15、the outer radius of the steel pipe is 20 mm and the inner radius is 15 mm. if it is close to the fixed wall before loading, what is the reaction force of the wall under the load shown? a、8.0kn,8.0kn b、11.2kn,4.8kn c、3.6kn,12.4kn d、12.0kn,4.0kn
16、steel bolts with a diameter of 10 mm are surrounded by bronze sleeves. the outer diameter of the sleeve is 20 mm and the inner diameter is 10 mm. if the yield stress of steel is 640mpa, e = 200gpa; if the yield stress of bronze is 520mpa, e = 100gpa. what is the maximum elastic load p that can be applied to the component? a、204kn b、50kn c、126kn d、150kn
17、teel bolts with a diameter of 10 mm are surrounded by bronze sleeves. the outer diameter of the sleeve is 20 mm and the inner diameter is 10 mm. the elastic modulus of steel and bronze are 200 gpa and 100 gpa respectively. if the bolt is subjected to a pressure of p = 20kn, what is the average stress of steel and bronze? a、80.2mpa,71.0mpa b、102.0mpa,50.9mpa c、121.0mpa,36.0mpa d、138.2mpa,21.0mpa
7 _ homework
1、
2、
3、
lecture 8
5.1 problem discussion_torque diagram随堂测验
1、point out the torque acting on section a. a、150nm b、-150nm c、50nm d、-50nm
1、locate the centroid c of the cross-sectional area for the t-beam shown in fig. (a).
2、
3、determine the moments of inertia of the beam's cross-sectional area shown in fig. (a) about the x and y centroidal axes.
4、
lecture 12
6.1 shear and moment at appointed section随堂测验
1、determine the shear force and bending moment on section c. a、30 kn， 0 b、0 kn， 30 kn.m c、30 kn， 30 kn.m d、30 kn， 60 kn.m
6.1 shear and moment diagrams随堂测验
1、draw the shear and moment diagrams for the following beam and point out the maximum shear force and bending moment on the beam. a、5kn, 5knm b、10kn, 10knm c、5kn, 10knm d、10kn, 5knm
12 _ homework
1、the dead-weight loading along the centerline of the airplane wing is shown. if the wing is fixed to the fuselage at a, determine the reactions at a, and then draw the shear and moment diagram for the wing.
2、draw the shear and moment diagrams for the overhang beam.
3、express the shear and moment in terms of x for 0 < x< 3m and 3m < x < 4.5 m, and then draw the shear and moment diagrams for the simply supported beam.
4、draw the shear and moment diagrams for the simply supported beam.
lecture 13
6.2 graphical method for constructing shear and moment diagrams随堂测验
1、draw the shear and moment diagrams for the simply supported beam. point out the maximum shear force and bending moment. a、12kn, 22knm b、12kn, 20 knm c、4 kn, 22.4knm d、4 kn, 20 knm
2、for the given shear force diagram, plot the bending moment diagram and point out the distributed load applied on the beam. a、6kn/m b、5kn/m c、4kn/m d、3kn/m
3、for the given moment diagram, plot the shear diagram and point out the distributed load applied on the beam. a、downward q b、downward 2q c、upward q d、upward 2q
13 _ homework
1、draw the shear and moment diagrams for the compound beam.
2、draw the shear and moment diagrams for the simply supported beam.
3、draw the shear and moment diagrams for the beam.
4、the compound beam is fixed at a, pin connected at b, and supported by a roller at c. draw the shear and moment diagrams for the beam.
lecture 15
6.4 the flexure formula_transverse bending随堂测验
1、 a、200 kn b、100 kn c、300 kn d、400 kn
2、 a、7.0 mpa b、6.0 mpa c、8.0 mpa d、9.0 mpa
15 _ homework
1、determine the moment m that will produce a maximum stress of 70 mpa on the cross-section.
2、determine the maximum tensile and compressive bending stress in the beam if it is subjected to a moment of m=6kn.m.
3、the beam is subjected to a moment m. determine the percentage of this moment that is resisted by the stresses acting on both the top and bottom boards, a and b, of the beam.
4、an a-36 steel strip has an allowable bending stress of 165 mpa. if it is rolled up, determine the smallest radius r of the spool if the strip has a width of 10 mm and a thickness of 1.5 mm. also, find the corresponding maximum internal moment developed in the strip.
1、determine the principal moments of inertia for the beam's cross-sectional area shown in fig. a-15 with respect to an axis passing through the centroid c.
lecture 14
6.2 construction of moment diagram by principle of superposition随堂测验
1、plot bending moment diagram by the priciple of superposition. point out the maximum value of bending moment. a、 b、 c、 d、
6.2 internal loading diagrams of inclined or curved beams随堂测验
1、plot the shear and moment diagrams for the following frame. please specify the maximum values of shear force and bending moment. a、qa, b、qa/2, c、qa, d、qa/2,
4、 a、v = -315 lb, m = {-630x 2400} lb · ft b、v = -315 lb, m = {-315x 1200} lb · ft c、v = -630 lb, m = {-630x 2400} lb · ft d、v = -630 lb, m = {-315x 1200} lb · ft
5、 a、v = {1050 - 150 x} lb, m = {-37.5x2 525x - 2000} lb • ft b、v = {525 - 75 x} lb, m = {-75x2 1050x - 4000} lb • ft c、v = {525 - 75 x} lb, m = {-37.5x2 5250x - 2000} lb • ft d、v = {1050 - 150 x} lb, m = {-75x2 1050x - 4000} lb • ft
6、 a、v = {30.0 - 2 x} kip, m = {-x2 30.0x - 216} kip • ft b、v = {15.0 - x} kip, m = {-0.5x2 15.0x - 108} kip • ft c、v = {15.0 - x} kip, m = {-x2 30.0x - 216} kip • ft d、v = {30.0 - 2 x} kip, m = {-0.5x2 15.0x - 108} kip • ft
7、 a、v = 31.2 n, m = {31.2x 200} n• m b、v = 31.2 n, m = {15.6x 100} n• m c、v = 15.6 n, m = {15.6x 100} n• m d、v = 15.6 n, m = {31.2x 200} n• m
8、 a、v = -1.0 kip, m = {-45 - 1.0x} kip • ft b、v = -1.0 kip, m = {-22.5 - 0.5x} kip • ft c、v = -0.5 kip, m = {-45 - 1.0x} kip • ft d、v = -0.5 kip, m = {-22.5 - 0.5x} kip • ft
9、 a、v = -16 kip, m = [8(18 - x)] kip • ft b、v = -16 kip, m = [16(36 - x)] kip • ft c、v = -8 kip, m = [16(36 - x)] kip • ft d、v = -8 kip, m = [8(18 - x)] kip • ft
10、 a、a b、b c、c d、d
11、 a、a b、b c、c d、d
12、 a、a b、b c、c d、d
13、the internal force on the right section of beam section c is ( ) a、 b、 c、 d、
14、the maximum shear force and bending moment on the beam shown in the figure are ( ) a、30kn, 29.36knm b、30kn, 20knm c、15kn, 29.36knm d、15kn, 20knm
15、is the shear moment diagram of the beam shown in the figure correct? a、correct b、section b bending moment error c、section b shear error d、section a bending moment error
16、is the shear force and bending moment diagram of the beam shown in the figure correct? a、correct b、wrong bending moment value of section d c、wrong shear value of section d d、the bending moment of section c is correct
17、the concentrated couple value of the beam corresponding to the shear diagram in the figure is a、0 b、5knm c、10knm d、15knm
18、the concentrated couple value of the beam corresponding to the shear diagram in the figure is a、0 b、0.2knm c、0.5knm d、0.8knm
19、the shear force on the beam corresponding to the bending moment diagram is a、0 b、1 kn c、2kn d、3kn
20、the distributed load on the beam corresponding to the bending moment diagram in the figure is a、0 b、q c、2q d、0.5q
21、the maximum shear force and bending moment on the beam shown in the figure are: a、5kn, 5knm b、5kn, 10knm c、10kn, 5knm d、10kn, 10knm
22、the maximum shear force and bending moment on the beam shown in the figure are: a、80kn, 160knm b、50kn, 160knm c、80kn, 100knm d、50kn, 100knm
23、the maximum shear force and bending moment on the beam shown in the figure are: a、 b、 c、 d、
24、the maximum shear force and bending moment on the beam shown in the figure are: a、38.5kn, 77.01knm b、32.625kn, 77.01knm c、38.5kn, 29.43knm d、32.625kn, 29.43knm
25、as shown in the figure, the simply supported beam is subjected to various external loads. when the distributed external force acts on section ab, and its concentration is w = 1 kn / m, the maximum shear force and bending moment on the beam are a、3.2kn, 6.01knm b、3.2kn, 5.67knm c、1.83kn, 6.01knm d、1.83kn, 5.67knm
14 _ homework
1、
2、draw the shear and moment diagrams for the compound beam.
3、for the given shear force diagram, construct moment and load diagrams. there is no concentrated moment applied on the beam.
4、for the given moment diagram, construct shear and load diagrams.
5、construct the shear and moment diagrams of the frame.
6、
lecture 16
6.5 unsymmetric bending随堂测验
1、 a、 b、 c、 d、
16 _ homework
1、the member has a square cross section and is subjected to the moment m = 850n. m as shown. determine the stress at each corner and sketch the stress distribution. set θ= 30°.
2、if the resultant internal moment acting on the cross section of the aluminum strut has a magnitude of m = 520n.m and is directed as shown, determine the bending stress at points a and b. the location y of the centroid c of the strut's cross-sectional area must be determined. also, specify the orientation of the neutral axis.
3、the 65-mm-diameter steel shaft is subjected to the two loads. if the journal bearings at a and b do not exert an axial force on the shaft, determine the absolute maximum bending stress developed in the shaft.
11、the load of the overhanging beam is shown in the figure. if the [σ] = 10mpa, [τ] = 1.5mpa, the beam diameter d = 200mm, a = 1m, determine the maximum load that the beam can bear. a、7.85kn b、8.85kn c、9.85kn d、10.85kn
12、determine the maximum normal stress and maximum shear stress on the cross section of the beam shown in the figure. a、297.4mpa， 39.6mpa b、297.4mpa， 29.6mpa c、197.4mpa， 39.6mpa d、197.4mpa， 29.6mpa
13、if the moment of inertia of the cross-section beam to the neutral axis is iz=2910000mm4，yc=65mm, and c is the centroid, determine the maximum tensile stress, maximum compressive stress and maximum shear stress on the beam. a、45.6mpa， -67mpa, 4.4mpa b、45.6mpa， -80mpa, 5.4mpa c、55.6mpa， -67mpa, 5.4mpa d、55.6mpa， -80mpa, 4.4mpa
14、the geometric dimensions l, b and h of the beam shown in the figure are known. if the allowable normal stress of the beam is [σ], determine the maximum shear stress in the beam when σ max = [σ]. a、τmax=h[σ]/3l b、τmax=2h[σ]/3l c、τmax=2h[σ]/l d、τmax=h[σ]/l
15、determine the maximum normal stress and maximum shear stress on the cross section of the beam shown in the figure. a、25.13mpa，2.04mpa b、25.13mpa，1.04mpa c、15.13mpa，2.04mpa d、15.13mpa，1.04mpa
16、as shown in the figure, the cross-section of the beam is welded by three steel plates. if the shear force acting on the cross-section is fs=18 kn, determine the force that must be borne by the weld per unit length. dimensions in mm. a、47.7n b、37.7n c、27.7n d、17.7n
17、the bending moment on the cross-section of the beam is m=60 kn·m, and the cross-section size is shown in the figure. determine the maximum normal stress on this section. (dimensions in the figure are in mm) a、59.3mpa b、49.3mpa c、39.3mpa d、29.3mpa
18、the diamond shaped beam is shown bending around the z-axis. given that the shear force on the cross-section is fs, determine the location of the maximum shear stress on the cross-section. (it can be calculated by shear stress formula of rectangular section beam) a、at neutral axis b、h / 2 from neutral axis c、h / 4 from neutral axis d、h / 8 from neutral axis
19、the cross section of the beam is shown in the figure. if the compressive strain of the upper longitudinal fiber is ε=－0.0003, and the tensile strain of the lower longitudinal fiber is ε=0.0006. determine the total normal internal force of the shadow part on the section. e = 200 gpa for known materials. a、700kn b、800kn c、900kn d、1000kn
20、the solid shaft is supported by smooth bearings a and b. the bearing only provides the reaction force in the vertical direction. if the diameter of the circular shaft d = 90mm, determine the maximum normal stress and maximum shear stress on the circular shaft. a、158mpa, 4.09mpa b、158mpa, 8.09mpa c、258mpa, 4.09mpa d、258mpa, 8.09mpa
21、the solid shaft is supported by smooth bearings a and b. the bearing only provides the reaction force in the vertical direction. if the allowable normal stress of the material is [σ] = 180mpa and the allowable shear stress is [σ] = 80mpa, determine the minimum diameter d of the circular shaft. a、8.63cm b、2.03cm c、10.63cm d、4.03cm
22、the cross-section steel beam is subjected to distributed load and the section size is shown in the figure. the normal stress and shear stress at the junction a of web and flange on section a are ( ) a、a b、b c、c d、d
23、two boards are nailed together to form a simply supported timber beam as shown in the figure. the bearing load is p = 20kn. if the maximum shear force that the nail can bear is 2.5kn and the cross section size is a = 5cm, determine the maximum spacing s of nails. a、0.15m b、0.16m c、0.17m d、0.18m
18 _ homework
1、
2、
3、
4、
lecture 26
13.3 columns having various types of supports随堂测验
1、 a、604 kn b、504 kn c、704 kn d、804 kn
26 _ homework
1、
2、
3、
4、
lecture 27
13.4 critical stress随堂测验
1、 a、ab: 2.125 in. , bc: 2 in. b、ab: 3.125 in. , bc: 2 in. c、ab: 2.125 in. , bc: 3 in. d、ab: 3.125 in. , bc: 3 in.
8、 a、d=9/4in. b、d=9/8 in. c、d=9/16 in. d、d=9/32 in.
9、the plane static analysis frame is shown in the figure. it is known that the diameter of each rod is d, the length is a, and the elastic modulus is e. try to calculate the ultimate load f that the structure can bear without instability of cd rod in the plane. a、a b、b c、c d、d
10、it is known that the material of each member of the plane rigid frame shown in the figure is the same, and the elastic modulus is e. if the cd member is a slender member and the cross section is a rectangular section, the flexibility of the cd member and the ultimate load f of the structure are ( ). a、a b、b c、c d、d
11、as shown in the figure, the structure is composed of vertical bar ab and inclined bar bc, both of which are slender bars with sectional bending stiffness ei, and bear the action of horizontal load f at node b. a = 4m and b = 3m, and try to calculate the allowable load of the structure. a、a b、b c、c d、d
12、four equilateral angle steels 125 × 125 × 12 are used to form two kinds of cross-section columns as shown in (a) and (b). if the constraint at the rod end is the same and δ = 16 mm is known, the ratio of the critical load of the column in the two cases is ( ). a、1/2 b、1/2.2 c、1/3.3 d、1/3
13、the square plane frame composed of five round section steel bars, the diameter of the bars is d = 40 mm, the elastic modulus of the material is e = 200 gpa, and the length of the bar is a = 1 m. try to calculate the minimum load when the structure reaches the critical state. if f force acts inward, what is the minimum load? a、124kn, 350.7kn b、114kn, 300.7kn c、124kn, 300.7kn d、114kn, 350.7kn
14、as shown in the figure, the bracket bears uniformly distributed load q, and the strut ab is a slender rod with relatively supported ends. when q reaches what value, the rod ab is in a critical state. a、a b、b c、c d、d
15、the structure shown in the figure is composed of three slender beams with the same bending stiffness ei. the two points b and d are connected by ammonium chains, while a and c are fixed ends, α = 30 ° try to calculate the critical value f of the system. a、a b、b c、c d、d
16、it is known that the material of each member of the plane rigid frame shown in the figure is the same, and the elastic modulus is e. if the cd member is a slender member and the cross section is a rectangular section, try to calculate the flexibility of the cd member and the ultimate load f of the structure. a、a b、b c、c d、d
17、as shown in the figure, load f is applied at the end of the horizontal rigid beam ab, and two columns cg and dh with the same length l are used at c and d respectively. if the bending stiffness of each column is ei, try to calculate the critical load f. a、a b、b c、c d、d
18、 a、74kn b、64kn c、84kn d、94kn
19、as shown in the figure, the two ends of three slender compression members of the same material are hinged, but the length and diameter of each member are different. is the critical stress of the three members the same? a、same b、(a)>(b)>(c) c、(b)>(a)>(c) d、(c)>(b)>(a)
20、three kinds of material, length are the same, both ends are spherical hinge support of slender rod structure, their cross-section shape is shown in the figure, the critical stress ratio is ( ), the critical force ratio is ( ). a、1:1:5， 1:2:20 b、1:2:20，1:1:5 c、1:1:4， 1:2:10 d、1:2:10，1:1:4
21、 a、6.94kn b、7.94kn c、8.94kn d、9.94kn
22、 a、71.6 kn b、61.6 kn c、81.6 kn d、91.6 kn
23、the rigid horizontal beam is supported by 1 and 2 rods of the same material. the two ends of the rod 1 are fixed, the cross section is square, and the side length is a.the two ends of the rod 2 are supported, with a circular cross section and a diameter of d.and d = 2a.the elastic modulus of the material is e, l= 30d, and the critical flexibility of euler formula is 100. try to find out where the force f acts on the beam ab, and the structure bears the maximum load. a、x=0.702l b、x=0.602l c、x=0.502l d、x=0.402l
24、 a、9.18kn b、10.18kn c、11.18kn d、12.18kn
25、 a、26.65kn b、36.65kn c、16.65kn d、46.65kn
27 _ homework
1、
2、
3、
4、an l-2 tool steel link in a forging machine is pin connected to the forks at its ends as shown. determine the maximum load p it can carry without buckling. use a factor of safety with respect to buckling of f.s. = 1.75. note from the figure on the left that the ends are pinned for buckling, whereas from the figure on the right the ends are fixed.
2、the stresses along two planes ab and ac at a point are indicated in fig.(a). draw mohr's circle, and determine the principal stresses acting at this point and the orientation of the element upon which they act.
3、
4、the stresses along two planes of ab and ac at a point are indicated in the figure. draw mohr's circle, and determine the principal stresses and the maximum in-plane shear stress acting at this point.
lecture 22
9.7 absolute maximum shear stress随堂测验
1、determine the principal stresses of the following element. a、σ1=523.2mpa, σ2=-103.2 mpa, σ3=-400 mpa, b、σ1=623.2mpa, σ2=-103.2 mpa, σ3=-400 mpa, c、σ1=523.2mpa, σ2=-203.2 mpa, σ3=-400 mpa, d、σ1=523.2mpa, σ2=-103.2 mpa, σ3=-500 mpa,
2、determine the principal stresses and absolute shear stress.
3、a segment of a generator shaft is subjected to a torque t and a bending moment m, as shown in the figure. strain gages a and b orientated in axis and 45° direction, respectively, are attached to the surface of the shaft. the gage readings give normal strain εa=5×10-4 and εb=4.3×10-4. knowing that e＝210 gpa, ν＝0.25, determine if failure has occurred on the basis of the maximum shear stress theory. the yield stress for the steel is σy=160 mpa.
4、
lecture 25
12.5 method of superposition随堂测验
1、determine the deflection of section c by method of superposition. ei=c a、/24ei b、/12ei c、/6ei d、/48ei
12.5 slope and deflection by energy method随堂测验
1、 a、/256ei b、/128ei c、/515ei d、/64ei
12.9 statically indeterminate beam and shaft —method of superposition随堂测验
1、 a、3.75 kn b、4.75 kn c、5.75 kn d、6.75 kn
25 _ homework
1、
2、
3、the shaft supports the two pulley loads shown. determine the deflection at the left end. the bearings at a and b exert only verticle reactions on the shaft. ei is constant.