理论力学复习题

Total Review of Theoretical Mechanics

一、静力学（STATICS）

1、由AC和CD构成的组合梁通过铰链C连接。它的支承和受力如图所示。已知均布载荷

强度q=10KN/m，力偶矩M= 40 KN?m，不计梁重。求支座A，B，D的约束力和铰链C处所受的力。

1. Beams AC and CD are joined by a smooth pin C, Knowing q=10KN/m, M=40KNm, other conditions are shown as figure. Determine the reaction forces at points A, B, D, C. Neglect the weights of the beams.

2、水平梁AB由铰链A和杆BC所支持，如图所示。在梁上D处用销子安装半径为r=0.1m的滑轮。有一跨过滑轮的绳子，其一端水平地系于墙上，另一端悬挂有重P=1800N的重物。如AD=0.2m， BD=0.4m， ? ? 45 0 ，且不计梁、杆、滑轮和绳的重量。求铰链A处的约束力和杆BC的内力。

2. A bracket consists of members AB, CB and pulley D as shown in figure. A string supporting a weight P=1800N passes through over pulley D, the other end of the string is secured to the wall. r=0.1m, AD=0.2m, BD=0.4m, ????? . Determine the reaction forces at points A and the internal force of rod BC. The weight of the members and pulley are negligible.

?3、在图示连续梁中，已知q，a及 。不计梁的自重。求梁在A，B，C三处的约束力。

3. Beams AB and BC are joined by a smooth pin B. Knowing q, a, and ? . The weights of the beams are negligible. Determine the reaction forces at points A, B and C.

?

4、图示构架中，物体重1200N，由细绳跨过滑轮E而水平系于墙上，尺寸如图，不计杆和滑轮的重量。求支承A和B处的约束力。

4. A composite truss is shown as figure. A block of weight 1200N is connected to a string wrapped around the pulley E，the other end of the string is secured to the wall. Other conditions are shown as figure. The weights of links and pulley are negligible. Determine the reaction forces at points A and B.

5、求A、B、C处的约束反力。

5. Find the reaction forces at points A, B and C. The weights of the elements are negligible.

6、图示构架中，各杆重均略去不计，B、C为光滑铰链，已知载荷P。试求固定端A及支座D的约束反力。

6. A composite truss is shown as figure. The weights of links are negligible. The pins B and C are smooth pins. Knowing the load P. Other conditions are shown as figure. Determine the reaction forces at points A and B.

7、无重水平梁的支承和载荷如图所示。已知集中力F、力偶矩M和均布载荷q。求支座A和B处的约束力。

7. A horizontal beam is shown as figure. The weight of the beam is negligible. Knowing F, M and q. Other conditions are shown as figure. Determine the reaction forces at points A and B.

a链C处所受的力。

a

8、由AC和CD构成的组合梁通过铰链C连接。不计梁重。求A，B，D处的约束力和铰

8. Beams AC and CD are joined by a smooth pin C. The weights of the beams are negligible. Other conditions are shown as figure. Determine the reaction forces at points A, B, D and C.

二、运动学（KINEMATICS）

填空题

（1）题1图所示平面机构中，AB杆的A端靠在光滑墙上，B端铰接在滑块上，若选AB上的A为动点，滑块为动系，则A的相对运动为 以B为圆心，AB为半径的圆周运动。 。

（2）圆盘以 ω＝3t rad／s绕水平轴AB转动，盘上M点沿半径按OM＝4t2 cm的规律运动，如题2图所示。当t＝1s时，科氏加速度ac＝ 24 cm/s 。

（题1图）

（题2图）

（3）在题3图所示的公路上行驶的两车的速度均为20m／s，图示瞬时，在A车中的观察者看来，B车的速度大小应为 38．6m／s 。

（题3图）

（题4图）

（4）平面机构如题4图所示，画出M点的速度方向 。

1、四连杆机构由杆O1A、O2B及半圆形平扳ADB组成，动点M沿圆弧运动，如图所示。已知O1A＝O2B＝18cm，R＝18cm，??绝对速度和绝对加速度。

?18t，s＝BM＝?t2cm。求：t ＝3s时，M点的

1.Consider a mechanism of four connecting rods shown in the figure. The

semi-circular plate ADB of radius R is supported by two parallel links, and O1A＝O2B＝18cm, R＝18cm.The angle of rotation of link is ???18t. At the same time, a moving

particle M moves along the circular path in the plate, and s＝BM＝?t2cm. Determine the absolute velocity and absolute acceleration of particle M at t =3s.

2、如图所示，半径为R＝43cm的圆盘，以匀角速度ωo＝1.5rad／s绕O轴转动，并带动连有螺旋弹簧且紧压在圆盘上的杆CD，使该杆绕Ol轴转动。试求?＝300时，杆CD的角速度与角加速度。

2. As shown in the figure, the disk A of radius R＝43cm rotates about axis O with a constant angular velocity ωo＝1.5rad／s. Rod CD, which is free to rotate about the axis O1, is leaning against the disk. Find the angular velocity and acceleration of rod CD when ?＝300

3、如图所示，曲柄OA长为40cm，以等角速度ω＝0.5rad／s绕O轴转动，曲柄的A端推动水平板B使得杆BC上升，求θ＝300时，滑杆BC的速度和加速度。

3.In the mechanism shown in the figure, crank OA of length l=40cm rotates about axis O with a constant angular velocity ω= 0.5 rad/s and pushes up a slide rod BC moving in a vertical runner. Determine the velocity and acceleration of slide rod BC whenθ＝300 .

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