You are required to design a Cantilever Rack for a car salvage yard to store wre

Question

You are required to design a Cantilever Rack for a car salvage yard to store wrecked cars. Figure shown below should be taken as the design concept. Take maximum weight of a car to be 3000 kg. You should calculate the maximum bending, shear and compressive stresses developed at the different members of the structure to identify maximum stresses. You may need to alter the number of cars from 0 to six to determine when the maximum stresses are developed. Calculate the bending stress using sigma = Mc/l, Where sigma is the normal stress (due to bending), M is the maximum bending moment and l is moment of inertia. l = bd^3/12 where b is width and d Is height of the beam, c is the maximum distance from the neutral axis (assume c = half of the height of the beam = d/2). Assume b and d as appropriate. Different combination of vehicle loads develop different bending stress in the pole close to the support. Calculate the compressive stress using sigma_c = F/A where sigma_c is compressive stress, F is the load applied and A is cross sectional area of the member. For shear stress use the shear force and the corresponding area parallel to the force.

Explanation / Answer

Starting from left, let the cars be numbered as 1,2,3,4,5 and 6.

So, Maximum Bending moment of each of the car, M = bd/12

where b is the width and d is the length of cantilever rack.

Let the whole length of the rack be d such that a car is place at d/3 distance.

Moment of inertia = bd3/12

So, maximum bending stress on

car 1 and 6 = b/12(d/3)*(d/6) / b/12(d/3)3 = 1/2d

car 2 and 4 = b/12(2d/3)*(2d/6) / b/12(2d/3)3 = 3/2d

car 3 and 6 = b/12(d)*(d/2) / b/12(d)3 = 1/2d

Shear force, F = mg

Area = length*breadth

shear stress on

car 1 and 6 = 3000*9.8/b*d/3 = 9*10^4/bd

car 2 and 4 = 2*3000*9.8/b*2d/3 = 9*10^4/bd

car 3 and 6 = 3*3000*9.8/bd = 9*10^4/bd

Also maximum compressive stress is equal to maximum shear stress.

So, cars in the middle of the rack will bear maximum stress.

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