Author Topic: 3/10/2014 Mechanics of Materials  (Read 1809 times)

FastTrack Guru

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3/10/2014 Mechanics of Materials
« on: March 10, 2014, 08:29:30 AM »
Question:

A simply supported steel beam, with a span of 15 feet,  is loaded with a distributed force of 15,000 lb/ft .

Calculate the maximum beam deflection (inches): Assume I = 254 ft4

FastTrack Guru

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Re: 3/10/2014 Mechanics of Materials**SOLUTION**
« Reply #1 on: March 11, 2014, 06:55:06 AM »
Refer to page 81 of the FE Handbook: "Simply Supported Beam Deflections and Slopes:"

Middle column for deflection:

Vmax = 5wL^4/ 384EI

Givens:

L = 15 ft, so L^4 = (15ft)^4 = 50,625 ft^4
w = 15,000 lb/ft
I = 254 ft4
E = The problem statement says a steel beam, therefore, Refer to page 80 of the FE Handbook to find the value of E for steel:

"Typical Material Properties:"
For steel, E = 29 Mpsi, or  29,000,000 psi

Therefore:
Vmax = 5wL^4/ 384EI
Vmax = [5(15,000 lb/ft) (50,625 ft4)] / [384(29 Mpsi) (254 ft^4)]
Vmax = [3,796,875,000 lb ft3)] / [2.8 x 1012   (lb/in2) ft4)] (144 in2/ft2)    (note: watch your units! we need to convert psi into psf)
Vmax = [3,796,875,000 lb ft3)] / [4 x 1014 (lb ft2)]
 Vmax = 9.3 x 10-6 ft    (note: the problem statement wants the answer to be in inches, not feet)
Vmax =  9.3 x 10-6 ft (12 in / 1 ft)
Vmax = .00001 in

The answer is  .00001 in.

vjd

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Re: 3/10/2014 Mechanics of Materials
« Reply #2 on: March 30, 2014, 07:10:19 AM »
Hello,

I am a new member. I could not understand the conversion part can you guide me? Where it is on page-2(Handbook)?
Vmax = [3,796,875,000 lb ft3)] / [2.8 x 1012   (lb/in2) ft4)] (144 in2/ft2)    (note: watch your units! we need to convert psi into psf)
Vmax = [3,796,875,000 lb ft3)] / [4 x 1014 (lb ft2)]

Thanks.

Jimbo123arrow

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Re: 3/10/2014 Mechanics of Materials
« Reply #3 on: April 04, 2014, 06:15:15 PM »
I think it is on page 84.

andrei

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Re: 3/10/2014 Mechanics of Materials
« Reply #4 on: March 02, 2015, 02:22:11 PM »
Could you please explain how you obtained factor:
2.8 x 1012 (lb/in2) ft4
in the denominator,
and then later turned it into
4 x 1014 (lb ft2)?