Stiffness

Structural Layout Vignette and Multiple Choice

Stiffness

Postby patjohns » Fri Nov 01, 2013 12:39 pm

The Modulus of Elasticity as the measure of stiffness of a member. So too, is the Moment of Inertia. Is E a measure of stiffness because the moment of Inertia is in the equation? If a question were to ask me which one is the measure of stiffness, and they listed both 'E' and 'I', which one would be the correct answer?
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Re: Stiffness

Postby matte » Fri Nov 01, 2013 1:45 pm

There is a pretty major distinction - E is material based, while I is based on the geometric section. Doubt very much the test woudld have a question worded this way.
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Re: Stiffness

Postby patjohns » Fri Nov 01, 2013 4:50 pm

Thanks matte.

So, they might ask which material has the greatest modulus of Elasticity and the answer would be steel. But, they also could ask which section has the greatest moment of inertia and could give a bunch of steel shapes and the one with the greatest amount of the material in the flange would be correct. Is that right?
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Re: Stiffness

Postby Mike-SE » Fri Nov 01, 2013 5:03 pm

The stiffness of a member is E*I. The deeper the member the greater the moment of inertia. Depth has more influence on I than the area of the webs.
THe moment of intertia of only the flanges is (2)*a*(d^2). The first two is because there are two flanges. If you double the area and maintain the depth, I doubles.
If you double the depth and maintain the area the I increases by a factor of 4! (2*d)^2 = (2^2) * (d^2) = 4*(d^2)
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Re: Stiffness

Postby patjohns » Fri Nov 01, 2013 5:17 pm

Mike-SE wrote:The stiffness of a member is E*I. The deeper the member the greater the moment of inertia. Depth has more influence on I than the area of the webs.
THe moment of intertia of only the flanges is (2)*a*(d^2). The first two is because there are two flanges. If you double the area and maintain the depth, I doubles.
If you double the depth and maintain the area the I increases by a factor of 4! (2*d)^2 = (2^2) * (d^2) = 4*(d^2)



I think I'm confusing deflection with moment of inertia. Whereas the efficiency of a beam is determined by the distance of the material from the n.a. the moment of inertia has d^2 or d^3 in the various formulas and therefore the depth rules. Did i say that right?
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Re: Stiffness

Postby Mike-SE » Fri Nov 01, 2013 7:32 pm

depth rules. That is why structural engineers want deeper beams rather than heavier beams
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Re: Stiffness

Postby patjohns » Sat Nov 02, 2013 9:47 am

Thanks, Mike, for the help.
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