The owner of a local parking garage has decided to install a

The owner of a local parking garage has decided to install a steel post set in concrete as a way to let the operators of vehicles who are backing their cars into parking spaces know that they have reached the limit of the parking space. You have been asked to do an analysis of this idea to see proposed post is robust enough to handle the task. The schematic for this is shown in the diagram above, mass if the speed of the car is 2 miles per hour when it impacts the post, answer the following questions: What will be the kinetic energy of the moving car (ft. lbf) that will need to be stored in strain energy in the cantilever beam to bring the car to zero velocity? If the strain energy for an end-loaded cantilever beam is related to the area under the load -vs-deflection curve, what will be the maximum load (Ibf) and the maximum deflection of the beam (inches) in stopping this car if the following design parameters for the beam are used: E = 30 times 10^6 psi for steel. Height of the post where the impact will occur is h = 24 in. The post is a piece of schedule 40 steel pipe with OD = 6.625 and ID = 6.065 inches. I lbf = 32.2 ft lbm/sec^2, What will be the largest stress on the cantilever post and where will this occur? Can you think of some ideas that might be used to improve this design?

Solution

a) Kinetic enery = 1/2*mass*(velocity*velocity)= 1/2*1815.5(in kg)*0.44704*0.44704 (in m/s)= 181.4 Joules= 133.8(ft-lbf)

B) Deflection of a cantilever beam with a load at end point is W*(L^3)/(3*E*I)

Stress, Sigma= M*Y/I

I = Second Moment of Inertia= Pi*(D^4-d^4)/64 for a hollow pipe

M= Fprce* Distance= W*2ft

Y = D/2 ( neutal axis)

So 1/2*Stress*strain= energy stored which is equivalent to 133.8

Solving above equation we get

W as 7.4 E8 N

c) 69.8N/m^2 at the joint between pole and ground

d) Imrpvement in the design is to use I section then hollow cylinder as this will reduce the stress. I section has better Section modulus .