中国大学Mechanics of Materials_3期末答案(慕课2023课后作业答案)

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Chapter 1: Stress

The中国作业 small quiz for Chapter 1

1、Mechanics of materials is 大学答案答案a study of the relationship between the ( ) applied to a body and the ( ) and ( ) caused by the ( ) within the body.
A、loads,期末 stress, strain, loads
B、external loads,慕课 stress, strain, internal loads
C、internal loads,课后 deformation, force, external loads
D、external loads,中国作业 force, deformation, internal loads

2、Linear distributed loadings produce a ( ) having a magnitude equal to the ( ),大学答案答案 and having a location that passes through the ( ).
A、resultant force,期末 external force, center of the area
B、force,慕课 external force, centroid of this area
C、resultant force,课后 area under the load diagram, centroid of this area
D、resultant force,中国作业 external force, centroid of this area

3、A support produces ( ) in a particular direction on its attached member if it prevents ( ) of the member in that direction,大学答案答案 and it produces ( ) on the member if it prevents ( ).
A、an external force,期末 translation, an external couple moment, rotation
B、an internal force,慕课 translation, an internal couple moment, rotation
C、an internal force,课后 movement, a couple moment, translation
D、an external force, translation, an internal couple moment, translation

4、The method of sections is used to determine the ( ) acting on the surface of the sectioned body. In general, these resultants consist of a ( ), ( ), ( ), and bending moment.
A、resultant loadings, force along x, a force along y axis, torsional moment
B、resultant loadings, normal force, shear force, external couple
C、external resultant loadings, normal force, shear force, torsional moment
D、internal resultant loadings, normal force, shear force, torsional moment

5、The intensity of the ( ) at a point in the body is referred to as stress. Stress is the ( ) value of force per unit area, as the area approaches ( ). For this definition, the material is considered to be ( ) and ( ).
A、internal force, limiting, zero, continuous, cohesive
B、external force, limiting, a specific value, continuous, cohesive
C、internal force, a fixed, zero, continuous, cohesive
D、external force, limiting, zero, discontinuous, linear

6、When a prismatic bar is made from ( ) and ( ) material, and is subjected to an axial force acting through the ( ) of the cross-sectional area, then the center region of the bar will deform ( ). As a result, the material will be subjected only to ( ). This stress is ( ) or averaged over the cross-sectional area.
A、unhomogeneous, anisotropic, centroid, uniformly, normal stress, uniform
B、homogeneous, isotropic, centroid, uniformly, normal stress, uniform
C、homogeneous, anisotropic, centroid, uniformly, shear stress, uniform
D、homogeneous, isotropic, centroid, uniformly, shear stress, nonuniform

7、When shear stress acts on a plane, then ( ) of a volume element of material at a point on the plane requires associated ( ) of the ( ) act on three adjacent sides of the element.
A、equilibrium, normal stress, same magnitude
B、equilibrium, shear stress, same magnitude
C、equilibrium, normal stress, same orientation
D、equilibrium, shear stress, same orientation

8、Design of a member for strength is based on selecting an ( ) that will enable it to safely support its intended load. Since there are many unknown factors that can influence the actual stress in a member, then depending upon the intended use of the member, ( ) is applied to obtain the ( ) the member can support.
A、allowable stress, a factor of safety, allowable load
B、allowable force, a factor of safety, allowable load
C、allowable force, a factor, allowable load
D、allowable stress, a factor, allowable load

Homework assignments for Chapter 1

1、The cable will fail when subjected to a tension of 4 kN. Determine the largest vertical load P the frame will support and calculate the internal normal force, shear force, and moment at the cross section through point C for this loading.

2、Determine the resultant internal loadings on the cross section through point D. Assume the reactions at the supports A and B are vertical.

3、The bars of the truss each have a cross-sectional area of 1.25 in . Determine the average normal stress in each member due to the loading P=10 kip. State whether the stress is tensile or compressive.

4、The beam is supported by a pin at A and a short link BC . Determine the maximum magnitude P of the loads the beam will support if the average shear stress in each pin is not to exceed 60 MPa. All pins are in double shear as shown, and each has a diameter of 16 mm.

5、Determine the average normal stress at section a–a and the average shear stress at section b–b in member AB. The cross section is square, 0.5 in. on each side.

6、The three steel wires are used to support the load. If the wires have an allowable tensile stress of , determine the required diameter of each wire if the applied load is P=10 kN.

7、The frame is subjected to the load of 4 kN which acts on member ABD at D . Determine the required diameter of the pins at D and C if the allowable shear stress for the material is Pin C is , subjected to double shear, whereas pin D is subjected to single shear.

8、The eye bolt is used to support the load of 5 kip. Determine its diameter d to the nearest 1/8 in. and the required thickness h to the nearest 1/8 in. of the support so that the washer will not penetrate or shear through it. The allowable normal stress for the bolt is and the allowable shear stress for the supporting material is .

2. Strain

A small quiz for Chapter 2

1、( ) is a measure per unit length of the elongation or contraction of a small line segment in the body, whereas ( ) is a measure of the change in ( ) that occurs between two small line segments that are originally ( ) to one another.
A、Normal strain, shear strain, angle, perpendicular
B、Shear strain, normal strain, angle, perpendicular
C、Normal strain, shear strain, length, perpendicular
D、Shear strain, normal strain, length, perpendicular

2、The state of strain at a point is characterized by ( ) strain components: ( ) normal strains and ( ) shear strains. These components depend upon the original ( ) of the line segments and their ( ) in the body.
A、nine, three, six, orientation, location
B、six, three, three, orientation, location
C、six, three, three, orientation, length
D、nine, three, six, orientation, length

3、 When force P is applied to the rigid lever arm ABC in the given figure, the arm rotates counterclockwise about pin A through an angle of 0.05°. The normal strain developed in wire BD is ( ).
A、0.116 mm/mm
B、0.00232 mm/mm
C、0.0116 mm/mm
D、0.00116 mm/mm

4、The slender rod shown in the given figure is subjected to an increase of temperature along its axis, which creates a normal strain in the rod of where z is measured in meters. The displacement of the end B of the rod due to the temperature increase is ( ) and the average normal strain in the rod is ( ).
A、7.02 mm (downward), 0.0119 mm/mm
B、2.39 m (downward), 0.0351 mm/mm
C、7.02 mm (upward), 0.0351 mm/mm
D、2.39 mm (upward), 0.0119 mm/mm

5、The rigid beam is supported by a pin at A and wires BD and CE. If the distributed load causes the end C to be displaced 20 mm downward, the normal strain developed in wires DB is ( ) and in wire CE is ( ).
A、0.00266 mm/mm, 0.001 mm/mm
B、0.00533 mm/mm, 0.005 mm/mm
C、0.00533 mm/mm, 0.01 mm/mm
D、0.00266 mm/mm, 0.005 mm/mm

Homework assignment for Chapter 2

1、A thin strip of rubber has an unstretched length of 15 in. If it is stretched around a pipe having an outer diameter of 6 in., determine the average normal strain in the strip.

2、The rigid beam is supported by a pin at A and wires BD and CE. If the load P on the beam causes the end C to be displaced 10 mm downward, determine the normal strain developed in wires CE and BD.

3、Part of a control linkage for an airplane consists of a rigid member CBD and a flexible cable AB. If a force is applied to the end D of the member and causes a normal strain in the cable of 0.0045 mm/mm, determine the displacement of point D. Originally the cable is unstretched.

4、The piece of rubber is originally rectangular and subjected to the deformation shown by the dashed lines. Determine the average normal strain along the diagonal DB and side AD.

5、Two bars are used to support a load P. When unloaded, AB is 5 in. long, AC is 8 in. long, and the ring at A has coordinates (0,0). If a load is applied to the ring at A, so that it moves it to the coordinate position (0.3 in.,-0.75 in.), determine the normal strain in each bar.

6、The material distorts into the dashed position shown. Determine the average normal strain that occurs along the diagonals AD and CF.

Chapter 3: Mechanical Properties of Materials

A small quiz for Chapter 3

1、The point of ( ) on the stress-strain diagram represents the proportional limit and the ultimate stress.
A、A, B
B、B, C
C、A, D
D、B, E

2、The material for the 50-mm-long specimen has the stress–strain diagram shown. If P = 100kN the elongation of the specimen is ( ).
A、0.0796 mm
B、0.001592 mm
C、318.31 MPa
D、0.01592 mm

3、A 100-mm long rod has a diameter of 15 mm. If an axial tensile load of 20 kN is applied to it, the change in its diameter is ( ). E = 70 GPa, = 0.35.
A、
B、
C、
D、

4、If the elongation of wire BC is 0.3 mm after the force P is applied, the magnitude of P is ( ). The wire is A-36 steel and has a diameter of 3 mm. The modulus of A-36 is 200 GPa and Poisson's ratio is 0.32.
A、942 N
B、628 N
C、1256 N
D、1256 N

5、A 150-mm long rod has a diameter of 10 mm. If an axial tensile load of 150 kN is applied, its change of length is ( ). E = 200 GPa. It is assumed that material behavior is linear elastic.
A、0.2829 mm
B、1.4324 mm
C、0.6366 mm
D、0.4244

6、A 20-mm-diameter brass rod has a modulus of elasticity of E = 100 GPa If it is 4 m long and subjected to an axial tensile load of 12 kN, its elongation is ( ).
A、1.5279 mm
B、6.1115 mm
C、3.06 mm
D、0.7639 mm

7、A solid circular rod that is 600 mm long and 20 mm in diameter is subjected to an axial force of P = 50 KN. The elongation of the rod is , and its diameter becomes = 19.9837 mm. the modulus of elasticity of the material is ( ). Assume that the material does not yield.
A、68.2 GPa
B、136.4 GPa
C、34.1 GPa
D、200 GPa

8、A 20-mm-wide block is firmly bonded to rigid plates at its top and bottom.When the force P is applied the block deforms into the shape shown by the dashed line. The block's material has shear modulus G = 52 GPa. Assume that the material does not yield and use small angle analysis. The magnitude of P is ( ).
A、460 KN
B、130 KN
C、260 KN
D、520 KN

Homework assignment for Chapter 3

1、A structural member in a nuclear reactor is made of a zirconium alloy. If an axial load of 4 kip is to be supported by the member, determine its required cross-sectional area. Use a factor of safety of 3 relative to yielding. What is the load on the member if it is 3 ft long and its elongation is 0.02 in.? , . The material has elastic behavior.

2、The strut is supported by a pin at C and an A-36 steel guy wire AB. If the wire has a diameter of 0.2 in., determine how much it stretches when the distributed load acts on the strut.

3、A bar having a length of 6 in. and cross-sectional area of 0.7 in is subjected to an axial force of 10000 lb. If the bar stretches 0.002 in., determine the modulus of elasticity of the material. The material has linear-elastic behavior.

4、The rigid pipe is supported by a pin at A and an A-36 guy wire BD. If the wire has a diameter of 0.25 in., determine the load P if the end C is displaced 0.075 in. downward.

5、The acrylic plastic rod is 200 mm long and 15 mm in diameter. If an axial load of 300 N is applied to it, determine the change in its length and the change in its diameter. , .

6、The aluminum block has a rectangular cross section and is subjected to an axial compressive force of 8 kip. If the 1.5-in. side changed its length to 1.500132 in., determine Poisson’s ratio and the new length of the 2-in. side. .

7、The block is made of titanium Ti-6A1-4V and is subjected to a compression of 0.06 in. along the y axis, and its shape is given a tilt of . Determine and .

8、The support consists of three rigid plates, which are connected together using two symmetrically placed rubber pads.If a vertical force of 5 N is applied to plate A, determine the approximate vertical displacement of this plate due to shear strains in the rubber. Each pad hascross-sectional dimensions of 30 mm and 20 mm. = 0.20 MPa.

Chapter 4: An axial loaded member

A small quiz for Chapter 4

1、Saint-Venant's principle states that both the localized ( ) which occur within the regions of load aplication or at the supports tend to "even out" at a distance sufficiently removed from these regions.
A、deformation
B、deformation and stress
C、stress
D、stress and strain

2、Since Hooke's has been used in the development of the displacement equations, it is important that the loads do not cause ( ) of the material and that the material is ( ) and behaves in a ( ) manner
A、yielding; homogeneous; linear-elastic
B、plastic deformation; isotropic; linear-elastic
C、yielding; isotropic; linear
D、yielding; homogeneous; elastic

3、Superposition requires that the loading be linearly related to the ( ) or ( ), and the loading does not significantly change the ( ) geometry of the member.
A、stress; displacement; original
B、deformation; strain; original
C、stress; strain; current
D、stress; strain; original

4、A member is statically ( ) if the equations of equilibrium are ( ) to determine ( ) on a member.
A、indeterminate; not sufficient; the external forces
B、determinate; sufficient; the reactions
C、indeterminate; sufficient; the internal forces
D、determinate; not sufficient; the reactions

5、( ) specify the displacement constraints that occur at the ( ) or others points on a member.
A、Compatibility conditions; supports
B、Equilibrium equations; supports
C、Equilibrium equations; point that the external load is applied
D、Compatibility conditions; point that the external load is applied

6、( ) occur at sections where the cross-secitonal area suddenly ( ).
A、Stress concentrations; changes
B、Stress concentrations; decreases
C、Stress concentrations; increases
D、Strain concentrations; changes

7、A stress concentration factor K can be determined through experiment and is only a function of the ( ) of the specimen.
A、material properties
B、geometry
C、boundary condtions
D、external loadings

8、The stress concentration in a ( ) specimen that is subject to a static loading will not have to be considered in design; however, if the material is ( ), or subjected to ( ) loadings, then stress concentrations becomes important.
A、ductile; brittle; fatigue
B、brittle; ductile; static
C、ductile; brittle; static
D、ductile; brittle; thermal

9、Thermal stress can occur in a ( ) with temperature variation.
A、statically indeterminate member
B、any loaded member
C、statically determinate member
D、statically indeterminate member with homogeneous and isotropic material property

10、The displacement of one point on the axially loaded member relative to the other point is determined by , which can be used for the ( ) material.
A、homogeneous and isotropic
B、homogeneous, isotropic and linear-elastic
C、anisotropic and linear-elastic
D、homogeneous and linear-elastic

11、The 30-mm-diameter A-36 steel rod is subjected to the loading shown. The displacement of end A with respect to end C is ( ).
A、-0.772 mm
B、0.772 mm
C、-0.858 mm
D、-0.686

12、The 20-mm-diameter 2014-T6 aluminum rod is subjected to the uniform distributed axial load. The displacement of end A is ( ).
A、0.882 mm
B、0.529 mm
C、-0.539 mm
D、0.705

13、The two pipes are made of the same material and are connected as shown. If the cross-sectional area of BC is A and that of CD is 2A, The reactions at B and D when a force P is applied at the junction C are ( ).
A、1/3P, -2/3P
B、2/3P, 1/2P
C、1/3P, 1/2P
D、-2/3P, 1/3P

14、The three suspender bars are made of the same material and have equal cross-sectional areas A. The average normal stress in the bar AB is ( ) if the rigid beam ACE is subjected to the force P.
A、(5P)/(12A)
B、(2P)/(3A)
C、P/(2A)
D、(7P)/(12A)

15、The wires AB and AC are made of steel, and wire AD is made of copper. Before the 200 lb force is applied, AB and AC are each 60 in. long and AD is 40 in. long. If the temperature is increased by 80 degree F. The force in the wire AC needed to support the load is ( ). , . , . Each wire has a cross-sectional area of 0.0123 in.
A、28.86 lb
B、10.05 lb
C、15.38 lb
D、20.67 lb

Homework assignment for Chapter 4

1、The assembly consists of a steel rod CB and an aluminum rod BA, each having a diameter of 12 mm. If the rod is subjected to the axial loadings at A and at the coupling B, determine the displacement of the coupling B and the end A. The unstretched length of each segment is shown in the figure. Neglect the size of the connections at B and C, and assume that they are rigid. = 200 GPa, = 70 GPa.

2、The bar has a cross-sectional area of 3 , and . Determine the displacement of its end A when it is subjected to the distributed loading.

3、The bar has a length L and cross-sectional area A. Determine its elongation due to the force P and its own weight.The material has a specific weight (weight / volume) and a modulus of elasticity E.

4、The post is made of Douglas fir and has a diameter of 60 mm. If it is subjected to the load of 20 kN and the soil provides a frictional resistance that is uniformly distributed along its sides of w= 4 kN/m, determine the force F at its bottom needed for equilibrium. Also, what is the displacement of the top of the post A with respect to its bottom B? Neglect the weight of the post.

5、The post is made of Douglas fir and has a diameter of 60 mm.If it is subjected to the load of 20 kN and the soil provides a frictional resistance that is distributed along its length and varies linearly from w = 0 at y = 0 to w = 3 kN/m at y = 2 m, determine the force F at its bottom needed for equilibrium. Also, what is the displacement of the top of the post A with respect to its bottom B? Neglect the weight of the post.

6、The assembly consists of two A-36 steel rods and a rigid bar BD. Each rod has a diameter of 0.75 in. If a force of 10 kip is applied to the bar as shown, determine the vertical displacement of the load.

7、The composite bar consists of a 20-mm-diameter A-36 steel segment AB and 50-mm-diameter red brass C83400 end segments DA and CB. Determine the displacement of A with respect to B due to the applied load.

8、The concrete post is reinforced using six steel reinforcing rods, each having a diameter of 20 mm. Determine the stress in the concrete and the steel if the post is subjected to an axial load of 900 kN. ,

9、The bolt has a diameter of 20 mm and passes through a tube that has an inner diameter of 50 mm and an outer diameter of 60 mm. If the bolt and tube are made of A-36 steel, determine the normal stress in the tube and bolt when a force of 40 kN is applied to the bolt. Assume the end caps are rigid.

10、The tapered member is fixed connected at its ends A and B and is subjected to a load P = 7 kip, at x = 30 in. Determine the reactions at the supports. The material is 2 in. thick and is made from 2014-T6 aluminum.

11、The tapered member is fixed connected at its ends A and B and is subjected to a load P. Determine the location x of the load and its greatest magnitude so that the average normal stress in the bar does not exceed , The member is 2 in. thick.

12、The rigid bar supports the uniform distributed load of 6 kip/ft. Determine the force in each cable if each cable has a cross-sectional area of , and .

13、The rigid bar is originally horizontal and is supported by two A-36 steel cables each having a crosssectional area of . Determine the rotation of the bar when the 800-lb load is applied.

14、Three bars each made of different materials are connected together and placed between two walls when the temperature is . Determine the force exerted on the (rigid) supports when the temperature becomes . The material properties and cross-sectional area of each bar are given in the figure.

15、The bronze C86100 pipe has an inner radius of 0.5 in. and a wall thickness of 0.2 in. If the gas flowing through it changes the temperature of the pipe uniformly from at A to at B. determine the axial force it exerts on the walls.The pipe was fitted between the walls when

16、The rigid block has a weight of 80 kip and is to be supported by posts A and B, which are made of A-36 steel, and the post C, which is made of C83400 red brass. If all the posts have the same original length before they are loaded, determine the average normal stress developed in each post when post C is heated so that its temperature is increased by 20°F. Each post has a cross-sectional area of 8

17、The three bars are made of A-36 steel and form a pin-connected truss. If the truss is constructed when , determine the force in each bar when , Each bar has a cross-sectional area of 2 .

18、The three bars are made of A-36 steel and form a pin-connected truss. If the truss is constructed when , determine the vertical displacement of joint A when . Each bar has a cross-sectional area of 2 .

19、The wires AB and AC are made of steel, and wire AD is made of copper. Before the 150-lb force is applied, AB and AC are each 60 in. long and AD is 40 in. long. If the temperature is increased by , determine the force in each wire needed to support the load. Take , , , . Each wire has a cross-sectional area of 0.0123 .

20、Determine the maximum normal stress developed in the bar when it is subjected to a tension of .

21、The member is to be made from a steel plate that is 0.25 in. thick. If a 1-in. hole is drilled through its center, determine the approximate width w of the plate so that it can support an axial force of 3350 lb. The allowable stress is .

22、The A-36 steel plate has a thickness of 12 mm. If there are shoulder fillets at B and C, and , determine the maximum axial load P that it can support. Calculate its elongation, neglecting the effect of the fillets.

Chapter 5: Torsion

A small quiz for Chapter 5

1、When a shaft having a circular cross section is subjected to a torque, the cross section remains plane while radial lines rotate. This causes a ( ) within the material that varies ( ) along any ( ) line.
A、shear strain; linearly; radial
B、normal strain; linearly; radial
C、shear strain; nonlinearly; radial
D、shear strain; nonlinearly; longitudinal

2、Due to ( ) of shear, the linear shear stress distribution within the plane of the cross section is also distributed along an adjacent ( ) of the shaft
A、complementary property; axial plane
B、equilibrium equation; axial plane
C、compatibility condition; axial plane
D、linear distribution; axial plane

3、The torsion formula is based on the requirement that the ( ) torque on the cross section is equal to the torque produced by the ( ) shear stress distribution about the ( ) of the shaft.
A、resultant; linear; longitudinal axis
B、resultant; nonlinear; longitudinal axis
C、external; linear; radial line
D、resultant; nonlinear; radial line

4、It is necessary that the shaft or tube have a ( ) cross section and it is made of ( ) material which has ( ) behavior.
A、circular; homogeneous; linear-elastic
B、circular; anisotropic; linear-elastic
C、circular; isotropic; linear-elastic
D、circular; homogeneous; linear

5、It is important for the development of the formula for the angle of twist, which is that the applied torques do not cause ( ) of the material and that the material is ( ) and behaves in a ( ) manner
A、yielding; homogeneous; linear-elastic
B、plastic deformation; inhomogeneous; linear-elastic
C、yielding; anisotropic; linear-elastic
D、yielding; homogeneous; elastic

6、The solid circular shaft is subjected to an internal torque of . The shear stress developed at points A and B are ( ) and ( ), respectively.
A、49.7 MPa, 37.3 MPa
B、79.58 MPa, 59.68 MPa
C、49700 Pa, 37300 Pa
D、79580 Pa, 59680 Pa

7、The shear stress developed at point A on the surface of the shaft is ( ). The shaft has a radius of 60 mm.
A、7.42 MPa
B、20. 37 MPa
C、39.79 MPa
D、11.79 MPa

8、The 40-mm-diameter A-36 steel shaft is subjected to the torques shown. The angle of twist of end A with respect to C is ( ). The shear modulus of A-36 steel is 75 GPa.
A、0.00838
B、-0.00174
C、-0.00838
D、-0.0424

9、A series of gears are mounted on the 60-mm diameter A-36 steel shaft. The angle of twist of gear B relative to gear A is ( ). The shear modulus of A-36 steel is 75 GPa.
A、0.0021
B、0.0106
C、-0.0106
D、0.0335

10、The hollow 6061-T6 aluminum shaft has an outer and inner radius of co 60 mm and ci 20 mm, respectively. The angle of twist of end A is ( ).The flexible support at B has a torsional stiffness of . The shear modulus of 6061-T6 aluminum is 26GPa.
A、0.07111
B、0.1126
C、0.0385
D、0.0352

Homework assignment for Chapter 5

1、The copper pipe has an outer diameter of 40 mm and an inner diameter of 37 mm. If it is tightly secured to the wall at A and three torques are applied to it as shown, determine the absolute maximum shear stress developed in the pipe.

2、The solid shaft is fixed to the support at C and subjected to the torsional loadings shown. Determine the shear stress at points A and B and sketch the shear stress on volume elements located at these points.

3、The solid 30-mm-diameter shaft is used to transmit the torques applied to the gears. Determine the absolute maximum shear stress on the shaft.

4、The coupling is used to connect the two shafts together. Assuming that the shear stress in the bolts is uniform, determine the number of bolts necessary to make the maximum shear stress in the shaft equal to the shear stress in the bolts. Each bolt has a diameter d.

5、The shaft consists of three concentric tubes, each made from the same material and having the inner and outer radii shown. If a torque of , is applied to the rigid disk fixed to its end, determine the maximum shear stress in the shaft.

6、The A-36 steel shaft is supported on smooth bearings that allow it to rotate freely. If the gears are subjected to the torques shown, determine the maximum shear stress developed in the segments AB and BC. The shaft has a diameter of 40 mm.

7、The 60-mm-diameter solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the absolute maximum and minimum shear stresses on the outer surface of the shaft and specify their locations, measured from the fixed end A.

8、The rod has a diameter of 1 in. and a weight of 10 lb/ft. Determine the maximum torsional stress in the rod at a section located at A due to the rod's weight.

9、The propellers of a ship are connected to a A-36 steel shaft that is 60 m long and has an outer diameter of 340 mm and inner diameter of 260 mm. If the power out putis 4.5 MW when the shaft rotates at determine the maximum torsional stress in the shaft and its angle of twist.

10、The assembly is made of A-36 steel and consists of a solid rod 20 mm in diameter fixed to the inside of a tube using a rigid disk at B. Determine the angle of twist at C. The tube has an outer diameter of 40 mm and wall thickness of 5 mm.

11、The steel shaft is made from two segments: AC has a diameter of 0.5 in, and CB has a diameter of 1 in. If it is fixed at its ends A and B and subjected to a torque of 500 lb·ft, determine the maximum shear stress in the shaft.

12、The shaft is made from a solid steel section AB and a tubular portion made of steel and having a brass core. If it is fixed to a rigid support at A, and a torque of T = 50 lb·ft is applied to it at C, determine the angle of twist that occurs at C and compute the maximum shear stress and maximum shear strain in the brass and steel. Take .

13、The 80-mm diameter shaft is made of 6061-T6 aluminum alloy and subjected to the torsional loading shown.Determine the angle of twist at end A.

14、A portion of the A-36 steel shaft is subjected to a linearly distributed torsional loading. If the shaft has the dimensions shown, determine the reactions at the fixed supports A and C. Segment AB has a diameter of 1.5 in. and segment BC has a diameter of 0.75 in.

15、The A-36 steel axle is made from tubes AB and CD and a solid section BC. It is supported on smooth bearings that allow it to rotate freely. If the gears, fixed to its ends, are subjected to torques, determine the angle of twist of gear A relative to gear D. The tubes have an outer diameter of 30 mm and an inner diameter of 20 mm. The solid section has a diameter of 40 mm.

A small quiz for Chapter 6: Bending

A small quiz for Chapter 6

1、Beams are ( ) straight members that carry loads ( ) their longitudinal axis.
A、short, perpendicular to
B、long, perpendicular to
C、short, parallel to
D、long, parallel to

2、In order to properly design a beam, it is import to know the variation of ( ) and ( ) along its axis in order to find the points where these values are a maximum.
A、the axial force, torsional moment
B、the axial force, bending moment
C、the shear, torsional moment
D、the shear, bending moment

3、Although the choice of a sign convention for a beam is ( ), we will use the one often used in engineering practice. The positive directions are as follows: the distributed load acts ( ) on the beam; the internal shear force causes a ( ) rotation of the beam segment on which it acts; and the internal moment causes ( ) in the top fibers of the segments.
A、specified; downward; clockwise; compression
B、arbitrary; downward; clockwise; compression
C、arbitrary; upward; counterclockwise; compression
D、arbitrary; downward; clockwise; tension

4、The cross section of a straight beam remains plane when the beam deforms due to bending. This causes ( ) on one side of the beam and ( ) on the other side. The neutral axis is subjected to ( ) .
A、tensile stress; compressive stress; zero stress
B、compressive stress; tensile stress; maximum normal stress
C、shear stress; normal stress; zero stress
D、normal stress; shear stress; zero stress

5、Due to the pure bending deformation, the longitudinal ( ) strain varies ( ) from ( ) at the neutral axis to a maximum at the outer fibers of the beam.
A、normal; linearly; zero
B、shear; nonlinearly; zero
C、shear; nonlinearly; zero
D、shear; nonlinearly; zero

6、Provided the material is ( ) and ( ), due to the pure bending deformation, the stress varies in a ( ) fashion on the cross section.
A、homogeneous; linear elastic; linear
B、nonhomogeneous; linear elastic; linear
C、nonhomogeneous; linear elastic; nonlinear
D、homogeneous; linear elastic; nonlinear

7、For linear-elastic material the neutral axis passes through the ( ) of the cross-sectional area. This conclusion is based on the fact that the resultant ( ) acting on the cross section must be ( ).
A、centroid; axial normal force; zero
B、centroid; shear force; zero
C、centroid; bending moment; zero
D、centroid; axial normal force; maximum

8、The flexure formula is based on the requirement that the ( ) on the cross section is equal to the ( ) produced by the ( ) distribution about the neutral axis.
A、resultant moment; moment; linear normal stress
B、resultant normal force; force; linear normal stress
C、resultant moment; moment; nonlinear normal stress
D、resultant moment; moment; nonlinear shear stress

9、The flexure formula can be applied only when bending occurs about axes that represent the principal axes of inertia for the cross section. These axes have their origin at ( ) and are orientated along ( ), if there is one, and perpendicular to it.
A、the centroid; an axis of symmetry
B、arbitrary point; an axis of symmetry
C、the centroid; an arbitrary axis
D、arbitrary point; an arbitrary axis

10、If the moment is applied about some arbitary axis, then the moment must be resolved into components along each of ( ) , and the stress at a point is determined by ( ) of the stress caused by each of the moment components.
A、the principal axes, superposition
B、perpendicular axes, decomposition
C、arbitrary axes, superposition
D、the principal axes, decomposition

11、If the beam is subjected to a bending moment of M = 16 kN.m, the maximum bending stress in the beam is ( ).
A、48.6 MPa
B、74.5 MPa
C、59.6 MPa
D、85.4 MPa

12、If the beam is subjected to a bending moment of M = 15 kN.m, the maximum bending stress in the beam is ( ).
A、5.88 MPa
B、3.92 MPa
C、1.96 MPa
D、7.84

13、If the beam is subjected to a bending moment of M = 10 kN.m, the bending stress developed at point A is ( ).
A、1.98 MPa (Tension)
B、1.98 MPa (Tension)
C、3.96 MPa (Compression)
D、3.96 MPa (Tension)

14、The bending stress developed at corners A is ( ).
A、30 MPa (Tension)
B、30 MPa (Compression)
C、42 MPa (Tension)
D、42 MPa (Compression)

15、The maximum stress in the beam's cross section is ( ).
A、40.4 psi
B、64.6 psi
C、48.0 psi
D、107.9 psi

Homework assignment for Chapter 6

1、Draw the shear and moment diagrams for the overhang beam.

2、Draw the shear and moment diagrams for the compound beam which is pin connected at B.

3、Draw the shear and moment diagrams for the beam.

4、A member having the dimensions shown is used to resist an internal bending moment of M = 90 kN·m. Determine the maximum stress in the member if the moment is applied (a) about the zaxis (as shown) (b) about the y axis. Sketch the stress distribution for each case.

5、Draw the shear and moment diagrams for the beam. The two segments are joined together at B.

6、If the beam is made of material having an allowable tensile and compressive stress of and , respectively, determine the maximum allowable internal moment M that can be applied to the beam.

7、Draw the shear and moment diagrams for the beam.

8、Draw the shear and moment diagrams for the beam, and determine the shear and moment throughout the beam as functions of x.

9、A box beam is constructed from four pieces of wood,glued together as shown. If the moment acting on the cross section is 10 kN·m, determine the stress at points A and B and show the results acting on volume elements located at these points.

10、The steel beam has the cross-sectional area shown. Determine the largest intensity of distributed load w that it can support so that the bending stress does not exceed .

11、The wood beam has a rectangular cross section in the proportion shown. If b= 7.5 in., determine the absolute maximum bending stress in the beam.

12、The beam has a rectangular cross section in the proportion shown. Determine its required dimension b if the allowable bending stress is .

13、If the allowable bending stress for the wood beam is , determine the required dimension b to the nearest 0.25 in. of its cross section. Assume the support at A is a pin and B is a roller.

14、A beam is made of a material that has a modulus of elasticity in compression different from that given for tension. Determine the location c of the neutral axis, and derive an expression for the maximum tensile stress in the beam having the dimensions shown if it is subjected to the bending moment M.

15、The beam is subjected to a bending moment of M = 20 kip·ft directed as shown. Determine the maximum bending stress in the beam and the orientation of the neutral axis.

Chapter 7 Transverse Shear

A small quiz for Chapter 7

1、Shear forces in beams cause ( ) shear-strain distributions over the cross-section, causing it to ( ).
A、nonlinear, warp
B、linear, warp
C、constant, rotate
D、linear, rotate

2、Due to the ( ) property of shear stress, the shear stress developed in a beam acts on both the cross section and on ( ) planes.
A、complementary, longitudinal
B、complementary, transverse
C、nonlinear, longitudinal
D、linear, longitudinal

3、The shear formula was derived by considering ( ) equilibrium of the longitudinal shear stress and ( ) distribution acting on a portion of a differential segment of the beam.
A、horizontal force, bending-stress
B、transverse force, bending-stress
C、horizontal force, transverse shear-stress
D、transverse force, transverse shear-stress

4、The shear formula is to be used on strainght prismatic members made of ( ) material that has ( ) behavior. Also, the internal resultant shear force must be directed along an axis of ( ) of the cross-sectional area.
A、homogeneous, linear-elastic, symmetry
B、homogeneous, elastic, asymmetry
C、unhomogeneous, linear, symmetry
D、homogeneous, linear-inelastic, symmetry

5、For a beam having a rectangular cross section, the shear stress varies ( ) with ( ). The maximum shear stress is along the ( ) axis.
A、parabolically, depth, neutral
B、linear, depth, neutral
C、parabolically, depth, longitudinal
D、linear, depth, longitudinal

6、Shear flow is a measure of the force per unit length along a ( ) axis of a beam. This value is found from the ( ) and is used to determine the shear force developed in fasteners and glue that holds the various segments of a beam together.
A、longitudinal, shear formula
B、transverse, shear formula
C、longitudinal, flexure formula
D、transverse, flexure formula

7、If a member is made from segments having thin walls under internal shear force, only the shear flow ( ) to the walls of the member is important. The shear flow varies ( ) along segments that are ( ) the direction of the shear force V.
A、parallel to, linear, perpendicular to
B、perpendicular to, linear, parallel to
C、parallel to, parabolically, perpendicular to
D、perpendicular to, parabolically, parallel to

8、The shear flow in the thin-walled member varies ( ) along the segments that are ( ) or ( ) the direction of the shear force V. On the cross section, the shear "flows" along the segments so that it contributes to the shear force V yet satisfies horizontal and vertical ( ).
A、parabolically, inclined, parallel to, force equilibrium
B、linearly, inclined, parallel to, force equilibrium
C、linearly, inclined, parallel to, moment equilibrium
D、parabolically, perpendicular to, parallel to, force equilibrium

9、If the beam is subjected to a shear force of V = 80 kN, determine the shear stress developed at point A. Represent the state of stress at A on a volume element.
A、14.7 MPa
B、18.4 MPa
C、12.6 MPa
D、22.4 MPa

10、Determine the absolute maximum shear stress developed in the beam.
A、187.5 psi
B、1125 psi
C、375 psi
D、750 psi

11、If the beam is subjected to a shear force of V = 10 kN, determine the maximum shear stress developed in the beam.
A、1.2 MPa
B、0.6 MPa
C、1.8 MPa
D、2.4 MPa

12、The two identical boards are bolted together to form the beam. Determine the maximum allowable spacing s of the bolts to the nearest mm if each bolt has a shear strength of 30 kN. The beam is subjected to a shear force of V = 40 KN.
A、80 mm
B、200 mm
C、100 mm
D、150 mm

13、Two identical 20-mm thick plates are bolted to the top and bottom flange to form the built-up beam. If the beam is subjected to a shear force of V = 200 KN determine the allowable maximum spacing s of the bolts to the nearest mm. Each bolt has a shear strength of 20 kN.
A、106 mm
B、90 mm
C、96 mm
D、86 mm

Homework assignment for Chapter 7

1、If the wide-flange beam is subjected to a shear of V = 20 kN, determine the shear stress on the web at A. Indicate the shear-stress components on a volume element located at this point.

2、If the wide-flange beam is subjected to a shear of V = 20 kN, determine the shear force resisted by the web of the beam.

3、If the T-beam is subjected to a vertical shear of V = 12 kip, determine the vertical shear force resisted by the flange.

4、If the applied shear force V= 18 kip, determine the maximum shear stress in the member.

5、Determine the maximum shear force V that the strut can support if the allowable shear stress for the material is .

6、Determine the maximum shear stress in the strut if it is subjected to a shear force of V = 600 kN.

7、Determine the maximum shear stress in the T-beam at point C. Show the result on a volume element at this point.

8、The beam is constructed from two boards fastened together with three rows of nails spaced s = 2 in. apart. If each nail can support a 450-lb shear force, determine the maximum shear force V that can be applied to the beam. The allowable shear stress for the wood is .

9、A beam is constructed from three boards bolted together as shown. Determine the shear force developed in each bolt if the bolts are spaced s = 250 mm apart and the applied shear is V = 35 kN.

10、The T-beam is nailed together as shown.If the nails can each support a shear force of 950 lb, determine the maximum shear force V that the beam can support and the corresponding maximum nail spacing s to the nearest 0.125 in. The allowable shear stress for the wood is .

学习通Mechanics of Materials_3相关文章

学习通Mechanics of Materials_3是一门力学课程，主要讲解材料力学相关内容。学习本门课程需要对基础力学知识有一定的掌握，并具备数学思维和分析能力。

材料力学是研究材料的力学性质和材料的变形和破坏的学科。在材料力学中，我们需要掌握杆件的力学分析、梁的力学分析和板的力学分析等。本门课程主要涉及到杆件的力学分析和梁的力学分析。

杆件的力学分析

在杆件的力学分析中，我们需要掌握杆件内力的计算原理、杆件中的应力和应变等相关知识。

杆件内力包括张力、压力、剪力和弯矩四种类型。杆件内力的计算原理是基于平衡方程和变形方程进行计算的。通过平衡方程和变形方程，我们可以求得杆件中的各种内力。

杆件中的应力和应变是杆件力学分析中非常重要的概念。应力是指单位面积上的力，应变是指单位长度上的变形量。对于杆件的应力和应变，我们需要掌握杨氏模量、泊松比等相关知识，同时需要掌握应力和应变的计算方法。

梁的力学分析

在梁的力学分析中，我们需要掌握梁的受力分析、梁的弯曲、梁的剪力和弯矩图等相关知识。

梁的受力分析是指对梁在受力状态下各点的内力和应力进行计算。梁的弯曲是指梁在受到外力作用下产生的弯曲变形。梁的剪力和弯矩图是指在分析梁的受力状态时，绘制出的表征梁内部受力状态的图形。

梁的力学分析中，我们需要掌握受力分析、弯曲分析和剪力弯矩图的绘制方法，同时需要掌握梁的截面性质等相关知识。

总结

学习通Mechanics of Materials_3课程内容涵盖杆件的力学分析和梁的力学分析两个重要部分。通过学习本门课程，可以使我们更深入地理解和掌握材料力学相关知识，为我们今后从事相关工作提供有力的支持。

中国大学《Mechanics of Materials_3》学习笔记

导论

《Mechanics of Materials_3》是中国大学的一门材料力学课程，主要涉及材料的静力学和应变力学。在此之前，需要学习其前置课程《Mechanics of Materials_1》和《Mechanics of Materials_2》。

此课程的学习需要掌握牛顿力学、静力学、应变力学等基础知识，同时也需要一定的数学基础，如微积分、矩阵、偏微分方程等。

课程内容

本课程主要涉及以下内容：

• 复合材料的弹性和破坏
• 混凝土断裂力学
• 金属和陶瓷中的裂纹扩展
• 材料的断裂和疲劳
• 蠕变和塑性变形
• 材料的残余应力和变形

复合材料的弹性和破坏

复合材料指的是由两种或两种以上不同的材料组成的材料。在本课程中，主要研究其弹性和破坏过程。

弹性是指材料在受到外力作用后，能够恢复其原本的形态和大小。而破坏是指材料在受到外力作用后，不能恢复其原本的形态和大小，甚至出现裂纹和断裂。

混凝土断裂力学

混凝土是一种广泛应用的建筑材料，其断裂力学研究是本课程的重要内容之一。

混凝土的断裂过程一般分为三个阶段：拉伸阶段、极限状态阶段和残余阶段。拉伸阶段是指在荷载作用下，混凝土开始发生拉伸变形；极限状态阶段是指混凝土开始断裂，强度逐渐降低；残余阶段是指混凝土已经完全破坏，但仍能承受少量的荷载。

金属和陶瓷中的裂纹扩展

金属和陶瓷中裂纹的扩展是一种常见的破坏形式。在本课程中，将研究其扩展机理和防止方法。

裂纹的扩展会导致材料的强度逐渐降低，并最终导致破坏。因此，在设计工程结构时需要采取措施防止裂纹的扩展。

材料的断裂和疲劳

材料的断裂和疲劳也是本课程的重要内容之一。在工程实践中，材料的疲劳破坏是一种常见的破坏形式。

疲劳破坏指的是材料在不断变化的荷载作用下，发生微小的裂纹，并逐渐扩展。这种破坏形式会导致材料的强度逐渐降低，最终导致破坏。

蠕变和塑性变形

蠕变指的是材料在高温、高应力下发生的形变，这种形变会导致材料的强度逐渐降低。而塑性变形则是材料在受到外力作用下，发生的可逆形变。

本课程将研究蠕变和塑性变形的机理和影响因素，以及如何避免这种形变对工程结构的影响。

材料的残余应力和变形

材料在受到外力作用后，往往会产生残余应力和变形。残余应力和变形对工程结构的影响很大，在本课程中将研究其机理和影响因素。

结语

《Mechanics of Materials_3》是一门非常重要的材料力学课程，学习此课程可以帮助学生更好地理解材料的力学行为，为工程实践提供理论基础。希望本文能够对读者有所帮助。