1 Tension, Compression, And Shear 2 Axially Loaded Members 3 Torsion 4 Shear Forces And Bending Moments 5 Stresses In Beams (basic Topics) 6 Stresses In Beams (advanced Topics) 7 Analysis Of Stress And Strain 8 Applications Of Plane Stress (pressure Vessels, Beams, And Combined Loadings) 9 Deflections Of Beams 10 Statically Indeterminate Beams 11 Columns Chapter7: Analysis Of Stress And Strain
Chapter Questions Section: Chapter Questions
Problem 7.2.1P: An clement m plane stress from the frame of a racing car is oriented at a known angle 8 (sec... Problem 7.2.2P: Solve the preceding problem for an element in plane stress on the bottom surface of a fuel tanker... Problem 7.2.3P: The stresses on an element are sx= 1000 Psi. sy= 500 psi, and txy= 350 psi. Find the stresses acting... Problem 7.2.4P: .4 The stresses on an clement arc known to be sx= 120 MPa, sy= 100 MPa, and txy= 75 MPa. Find the... Problem 7.2.5P: The stresses acting on element A on the web of a train rail (sec figure part a) a re found to be... Problem 7.2.6P: Solve the preceding problem if the stresses acting on element A on the web of a train rail (see... Problem 7.2.7P: The stresses acting on element B on the web of a train rail (see figure part a of Problem 7.2-5) arc... Problem 7.2.8P: An element in plane stress on the fuselage of an airplane (figure part a) is subjected to... Problem 7.2.9P: The stresses acting on element B (see figure part a) on the web of a wide-flange beam are found to... Problem 7.2.10P: Solve the preceding problem if the normal and shear stresses acting on element B are 56 MPa, 17 MPa,... Problem 7.2.11P: The polyethylene liner of a settling pond is subjected to stresses ax= 350 psi. a = 112 psi. and =... Problem 7.2.12P: Solve the preceding problem if the norm al and shear stresses acting on the element are sx = 2100... Problem 7.2.13P: Two steel rods are welded together (see figure): the seam is oriented at angle ? = 50°. The stresses... Problem 7.2.14P: Repeat the previous problem using ? = 50° and stresses on the rotated element: sy1= 70 MPa, ??y1=-82... Problem 7.2.15P: A rectangular plate of dimensions 3.0 in. × 5.0 in. is formed by welding two triangular plates (see... Problem 7.2.16P: Solve the preceding problem for a plate of dimensions 100 mm × 250 mm subjected to a compressive... Problem 7.2.17P: A simply supported beam is subjected to point load P at mid-span. The normal stress on an element at... Problem 7.2.18P: Repeat the previous problem using sx= 12 MPa. Problem 7.2.19P: At a point on the surface of an elliptical exercise machine, the material is in biaxial stress with... Problem 7.2.20P: Solve the preceding problem for sx= 11 MPa and ??y= -20 MPa (see figure). Problem 7.2.21P: An clement m plane stress from the frame of a racing car is oriented at a known angle 8 (sec... Problem 7.2.22P: Solve the preceding problem for the element shown in the figure. Problem 7.2.23P: : A gusset plate on a truss bridge is in plane stress with normal stresses axand a and shear stress... Problem 7.2.24P: The surface of an airplane wing is subjected to plane stress with normal stresses x and cr and shear... Problem 7.2.25P: At a point on the web of a girder on an overhead bridge crane in a manufacturing facility, the... Problem 7.2.26P: -26 A rectangular plate of dimensions 125 mm × 75 mm is subjected to tensile stress sy= 67 kPa and... Problem 7.2.27P: -27 A square plate with side dimension of 2 in. is subjected to compressive stress a and tensile... Problem 7.3.1P: The stresses acting on an element are x= 750 psi, y= 600 psi, and xy = 400 psi. Determine the... Problem 7.3.2P: Repeat the preceding problem using sx= 5.5 MPa. ??y= 4 MPa. and txy= 3.2 MPa. Problem 7.3.3P: An element in plane stress is subjected to stresses ??x= 5750 psi, sy = 1100 psi, and txy= 750 psi... Problem 7.3.4P: -4. - An element in plane stress is subjected to stresses ??x= 105 MPa, ??y= 75 MPa, and sxy= 25 MPa... Problem 7.3.5P: An element in plane stress is subjected to stresses sx= -5500 psi, sy= -2000 psi, and Tx. = 1900 psi... Problem 7.3.6P: The stresses acting on element A in the web of a train rail are found to be 40 M Pa tension in the... Problem 7.3.7P: The normal and shear stresses acting on element A are 6500 psi, 17,300 psi, and 2900 psi (see the... Problem 7.3.8P: An element in plane stress from the fuselage of an airplane is subjected to compressive stresses of... Problem 7.3.9P: -9The stresses acting on element B in the web of a wide-flange beam are found to be 14,000 psi... Problem 7.3.10P: The normal and shear stresses acting on element B are ??x= -46 MPa, sy= -13 MPa, and txy= 21 MPa... Problem 7.3.11P: ‘7.3-11 The stresses on an element are sx= -300 psi and sy= 600 psi. Find the maximum shear stresses... Problem 7.3.12P: - 7.3-12 A simply supported beam is subjected to two point loads as shown in the figure. The... Problem 7.3.13P: A shear wall in a reinforced concrete building is subjected to a vertical uniform load of intensity... Problem 7.3.14P: The state of stress on an element along the hydraulic lift cylinder on a truck is trv= — 5 MPaLFind... Problem 7.3.15P: -15 Repeat the preceding problem using ??. = - 750 psi. Problem 7.3.16P: A propeller shaft subjected to combined torsion and axial thrust is designed to resist a shear... Problem 7.3.17P: 3-17 The stresses at a point along a beam supporting a sign (see figure) are sx= 2250 psi, sy,. =... Problem 7.3.18P: -18 through 7.3-22 An element in plane stress (see figure) is subjected to stresses o, a., and (a)... Problem 7.3.19P: -18 through 7.3-22 An element in plane stress (see figure) is subjected to stresses o, a., and (a)... Problem 7.3.20P: -18 through 7.3-22 An element in plane stress (see figure) is subjected to stresses o, a., and (a)... Problem 7.3.21P: -18 through 7.3-22 An element in plane stress (see figure) is subjected to stresses o, a., and (a)... Problem 7.3.22P: -18 through 7.3-22 An element in plane stress (see figure) is subjected to stresses o, a., and (a)... Problem 7.3.23P: At a point on the web of a girder on a gantry crane, the stresses acting on the x face of a stress... Problem 7.3.24P: The stresses acting on a stress element on the arm of a power excavator (see figure) are ax= 52 MPa... Problem 7.3.25P: The stresses at a point on the down tube of a bicycle frame are trx= 4800 psi and t = -1950 psi (see... Problem 7.3.26P: An element in plane stress on the surface of an automobile drive shaft (see figure) is subjected to... Problem 7.3.27P: A simply supported wood beam is subjected to point load P at mid-span. The stresses on element C are... Problem 7.3.28P: A simply supported wood beam is subjected to point load P at mid-span. The normal stress on element... Problem 7.4.1P Problem 7.4.2P: .4-2 An element in uniaxial stress is subjected to tensile stresses sx= 57 MPa. as shown in the... Problem 7.4.3P: An element on the gusset plate in Problem 7.2-23 in uniuxial stress is subjected to compressive... Problem 7.4.4P: An element on the top surface of the fuel tanker in Problem 7.2-1 is in biaxial stress and is... Problem 7.4.5P: An element on the top surface of the fuel tanker in Problem 7.2-1 is in biaxial .is in the and is... Problem 7.4.6P: An element in biaxial stress is subjected to stresses a = -29 MPa and sy = 57 MPa. as shown in the... Problem 7.4.7P: • - 7.4-7 An element on the surface of a drive shaft is in pure shear and is subjected to stresses... Problem 7.4.8P: - A specimen used in a coupon test has norm al stress ??. = 15 MPa (see figure). Using Mohr’s... Problem 7.4.9P: A specimen used in a coupon test is shown in the figure. The stresses on element A are known to be... Problem 7.4.10P: The rotor shaft of a helicopter (see figure part a) drives the rotor blades that provide the lifting... Problem 7.4.11P: An element in pure shear is subjected to stresses ??xy= 3750 psi, as shown in the figure. Using... Problem 7.4.12P: An clement in plane stress is subjected to stresses a,. cry, and (see figure). Using Mohr’s circle,... Problem 7.4.13P Problem 7.4.14P: An clement in plane stress is subjected to stresses a,. cry, and (see figure). Using Mohr’s circle,... Problem 7.4.15P: An clement in plane stress is subjected to stresses a,. cry, and (see figure). Using Mohr’s circle,... Problem 7.4.16P: An clement in plane stress is subjected to stresses a, and (see figure). Using Mohr’s circle,... Problem 7.4.17P Problem 7.4.18P: -18 through 7.4-25 An clement in plane stress is subjected to stresses ax,ay., and txy. (see... Problem 7.4.19P: -18 through 7.4-25 An clement in plane stress is subjected to stresses sx,??y, and r. (see figure).... Problem 7.4.20P Problem 7.4.21P: -18 through 7.4-25 An clement in plane stress is subjected to stresses a,, ay., and axy. (see... Problem 7.4.22P: Through 7.4-25 An clement in plane stress is subjected to stresses x,y, and r. (see figure). Using... Problem 7.4.23P: -18 through 7.4-25 An clement in plane stress is subjected to stresses sx,??y, and r. (see figure).... Problem 7.4.24P: through 7.4-25 An clement in plane stress is subjected to stresses sx,??y,and txy. (see figure).... Problem 7.4.25P: -18 through 7.4-25 An clement in plane stress is subjected to stresses sx,,sy., andtxy(see figure).... Problem 7.5.1P: 1 A rectangular steel plate with thickness t = 5/8 in. is subjected to uniform normal stresses a and... Problem 7.5.2P: Solve the preceding problem if the thickness of the steel plate is. t = 12 mm. the gage readings are... Problem 7.5.3P: The state of stress on an element of material is shown in the figure. Calculate the unit volume... Problem 7.5.4P: An element of a material is subjected to plane stresses as shown in the figure. The stresses o,... Problem 7.5.5P: Assume that the normal strains x and y , for an clement in plane stress (see figure) are measured... Problem 7.5.6P: A cast-iron plate in biaxial stress is subjected to tensile stresses x= 31 MPa and y. = 17 MPa (see... Problem 7.5.7P: Solve the preceding problem for a steel plate with x= 11,600 psi (tension). y= -5700 psi... Problem 7.5.8P: • - 3 A rectangular plate in biaxial stress (see figure) is subjected to normal stresses u = 67 MPa... Problem 7.5.9P: Solve the preceding problem for an aluminum plate with sx= 12,000 psi (tension). sy= -3000 psi... Problem 7.5.10P: A brass cube of 48 mm on each edge is comp ressed in two perpendicular directions by forces P = 160... Problem 7.5.11P: 7.5-11 in. cube of concrete (E = 4.5 X 106 psi. v = 0.2) is compressed in biaxial stress by means of... Problem 7.5.12P: -12 A square plate of a width h and thickness t is Loaded by normal forces Pxand P and by shear... Problem 7.5.13P: Solve the preceding problem for an aluminum plate with h = 10 in.. i = 0.75 in., E = 10,600 ksi, v =... Problem 7.5.14P: A circle of a diameter d = 200 mm is etched on a brass plate (see figure). The plate has dimensions... Problem 7.5.15P: The normal stress on an elastomeric rubber pad in a test machine is av= — 100 psi (sec figure).... Problem 7.5.16P: A rubber sheet in biaxial stress is subjected to tensile stresses ax= 270 Pa ander,. = 144 Pa. The... Problem 7.6.1P: An element of aluminum is subjected to tri-axial stresses. Calculate the strains in the element in... Problem 7.6.2P: An element of aluminum is subjected to tri- axial stresses. Calculate the strains in the element in... Problem 7.6.3P: -3 An element of aluminum in the form of a rectangular parallelepiped (see figure) of dimensions a =... Problem 7.6.4P: Solve the preceding problem if the element is steel (E = 200 GPa. p = 0.30) with dimensions a = 300... Problem 7.6.5P: A cube of cast iron with sides of length a = 4.0 in. (see figure) is tested in a laboratory under... Problem 7.6.6P: Solve the preceding problem if the cube is granite (E = 80 GPa, v = 0.25) with dimensions E = 89 mm... Problem 7.6.7P: An element of aluminum is subjected to iriaxial stress (see figure). (a) Find the bulk modulus A^for... Problem 7.6.8P Problem 7.6.9P: A rubber cylinder R of length L and cross- sectional area A is compressed inside a steel cylinder S... Problem 7.6.10P: A block R of rubber is confined between plane parallel walls of a steel block S (see figure). A... Problem 7.6.11P: -11 A rubber cube R of a side L = 3 in. and cross- sectional area A = 9 in2 is compressed inside a... Problem 7.6.12P: A copper bar with a square cross section is inserted into a square rigid tube as shown in the... Problem 7.6.13P: A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean... Problem 7.6.14P: A solid steel sphere (E = 210 GPa, v = 0.3) is subjected to hydrostatic pressure p such that its... Problem 7.6.15P Problem 7.7.1P: An element of material in plain strain has the following strains: x = 0.001 and y = 0.0015. (a)... Problem 7.7.2P: An clement of material in plain strain has the following strains: x = 0.002 and, y = 0.0015. (a)... Problem 7.7.3P: An element of material in plain strain is subjected to shear strain xy = 0.0003. (a) Determine the... Problem 7.7.4P: An element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy =... Problem 7.7.5P: A thin rectangular plate in biaxial stress is subjected to stresses axand t7v, as shown in part a of... Problem 7.7.6P Problem 7.7.7P: A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the... Problem 7.7.8P Problem 7.7.9P: An clement of material subjected to plane strain (see figure) has strains of x=280106 , y=420106 ,... Problem 7.7.10P: Solve the preceding problem for the following data: x=190106,y=230106,xy=160106,and=45. Problem 7.7.11P: The strains for an element of material in plane strain (see figure) are as follows: x = 480 ×10-6. y... Problem 7.7.12P: Solve the preceding problem for the following strains: x=120106,y=450106,andxy=360106. Problem 7.7.13P: An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 ×... Problem 7.7.14P: Solve the preceding problem for the following data: x=1120106,y=430106,xy=780106,and=45. 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... Problem 7.7.16P: Solve the preceding problem if the plate is made of aluminum with E = 72 GPa and Poisson’s ratio v =... Problem 7.7.17P: An element in plane stress is subjected to stresses ?? = -8400 psi, ??y = 1100 psi, and (see... Problem 7.7.18P Problem 7.7.19P: During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as... Problem 7.7.20P: A strain rosette (see figure) mounted on the surface of an automobile frame gives the following... Problem 7.7.21P: A solid circular bar with a diameter of d = 1.25 in. is subjected to an axial force P and a torque... Problem 7.7.22P: A cantilever beam with a rectangular cross section (width b = 20 mm, height Ii = 175 mm) is loaded... Problem 7.7.23P: Solve the preceding problem if the cross- sectional dimensions are b = 1.5 in. and h = 5.0 in., the... Problem 7.7.24P: A 600 strain rosette, or delta rosette, consists of three electrical-resistance strain gages... Problem 7.7.25P: On the surface of a structural component in a space vehicle, the strains arc monitored by means of... Problem 7.7.26P: - 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v... Problem 7.7.27P: Solve Problem 7.7-9 by using Mohr’s circle for plane strain. Problem 7.7.28P: 7.7-28 Solve Problem 7.7-10 by using Mohr’s circle for plane strain. Problem 7.7.29P: Solve Problem 7.7-11 by using Mohr’s circle for plane strain. Problem 7.7.30P: Solve Problem 7.7-12 by using Mohr’s circle for plane strain. Problem 7.7.31P: Solve Problem 7.7-13 by using Mohr’s circle for plane strain. Problem 7.7.32P Problem 7.7.3P: An element of material in plain strain is subjected to shear strain xy = 0.0003. (a) Determine the...
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Transcribed Image Text: The state of strain at a point on a wrench has
components € = 120(106), -180(10-6),
Ey
Yry = 150(10-6). Use Mohr's circle to solve the problem.
Part A
Determine the in-plane principal strains.
Express your answers using three significant figures separated by a comma.
VAΣo↓↑vec
?
€1, €2 =
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Part B
Determine the orientations of the element at which the principal strains occur.
Express your answers using three significant figures separated by a comma.
VAΣ vec
?
Op₁¹ , Өрг
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Branch of science that deals with the stationary and moving bodies under the influence of forces.
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