材料力学试卷：201401 Mechanics of__ materials_final exam_A

1、姓名 学号 学院 专业 座位号 ( 密 封 线 内 不 答 题 )密封线线_ _ 诚信应考,考试作弊将带来严重后果！ 华南理工大学期末考试Mechanics of Materials试卷A注意事项：1. 考前请将密封线内填写清楚； 2. 所有答案请直接答在试卷上(或答题纸上)； 3考试形式：闭卷； 4. 本试卷共六大题，满分100分，考试时间120分钟。ProblemIIIIIIIVVVITotal scorescoreGrading personI. Simple calculation problems（5 problems, 5 points each, total 25 points）

2、01. A prismatic bar AB, fixed at one end and free at the other, is loaded by a distributed torque of constant intensity t per unit distance along the axis of the bar. Find the angle of rotation B at free end B if the data are as follows: t=2100 Nm/m, L=3.7 m, G=80 GPa, and Ip=7.1510-6 m4.02. A punch

3、 for making holes in steel plates is shown in Fig.a. Assume that the punch having diameter d=20 mm is used to punch a hole in an 8-mm plate, as shown in the cross-sectional view (Fig.b). If the allowable shear stress of the steel plate is =220MPa, what should be the magnitude of the load P? 03. A ci

4、rcular bar of diameter D=10 mm is tensioned by an axial force F=200 kN and the change in diameter D=0.096 mm.The material has modulus of elasticity E=200 GPa and behaves linearly elastically. Determine the Poissons ratio . 04. Find the maximum normal stresses in the frame ABC under the suddenly appl

5、ied load Q. (The section modulus along the frame is constant S and disregard the effects of an axial force)05. A simple beam ACB supports a uniform load of intensity q on the left-hand half of the span (see figure). Span AB has length L. Determine the strain energy of the beam. (Assume that the beam

6、 has constant flexural rigidity EI.)II. A beam ABC with an overhang at the left-hand end is shown in Figure. The beam is subjected to a uniform load of intensity q=1.0 kN/m on the overhang AB and a counterclockwise couple M0=12.0 kNm acting midway between the supports at B and C. Draw the shear-forc

7、e and bending-moment diagrams for this beam.（15 points） III. A framework shown in the figure having pin supports at point A and D is loaded by a force Fp=58 kN. Two wooden bars AB and AC have same cross-sectional areas Aw and two steel bars CD and CB have same cross-sectional areas As. All the bars

8、are pin-connected. The lengths of bars BC, AB, AC, and CD are 5 m, 4 m, 3 m, and 2 m, respectively. Determine the required cross-sectional areas Aw and As if the allowable normal stress in bars CD and CB is s=120MPa and the allowable normal stress in bars AB and AC isw= 20MPa. （15 points）IV. A propp

9、ed cantilever beam of length 2a has a fixed support at A and a roller support at midpoint C (see figure). A concentrated load F acts at the free end B. Assume that the flexural rigidity EI is constant throughout the beam. Find the reaction RC for the beam. (Note: Assume the deflections and angle of

10、rotation for a cantilever beam as follows.) （15 points） Note: V. An L-shaped bracket lying in a horizontal plane supports a load P (see figure). The bracket has a circular cross section with diameter d=100 mm in segment AB and centerline length a=400mm. The material of the bracket is linearly elasti

11、c and the modulus of elasticity is E=200 GPa. Point K is located on the top of the cross section D and its axial normal strain is measured =2.7510-9. If the allowable stress in the bracket is s =160 MPa. (a) Determine the normal stress and shear stress at the critical points and show them on a sketc

12、h of a properly oriented element.(b) Check the strength of the bracket with the third strength theory. (15points)VI. A long, slender column ABC is pin-supported at the ends and compressed by an axial load P. Lateral support is provided at the midpoint B in the plane of the figure. However, lateral support perpendicular to the plane of the figure is provided only at the ends. ABC is a rectangular column with cross-sectional dimensions b=50 mm and h=80 mm. Assume E=200 GPa and