Derive the following equation for computing shear stress in a solid bar along an oblique plane with angle B with respect to the vertical plane. The bar is subjected to centric axial loading. P sin 0 cos 0 A. T = -

Derive the following equation for computing shear stress in a solid bar along an oblique plane with angle B with respect to the vertical plane. The bar is subjected to centric axial loading. P sin 0 cos 0 A. T = -

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.7.15P: A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded...

See similar textbooks

Related questions

Q: Problem 1 (6-1 , Eringen) Prove that in a nonlinear, isotropic, elastic solid the only possible…

A: given; prove that in a nonlinear ,isotropic , elastic solid the only possible initial stress is a…

Q: A 100in. diameter cylinder (closed ends) made of a material having an allowable yield strength in…

A: The given data are: d=100 inτ=10000 psiP=300 psi Here, d, τ, and P represent the diameter, allowable…

Q: ort square is 1 1/2 inches x 1 1/2 inches in cross section. it is on an axial tensile load of 11,000…

Q: 2) A simply supported timber beam with a rectangular cross-section has been loaded perpendicular to…

A: Given beam:

Q: 1) A rectangular plate is under biaxial stress o, = 65 MPa (tensile) and ay = 20 MPa %3D…

Q: 5 (a) A steel bar is subjected to a sequence of completely reversed stress cycles which vary over a…

A: Given , Endurance Limit(Se) = 430 N/mm2 Completely reversed stress cycle, S1 = 570 N/mm2 S2 = 630…

Q: e state of stress at a point in a circular bar under pure torsion is given by T xy = T yx= t and…

Q: The data shown in the accompanying table are From a tensile test of high-strength steel. The test…

Q: 9-b) A circular bar is 0.200 m long and 25 mm diameter. It carries a load of 50 KN. Given that…

Q: Define the term maximum in-plane shear stress?

A: Consider the diagram shown below for the principal stresses at a point.

Q: An axially loaded bar has normal stress 173 MPa. The shear stress in the bar is

A: given data : Maximum principal stress (σ1)=173 MPaMinimum principal stress (σ2)=0

Q: According to the maximum strain energy hypothesis, what should be the length L2 in order for the…

A: Given dataTransverse load F1 = 18kNAxial load F2 = 20kNLarger diameter D = 58mmSmaller diameter d =…

Q: A bar is machined from steel and subjected to a static load of 5000 N. Assume the stress…

A: We can answer up to 3 subparts so we will answer first 3. Please resubmit the question by specifying…

Q: 1. As a section cut in a prismatic bar varies from 0 = 0° to 180° at what values of 0 will the…

A: To find:

Q: Safe stress for the steel bar shown in the figure is sigma(safe)= 160 MPa. According to The greatest…

Q: The formula for Critically Resolved Shear Stress is

Q: Ex 5.2: Calculate the lateral strain for a mild steel rod subjected to an axially load causing an…

A: Given data : The value of axial strain is given in question . Axial strain is strain along the…

Q: 2. A punch for making holes in steel plates is shown in Figure - 2 (a & b). Assume that a punch…

Q: Using the maximum-shear-stress (MSS) theory determine the factor of safety for a bar of AISI 1020…

A: Given Data σx = 199 MPa σy = 76 MPa

Q: Given the shear modulus(G) for aluminum as 2.4e+10 N/m2 and the shear strain is given as 6e-5. What…

A: From hook's law Shear stress is directly proportional to shear strain within elastic limit

Q: 8. Find the minimum size of a hole that can be punched in a 20 mm thick mild steel plate having an…

Q: A 6 mm thick plate is to be punched of a shape shown in figure. Determine the minimum punching force…

Q: A tool steel cylindrical specimen, 6 in. long and 0.25 in. in diameter, is kept rotating like a…

Q: Problem 1: For a 20-ply lay-up [(0/90)s]s in which ply thickness is 0.1 mm and stiffness is: 20. 0.7…

A: Solution: Given Data:

Q: 7 Principal stresses of a point in a critical section of a machine component are: ₁= 80 MPa 0₂= 5…

Q: PROBLEM 3 Steel: A = 500 mm ,= 120 MPa 1.8 Find the maximum allowable value of P for the column. The…

A: The normal stress developed inside a member when acted upon by an axial force ca be calculated using…

Q: 3. Which statement is correct? (1 pt) (a) Normal stress is proportional to normal strain (b) Shear…

A: 3) option a is correct.

Q: A 1.25 inch diameter hole is drilled on the centerline of a steel bar 3.5 inches wide by 3/8 inches…

Q: 2. In the stress-strain curve for steel shown below, identify following stresses in ksi and write…

A: Yeild point - Yeild point is the point at which the material will have an appreciable elongation…

Q: Copper has a rigidity modulus 45 GPa. A cube of copper with 500 mm sides i tubjected to a shear…

Q: 1.4-7 The data shown in the table below were obtained from a tensile test of high-strength steel.…

A: Only one question can be answered according to the rules. Kindly upload the other question to be…

Q: A rod specimen of ductile cast iron was tested in a torsion-testing machine. The rod diameter was 14…

Q: Problem #3 (5 points): A mechanical system is subjected to normal and shear forces that cause normal…

Q: 3. A circular steel bar is subjected to an axial compressive load of 175 kN. The bar has a diameter…

Q: Question: Consider that the fit between the elements shown in the Figure below is H6/s5. They are…

A: given data

Q: The state of stress shown below is from the surface of a bar under axial and torsion loading.…

A: Given data: The value of stress in x-direction is, σx=60 MPa. The value of stress in y-direction…

Q: PROBLEM NO. 4 In Fig. 4, determine the normal stress and change in length of the aluminum rod if the…

Q: Problem 9.51 In (Figure 1), Tzy = 55.3 MPa. Figure 80 MPa 1 of 1 > Part A Determine the principal…

Q: 12 in 14-in D -in R. 2 in C 1-in D. 15 in 1-in D. Figure (2-1) A stress element at A on the top…

A: For solution refer below images.

Q: n Figure 1, with its dimensions, loading status and material properties, different full circle…

A: Given data

Q: Calculate the maximum stress in a 25 mm thick perforated bar and show its location on the figure.…

Q: GPa, G = 83 GPa), the state of the stress is illustrated in the figure below. For the given plane…

Q: A bar of 6-mm in diameter is only allowed to decrease at a maximum of 3.96% of its total length.…

A: Givend=6mmdecrease in lenght ∆L=3.96%×LG=602 Mpaμ=0.20

Q: An axial bar fixed at both ends with no loads applied is subjected to an increase of temperature.…

Q: For a point on a steel specimen, the principal stresses o of 230 MPa and o2 of 15 MPa are given.…

Q: 214 GPa, G = 83 GPa), the state of the stress is illustrated in the figure below. For the given…

Concept explainers

Thermal Properties of Materials

In mechanical engineering, the thermal property is represented as the physical quantity that is relevant to the application of heat. The thermal properties are evaluated by variations in any specific material due to low heat or high heat. The quantities that influence the thermal property of the materials are mass, density, temperature, and many others.

Question

Derive the following equation for computing shear stress in a solid bar along an oblique plane
with angle B with respect to the vertical plane. The bar is subjected to centric axial loading.
sin 0 cos 0
T =
Ao

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Types of Properties of Engineering Materials

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) Solve part (a) of the preceding problem if the pressure is 8.5 psi, the diameter is 10 in., the wall thickness is 0,05 in., the modulus of elasticity is 200 psi, and Poisson's ratio is 0.48. (b) If the strain must be limited to 1.01, find the maximum acceptable inflation pressure
A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded in biaxial stress by normal stresses r and cry. (sec figure). A strain gage is bonded to the plate at an angle 4 = 350 If the stress o is 10,700 psi and the strain means used by the gageise = 390 X 106.whatisthcmax- imum in-plane shear stress (Tr, ),. and shear strain (>‘ ).? What is the maximum shear strain (y ) in the x-: plane? What is the maximum shear strain (y ).. in the y-r plane?
-4. - An element in plane stress is subjected to stresses ??x= 105 MPa, ??y= 75 MPa, and sxy= 25 MPa (see the figure for Problem 7.3-1). Determine the principal stresses and show them on a sketch of a properly oriented element.
A spherical steel pressure vessel (diameter 500 mm, thickness 10 mm) is coated with brittle lacquer that cracks when the strain reaches 150 X 10~ (see figure). (a) What internal pressure p will cause the lacquer to develop cracks? (Assume E = 205 GPa and v = 0.30.) (b) If the strain is measured at 125 x 10-6, what is the internal pressure at that point?
The rails of a railroad track are welded together at their ends (to form continuous rails and thus eliminate the clacking sound of the wheels) when the temperature is 60°F. What compressive stress ?? =6.5×10-6 /? is produced in the rails when they are heated by the sun to 120"F if the coefficient of thermal expansion a = the modulus of elasticity E = 30 × 106 psi?
Solve the preceding problem if the diameter is 480 mm, the pressure is 20 MPa, the yield stress in tension is 975 MPa, the yield stress in shear is 460 MPa, the factor of safety is 2,75, the modulus of elasticity is 210 GPa, Poissorfs ratio is 0.28, and the normal strain must not exceed 1190 x 10" . For part (b), assume that the tank thickness is 8 mm and the measured normal strain is 990 x 10~ .
- A specimen used in a coupon test has norm al stress ??. = 15 MPa (see figure). Using Mohr’s circle, find the state of stress on the element oriented at angle ? = 20° and show the full stress state on a sketch of a properly oriented element.
A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?
An aluminum bar has length L = 6 ft and diameter d = 1.375 in. The stress-strain curse for the aluminum is shown in Fig. 1.34. The initial straight, line part of the curve has a slope (modulus of elasticity) of 10.6 × 106 psi. The bar is loaded by tensile forces P = 44.6 k and then unloaded. (a) That is the permanent set of the bar? (b) If the bar is reloaded. what is the proportional limit? hint: Use the concepts illustrated in Figs. l.39b and 1.40.
A spherical balloon is filled with a gas. The outer diameter of the balloon is 20 in. and the thickness is 0,012 in. Calculate the maximum permissible pressure in the balloon if the allowable tensile stress and the allowable shear stress in the balloon are 1 ksi and 0.3 ksi, respectively.
A punch for making a slotted hole in ID cards is shown in the figure part a. Assume that the hole produced by the punch can be described as a rectangle (12 mm X 3 mm) with two half circles (r = 1.5 mm) on the left and the right sides. If P = 10 N and the thickness of the ID card is 1 mm, what is the average shear stress in the card?
At a point on the web of a girder on an overhead bridge crane in a manufacturing facility, the stresses arc known to be x = —4300 psi, a = 1700 psi, and r = 3100 psi (the sign convention for these stresses is shown in Fig, 7-1). A stress clement located at the same point in the structure (but oriented at a counterclockwise angle 0, with respect to the _y axis) is subjected to the stresses shown in the figure {b, r», and 2100 psi). Assuming that the angle 8Xis between zero and 90°, calculate the normal stress trA, the shear stress ta, and the angle Bv