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 7.7.25P: On the surface of a structural component in a space vehicle, the strains arc monitored by means of...
Related questions
Concept explainers
Need help with this Mechanics of Materials review
Transcribed Image Text: General Equations of Plane Strain
Learning Goal:
To become familiar with the general equations of plane
strain used for determining in-plane principal strain,
maximum in-plane shear strain, and average normal
strain.
The state of strain at a point has components of
€ = 400.0 × (10-6), y = −215.0 × (10-6), and
Yzy = 200.0x (10–6).
Part A - Equivalent in-plane strains on the oriented element
Determine the equivalent in-plane strains on an element rotated counterclockwise at an angle of 0 = 60.0°
Express your answers, separated by commas, to three significant figures.
► View Available Hint(s)
AΣo↓↑ vec
?
€2¹, Cy', Ya'y' = 25.35 • 10¯6,159.64 • 10¯6, − 316.3 • 10¯6
Submit Previous Answers
X Incorrect; Try Again; 7 attempts remaining
Part B - In-plane principal strains on the oriented element
Determine the in-plane principal strains on the oriented element.
Branch of science that deals with the stationary and moving bodies under the influence of forces.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 7 images
