DYNAMIC LOAD 1 Dynamic stress of the body in the straight-line motion Example 1 The effective area of the steel wire rope in a crane is A, [d] is known. Weight per unit volume of the body is r and the body moves up at the acceleration. Try to check the strength of the rope (neglect the weight ofthe rope Solution: (1 Analysis of the forces is shown in the figure Inertial force x g L N=(q1+q0)x=4x(1+一) N d g mIn ② Dynamic stress x aG N (1+) A
a g A q G = ( ) (1 ) g a N q q x Ax d = j + G = + (1 ) g a x A Nd d = = + Solution：①Analysis of the forces is shown in the figure: ②Dynamic stress 1、Dynamic stress of the body in the straight-line motion L x m n a x a Nd qj qG Inertial force Example 1 The effective area of the steel wire rope in a crane is A , [] is known . Weight per unit volume of the body is and the body moves up at the acceleration a. Try to check the strength of the rope（neglect the weight of the rope）
直线运动构件的动应力 「例1起重机钢丝绳的有效横截面面积为A,已知[,单位 体积重为y,以加速度a上升,试校核钢丝绳的强度(不计绳 重)。 解:①受力分析如图: 惯性力:qG=a x L N=(q1+q0)x=4x(1+一) N d g mIn ②动应力 x G Nd=(1+-) A
a g A qG 惯性力： = ( ) (1 ) g a N q q x Ax d = j + G = + (1 ) g a x A Nd d = = + [例1 ] 起重机钢丝绳的有效横截面面积为A , 已知[], 单位 体积重为 , 以加速度a上升，试校核钢丝绳的强度（不计绳 重）。 解：①受力分析如图: ②动应力 一、直线运动构件的动应力 L x m n a x a Nd qj qG
DYNAMIC LOAD Odma -y(h )=K, d jmax C Coefficient of the dynamic load=1+- Strength condition: Omx =K,omx<o If: Cdma o) then the strength condition is satisfied
max max (1 ) d Kd j g a =L + = g a Coefficient of the dynamic load： Kd =1+ = Strength condition： dmax Kd jmax If ： max , d max , d then the strength condition is satisfied. If ： then the strength condition is not satisfied
-y(+o=Kdo C 动荷系数:a=1+ g 强度条件:口mN=Km 若 σm(]满足 oam{]不满足
max max (1 ) d Kd j g a =L + = g a 动荷系数： Kd =1+ = 强度条件： dmax Kd jmax 若： max d max d 满足 不满足
DYNAMIC LOAD Example 2 Length of the steel rope of a crane is 60m, its nominal diameter is 28cm, its effective cross-section area is A=2. 9cm, weight per unit length is q=25 5N/m and [o=300MPa. The acceleration when the rope lifts an object of 50kn is a=2m/s, Try to check the strength of the steel rope Solution: (1 The free body N diagram is shown in the figure N=(G+qL)(1+) g L(ltalg) ② Dynamic stress G+qL(1+) AA g ,(50×103+25.5×60/人 2.9×10 9.8 G(1+a/g) -214MPao300MPa
( )(1 ) g a Nd = G+qL + ) 9.8 2 (50 10 25.5 60)(1 2.9 10 1 3 4 + + = − =214MPa=300MPa Example 2 Length of the steel rope of a crane is 60m，its nominal diameter is 28cm，its effective cross-section area is A=2. 9cm2 , weight per unit length is q=25. 5N/m and [] =300MPa. The acceleration when the rope lifts an object of 50kN is a=2m/s2 , Try to check the strength of the steel rope. G(1+a/g) Nd L q(1+a/g) ( )(1 ) 1 g a G qL A A Nd d = = + + Solution：①The free body diagram is shown in the figure: ②Dynamic stress