Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 2 Terms (12 Months) Printed Access Card
9th Edition
ISBN: 9781337594301
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 7, Problem 7.5.6P
A cast-iron plate in biaxial stress is subjected to tensile stresses σx= 31 MPa and σy. = 17 MPa (see figure). The corresponding strains in the plate are
Determine Poisson’s ratio v and the modulus of elasticity C for the material.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
A very thin rectangular plate (see figure (a)) is subjected to a biaxial plane stress state (σx, σy). The width and height of the plate are b = 7.5 [in] and h = 2.5 [in], respectively. The measures show that the strains in the (x, y) directions are εxx = 2.85x10−4 and εyy = −1.90x10−4, respectively. Figure (b) shows a 2D front view of the plate.
Calculate
i) The increment ΔL = Lfinal - Linitial in the length of the diagonal Od.
ii) The change ΔΦ = Φfinal - Φinitial of the angle formed between the diagonal Od and the x axis.
iii) The change ΔΨ = Ψfinal - Ψinitial of the angle formed between the diagonal Od and the y axis.
Note: remember that in a plane stress state we have σz = τxz = τyz = 0 and if it is also bi-axialwe have τyx = 0.
4. A rigid steel bar is supported by three circular rods as shown in Figure below. There is no
strain in the rods before the load P is applied. After load P is applied,
in rod (2) is 1,090 µ. Assume initial rod lengths of L1 = 3400mm. and L2 = 1800mm.
Assuming the system is symmetrical, determine:
a. The normal strain in rods (1).
b. The normal strain in rods (1) if there is a 2mm gap in the connections between
normal strain
the rigid bar and rods (1) at joints A and C before the load is applied.
c. The normal strain in rods (1) if there is a 2mm gap in the connection between
the rigid bar and rod (2) at joint B before the load is applied.
(1)
(1)
(2)
L
Rigid har
O O
QUESTION 2
The rigid bar ACE is supported by two steel rods AB and CD (Esteel = 200 GPa) with the
cross sectional areas of each rod is given as shown in Figure Q2.
(a) Determine the position d of the 30 kN load so that the average normal stress in each rod
is the same.
(b) Find the strain in rod CD, ɛcD
(c) Determine the horizontal displacement of point E
1.2 m
ACD = 600 mm?
0.8 m
E
30 kN
AAB = 900 mm2
d
B
1.8 m
Figure Q2
Chapter 7 Solutions
Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 2 Terms (12 Months) Printed Access Card
Ch. 7 - An clement m plane stress from the frame of a...Ch. 7 - Solve the preceding problem for an element in...Ch. 7 - The stresses on an element are sx= 1000 Psi. sy=...Ch. 7 - .4 The stresses on an clement arc known to be sx=...Ch. 7 - The stresses acting on element A on the web of a...Ch. 7 - Solve the preceding problem if the stresses acting...Ch. 7 - The stresses acting on element B on the web of a...Ch. 7 - An element in plane stress on the fuselage of an...Ch. 7 - The stresses acting on element B (see figure part...Ch. 7 - Solve the preceding problem if the normal and...
Ch. 7 - The polyethylene liner of a settling pond is...Ch. 7 - Solve the preceding problem if the norm al and...Ch. 7 - Two steel rods are welded together (see figure):...Ch. 7 - Repeat the previous problem using ? = 50° and...Ch. 7 - A rectangular plate of dimensions 3.0 in. × 5.0...Ch. 7 - Solve the preceding problem for a plate of...Ch. 7 - A simply supported beam is subjected to point load...Ch. 7 - Repeat the previous problem using sx= 12 MPa.Ch. 7 - At a point on the surface of an elliptical...Ch. 7 - Solve the preceding problem for sx= 11 MPa and...Ch. 7 - An clement m plane stress from the frame of a...Ch. 7 - Solve the preceding problem for the element shown...Ch. 7 - : A gusset plate on a truss bridge is in plane...Ch. 7 - The surface of an airplane wing is subjected to...Ch. 7 - At a point on the web of a girder on an overhead...Ch. 7 - -26 A rectangular plate of dimensions 125 mm × 75...Ch. 7 - -27 A square plate with side dimension of 2 in. is...Ch. 7 - The stresses acting on an element are x= 750 psi,...Ch. 7 - Repeat the preceding problem using sx= 5.5 MPa....Ch. 7 - An element in plane stress is subjected to...Ch. 7 - -4. - An element in plane stress is subjected to...Ch. 7 - An element in plane stress is subjected to...Ch. 7 - The stresses acting on element A in the web of a...Ch. 7 - The normal and shear stresses acting on element A...Ch. 7 - An element in plane stress from the fuselage of an...Ch. 7 - -9The stresses acting on element B in the web of a...Ch. 7 - The normal and shear stresses acting on element B...Ch. 7 - ‘7.3-11 The stresses on an element are sx= -300...Ch. 7 - - 7.3-12 A simply supported beam is subjected to...Ch. 7 - A shear wall in a reinforced concrete building is...Ch. 7 - The state of stress on an element along the...Ch. 7 - -15 Repeat the preceding problem using ??. = - 750...Ch. 7 - A propeller shaft subjected to combined torsion...Ch. 7 - 3-17 The stresses at a point along a beam...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - At a point on the web of a girder on a gantry...Ch. 7 - The stresses acting on a stress element on the arm...Ch. 7 - The stresses at a point on the down tube of a...Ch. 7 - An element in plane stress on the surface of an...Ch. 7 - A simply supported wood beam is subjected to point...Ch. 7 - A simply supported wood beam is subjected to point...Ch. 7 - Prob. 7.4.1PCh. 7 - .4-2 An element in uniaxial stress is subjected to...Ch. 7 - An element on the gusset plate in Problem 7.2-23...Ch. 7 - An element on the top surface of the fuel tanker...Ch. 7 - An element on the top surface of the fuel tanker...Ch. 7 - An element in biaxial stress is subjected to...Ch. 7 - • - 7.4-7 An element on the surface of a drive...Ch. 7 - - A specimen used in a coupon test has norm al...Ch. 7 - A specimen used in a coupon test is shown in the...Ch. 7 - The rotor shaft of a helicopter (see figure part...Ch. 7 - An element in pure shear is subjected to stresses...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - Prob. 7.4.13PCh. 7 - An clement in plane stress is subjected to...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - Prob. 7.4.17PCh. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - Prob. 7.4.20PCh. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - Through 7.4-25 An clement in plane stress is...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - through 7.4-25 An clement in plane stress is...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - 1 A rectangular steel plate with thickness t = 5/8...Ch. 7 - Solve the preceding problem if the thickness of...Ch. 7 - The state of stress on an element of material is...Ch. 7 - An element of a material is subjected to plane...Ch. 7 - Assume that the normal strains x and y , for an...Ch. 7 - A cast-iron plate in biaxial stress is subjected...Ch. 7 - Solve the preceding problem for a steel plate with...Ch. 7 - • - 3 A rectangular plate in biaxial stress (see...Ch. 7 - Solve the preceding problem for an aluminum plate...Ch. 7 - A brass cube of 48 mm on each edge is comp ressed...Ch. 7 - 7.5-11 in. cube of concrete (E = 4.5 X 106 psi. v...Ch. 7 - -12 A square plate of a width h and thickness t is...Ch. 7 - Solve the preceding problem for an aluminum plate...Ch. 7 - A circle of a diameter d = 200 mm is etched on a...Ch. 7 - The normal stress on an elastomeric rubber pad in...Ch. 7 - A rubber sheet in biaxial stress is subjected to...Ch. 7 - An element of aluminum is subjected to tri-axial...Ch. 7 - An element of aluminum is subjected to tri- axial...Ch. 7 - -3 An element of aluminum in the form of a...Ch. 7 - Solve the preceding problem if the element is...Ch. 7 - A cube of cast iron with sides of length a = 4.0...Ch. 7 - Solve the preceding problem if the cube is granite...Ch. 7 - An element of aluminum is subjected to iriaxial...Ch. 7 - Prob. 7.6.8PCh. 7 - A rubber cylinder R of length L and cross-...Ch. 7 - A block R of rubber is confined between plane...Ch. 7 - -11 A rubber cube R of a side L = 3 in. and cross-...Ch. 7 - A copper bar with a square cross section is...Ch. 7 - A solid spherical ball of magnesium alloy (E = 6.5...Ch. 7 - A solid steel sphere (E = 210 GPa, v = 0.3) is...Ch. 7 - Prob. 7.6.15PCh. 7 - An element of material in plain strain has the...Ch. 7 - An clement of material in plain strain has the...Ch. 7 - An element of material in plain strain is...Ch. 7 - An element of material in plain strain is...Ch. 7 - A thin rectangular plate in biaxial stress is...Ch. 7 - Prob. 7.7.6PCh. 7 - A thin square plate in biaxial stress is subjected...Ch. 7 - Prob. 7.7.8PCh. 7 - An clement of material subjected to plane strain...Ch. 7 - Solve the preceding problem for the following...Ch. 7 - The strains for an element of material in plane...Ch. 7 - Solve the preceding problem for the following...Ch. 7 - An clement of material in plane strain (see...Ch. 7 - Solve the preceding problem for the following...Ch. 7 - A brass plate with a modulus of elastici ty E = 16...Ch. 7 - Solve the preceding problem if the plate is made...Ch. 7 - An element in plane stress is subjected to...Ch. 7 - Prob. 7.7.18PCh. 7 - During a test of an airplane wing, the strain gage...Ch. 7 - A strain rosette (see figure) mounted on the...Ch. 7 - A solid circular bar with a diameter of d = 1.25...Ch. 7 - A cantilever beam with a rectangular cross section...Ch. 7 - Solve the preceding problem if the cross-...Ch. 7 - A 600 strain rosette, or delta rosette, consists...Ch. 7 - On the surface of a structural component in a...Ch. 7 - - 7.2-26 The strains on the surface of an...Ch. 7 - Solve Problem 7.7-9 by using Mohr’s circle for...Ch. 7 - 7.7-28 Solve Problem 7.7-10 by using Mohr’s circle...Ch. 7 - Solve Problem 7.7-11 by using Mohr’s circle for...Ch. 7 - Solve Problem 7.7-12 by using Mohr’s circle for...Ch. 7 - Solve Problem 7.7-13 by using Mohr’s circle for...Ch. 7 - Prob. 7.7.32P
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
- An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 × l0-6, and yxy= 420 × l0-6. Determine the following quantities: (a) the strains for an element oriented at an angle 0 = 75°, (b) the principal strains, and (c) the maximum shear strains. Show the results on sketches of properly oriented elements.arrow_forwardA circular aluminum tube of length L = 600 mm is loaded in compression by forces P (see figure). The outside and inside diameters are d2= 75 mm and d1= 63 mm, respectively. A strain gage is placed on the outside of the lube to measure normal strains in the longitudinal direction. Assume that E = 73 GPa and Poissons ratio is v = 0.33. (a) IF the compressive stress in the tube is 57 MPa, what is the load P? (b) If the measured strain is e = 78 J X 10-6, what is the shorteningarrow_forwardThe strains for an element of material in plane strain (see figure) are as follows: x = 480 ×10-6. y = 140 × l0-6, and xy = —350 x 10”. Determine the principals strains and maximum shear strains, and show these strains on sketches of properly oriented elements.arrow_forward
- An element of a material is subjected to plane stresses as shown in the figure. The stresses o, cry., and are 10 MPa, —15 MPa, and 5 MPa. respectively. Assume E = 200 GPa and v = 0.3. (a) Calculate the normal strain in the x, v. and z directions and the shear strain. (b) Calculate the strain-energy density of the element.arrow_forwardPlastic bar of diameter d = 32 mm is compressed in a testing device by a Force P = 190 N that is applied as shown in the figure. (a) Determine the normal and shear stresses acting: on all faces of stress elements oriented at (1 ) an angle 8 = 00, (2) an angle ?? = 22.5s, and (3) an angle ?? = 45°. In each case, show the stresses on a sketch of a properly oriented element. What are smaxtmax (b) Find smax and tmax in the plastic bar if a re-cantering spring of stiffness k is inserted into the testing device, as shown in the figure. The spring stillness is 1/6 of the axial stiffness of the plastic bar.arrow_forwardA cube of cast iron with sides of length a = 4.0 in. (see figure) is tested in a laboratory under triaxialsire.ss. Gages mounted on the testing machine show that the compressive strains in the material arc a = -225 X l06and,ay = 37.5 X l0_. Determine the following quantities: (a) the norm al stresses i. r,.. and acting on the x, y, and z faces of the cube; (b) the maximum shear stress r in the material; (C) the change ..W in the volume of the cube: (d) the strain energy U stored in the cube; (e) the maximum value of s when the change in volume must be limited to O.O28%; and (f) the required value of when the strain energy must be 38 in.-lb. (Assume £ = 14,000 ksi and v = 0.25.)arrow_forward
- A 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_forward- 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction?arrow_forwardA slightly tapered bar AB of rectangular cross section and length L is acted upon by a force P (see figure). The width of the bar varies uniformly From b2at end A to b1at end B. The thickness t is constant. (a) Determine the strain energy U of the bar. (b) Determine the elongation ?? of the bar by equating the strain energy to the work done by the force P.arrow_forward
- An aluminum bar subjected to tensile Forces P has a length L = 150 in. and cross-sectional area A = 2.0 in2 The stress-strain behavior of the aluminum may be represented approximately by the bilinear stress-strain diagram shown in the figure. Calculate the elongation S of the bar for each of the following axial loads: p = 8 kips, 16 kips. 24 kips, 32 kips, and 40 kips. From these results, plot a diagram of load P versus elongation S (load-displacement diagram).arrow_forwardA three-story steel column in a building supports roof and floor loads as shown in the figure. The story height H is 10.5 ft. the cross-sectional area A of the column is 15.5 in2, and the modulus of elasticity E of the steel is 30 × 106 psi. Calculate the strain energy U of the column assuming P1= 40 kips and P2= P3= 60 kips.arrow_forwardA copper bar with a rectangular cross section is held without stress between rigid supports (see figure). Subsequently, the temperature of the bar is raised 50°C (a) Determine the stresses on all faces of the elements A and B, and show these stresses on sketches of the elements. (Assume = 17.5 × 10-6/? and E = 120 GPa ) (b) If the shear stress at B is known to be 48 MPa at some inclination 8, find anglearrow_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
An Introduction to Stress and Strain; Author: The Efficient Engineer;https://www.youtube.com/watch?v=aQf6Q8t1FQE;License: Standard YouTube License, CC-BY