材料力學(xué)試卷：201312 final exercise 3

1、姓名 學(xué)號(hào) 學(xué)院 專業(yè) 座位號(hào) ( 密 封 線 內(nèi) 不 答 題 )密封線線_ _ 誠(chéng)信應(yīng)考,考試作弊將帶來(lái)嚴(yán)重后果！ 華南理工大學(xué)期末練習(xí)Mechanics of Materials注意事項(xiàng)：1. 考前請(qǐng)將密封線內(nèi)填寫清楚； 2. 所有答案請(qǐng)直接答在試卷上(或答題紙上)； 3考試形式：閉卷； 4. 本試卷共六大題，滿分100分，考試時(shí)間120分鐘。ProblemIIIIIIIVVVITotal scorescoreGrading personI. Simple calculation problems（ total score 44）01. Determine the moment of in

2、ertia with respect to centroid axis zc.(Note: C is the centroid.) (score 6)02. A bar made of low carbon steel having the stress-strain diagram shown in the figure had a initial gage length of L0 and initial cross-sectional area A0. At fracture, the bar had the gage length L1. Determine the ultimate

3、stress y, ultimate stress u and the percent elongation .(score 3)03. An element of material (E=200GPa, =0.20) shown in the figure is subjected to normal stress and shear stress. (a) Determine the three principle stresses and the maximum shear stress. (b) Determine the three principle strains and the

4、 equivalent stress r3 with the third strength theory (score 8) 04. Find the maximum bending moment in the beam AB under the suddenly applied load Q. (score 4)05. The simple beam AB shown in the figure supports a concentrated load F. Assume the angle of rotation at section C is c .(a) Determine the a

5、ngle of rotation at section C if the concentrated load F is reduced to F/2.(b) Determine the angle of rotation at section C if the length of the beam l is increased to 2l. (Note: The ratio a/l and b/l are not change)(score 4)06. A shaft ABC consisting of two solid circular segments is subjected to t

6、orques shown in the figure. The maximum shear stresses in two segments are same. (a)Determine the ratio of diameter d1 / d2. (b)Determine the ratio of angle of twist AB/ BC.(score 8)07. The bolt of diameter d is loaded by an axial force F. The allowable shear stress and allowable tensile stress in t

7、he bolt are and , respectively. =0.6. If the normal stress and shear stress in the bolt occur the allowable stresses at the same time, determine the ratio of diameter d and height h of the bolt.(score 4)08. The structure shown in figure consists of horizontal beam AB (assumed to be rigid) supported

8、by two identical bars (bars 1 and 2). Assume l1 and l2 are changes in length of two bars. , and a are known. Find the equation of compatibility. (score 4)二、Draw shear-force V and bending-moment M diagrams for the beam (see figure).（score 12） 3、 The rigid frame ABCD supports two concentrated loads P.

9、 Assume that the flexural rigidity EI is constant throughout the frame. Disregard the effects of axial force deformations and consider only the effects of bending due to load P Find the angle of rotation D at section D using the energy method.（score 10）4、 A rectangular simple beam AB shown in figure

10、 is subjected to a uniform load of intensity q acting through its length l=1000mm. Determine the maximum shear stress when the normal stress reaches maximum value max =120MPa.5. A circular cantilever beam AB with diameter d shown in the figure supports a vertical concentrated load P1 acting at the f

11、ree end B, a horizontal concentrated load P2 and a couple m acting at section C. Assume the allowable normal stress of the bar =110MPa, d=7cm, P1=2kN, P2=6kN, AC=CB=30cm, m=1.8kNm. Check the strength of the bar with the third strength theory.（score 12）6. The rectangular beam AB has cross- sectional area A=21.5cm2. The section modulus along the beam is constant S=102cm3 and allowable normal stress of the beam is =180MPa. A circular bar CD has diameter d=20mm, the material of bar CD has modulus of elasticity E=200GPa and the proportional limit p =200MPa. A,