A metal beam is welded to another metal beam and the ensemble is supported at bo

Question

A metal beam is welded to another metal beam and the ensemble is supported at both ends, with dimensions as shown: Also shown is a load at a distance x from the left. The weld can be handle a maximum torque of 110 m N and the load has a mass of 6O kg. The question you will answer is what the maximum value is for x beyond which the weld would fail assuming the metal beams themselves have negligible mass Start by finding expressions for the two support forces, on the left and on the right. Do this by recognizing that the sum of these two forces equals the weight of the load and then by analyzing the torques of those two forces relative to the point where the load is, or if you'd like to try a different approach, that is fine, too. Calculate the torque applied to the weld by analyzing the system of the right metal beam. Define the torque relative to a point in the middle of the weld and the torque will balance against that supplied by the weld. You might also think about how the weld would fail to understand how there is a torque there.

Explanation / Answer

here,

mass of metal bob , m = 60 kg

let the normal reaction at the left end and the right end be Nl and Nr

taking torque at the left end to zero

x*m*g - 1.00 * Nr = 0

Nr = x*m*g

taking torque about the right end be zero

(1.00 - x) * m*g - 1.00 *Nl = 0

Nl = (1- x) *m*g

the maximum net torque about the joint

Nr( 0.60 - 0.40) + m*g*( 0.60 - x) - Nl*0.60 = - 110

x*m*g * ( 0.2) + m*g*( 0.6 - x)- (1-x) * m*g *0.6 = - 110

x*60*9.8 * 0.2 + 60*9.8*( 0.6-x) - ( 1-x) *60*9.8*0.6 = - 110

x = 0.935 m

x = 93.5 cm

the maximum value of x is 93.5 cm

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