Shear problems? I need to pass physics...Help!?

Question

I need for a science genius to answer these questions.

1.) A concrete coulumn is to support a 2100000-lb load with a safety factor of 2.5. What must its cross-sectional area be?

2.) If its unstressed height is 80 ft, what will its loaded height be?

Please help, I need to graduate, i will appriecate it.

I mean shear. Its a 20 inch long triangle k.

Answer 1

An object under shear stress has an equal and opposite forces applied across its oposite faces... I can't quite imagine the picture for this problem. Could you clarify? Is it a vertical column and there is a weight on top? (then it's not shear stress, it's different kind)? Or is the column is being pushed from the side somehow (doesn't sound that way)?

1) I'll assume that the word "shear" was accidental and you ment "stress":

stress = force/area.

Maximun allowed stress is less than that, we take into account the safety fastor:
Max allowed stress = stress/safety factor

From the above, we conclude
Area = (safety factor * force)/stress

Force = mg
m = 21000000 * 2.21 = 4641000 kg
Force = 4641000 * 9.8 = 45481800 N
Stress = compressive strength = 20*10^6 N/m^2

Now you can substitute everything into the expression for the area (6 lines above from here)
I hope it helps. You'll have to write it out nicely, sorry, I'm a bit lazy.

2) Assume the unstressed height is Lo
stressed lenght is L1

L1 = Lo - delta L
L1 = Lo - F*Lo/(E*A)
where F is applied force calculated above, E is Young's modulus, A is cross-sectional area.

Answer 2

1. the area = load/conc. strength. With factor of safety, multiply the load by 2.5, and divide by concrete strength and you will get the area in sq. in. Your teacher should have given you the concrete strength (about 5,000 psi).

2. the deformation, d = strain x 80 ft.
the strain = stress/E
E is the modulus of elasticity, and your teacher should have given it to you (about 30 x 10^6 psi).
The stress (with factor of safety) is the conc. strength/2.5. DOES your teacher want you to take into account the factor of safety when calculating the column height under load? MAKE SURE. The final height of the column is 80 ft x (1 - strain)

Answer 3

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