kN · m, as shown. Determine the orientation of the neutral axis and calculate the maximum tensile stress c1and maximum compressive stress ocin the beam. Use the following numerical data: height; = 200 mm, width ft = 90 mm, constant thickness a = 15 mm, and B = 19.2e. Use = 32.6 × 106 mm4 and I2= 2.4 × 10e mm4 from Example D-7arrow_forward
- A U-shaped cross section of constant thickness is shown in the figure. Derive the following formula for the distance e from the center of the semicircle to the shear center. Also, plot a graph showing how the distance e (expressed as the non dimensional ratio e/r varies as a function of the ratio b/r. (Let b/r range from 0 to 2.)arrow_forwardA beam has a bending moment of 4.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3.1 cm and internal diameter 2.1 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis Solution: - The bending stress at the point 0.6 cm from the neutral axis isarrow_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_forward
- B d₁ dz A M₁ d3 A copper core is bonded to a steel tube. The inner and outer diameters of the steel tube are d₂ = 90 mm and da = 45 mm, respectively. The copper and steel have shear moduli of Geu = 24 GPa and Gst = 75 GPa. If a moment of M₁ = 600 Nm is applied at the end of the composite shaft, find a. The portion of the applied moment carried by the steel tube Tat= Nm b. The portion of the applied moment carried by the copper core Teu = Nm c. The maximum shear stress in the steel tube Tst= MPa d. The maximum shear stress in the copper core Tex = MPaarrow_forwardA leaf spring 75 cm long is required to carry a central load of 8 kN. If the central deflection is not to exceed 2 cm and bending stress no greater than 200 MPa, determine the thickness, width and number of plates. Also compute the radius to which plates should be curved. As- sume width of plate to be 12 times its thickness and E = 200 GPa.arrow_forward6. Compute the maximum shear stress and the statical moment for a steel rod with a diameter of 10 in, with a maximum moment of 520 lb ft and a maximum shear of 12 kips (see image below to see information regarding centroids). Data: D = 10 in M = 520 lb-ft V = 12 kips Solution: 1= Ap πT Dª = 64 1 = 490.87 in¹ · (H-DP-²) = Tmax= 2D y === 2.12 in 3m Q=A, y = 83.33 in³ = 39.27 in² V.Q 1 t = 203.72 psi Circular Ap. y= 2D 3marrow_forward
- Consider the beam shown in sketch below, hinge supported at point A and roller supported at point D. The beam is subjected to a uniformly distributed load of 30 kiloNewtons per meter from points C to D and a concentrated load of 20 kiloNewtons applied at point B. The beam cross section is as shown in the sketch on the right. Determine the maximum tensile and compressive bending stresses in the beam.arrow_forwardA steel cantilever beam of length L = 1m has a hollow rectangular cross section. The outside width and height of the cross section are b = 100mm and h = 271mm respectively and the wall thickness is 8mm. A point force of 212kN is applied at the free end of the cantilever beam. The yield strength of the steel is 290MPa. The coordinates of Point H are x = -75mm, y = 0mm, z = -46mm. Please help me calculate the factors of safety predicted at point H by the maximum shear stress theory of failure. (Tresca criterion)arrow_forwardA shaft is subjected to a bending load of 50 kN , and a torsion moment of 275000 N.mm as shown in the figure below. Design the outer and inner diameter of the shaft, Oall = 180 Mpa T= 275000 N.mm | P= 500 N L=25 cmarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Everything About COMBINED LOADING in 10 Minutes! Mechanics of Materials; Author: Less Boring Lectures;https://www.youtube.com/watch?v=N-PlI900hSg;License: Standard youtube license