MD&M practice problem of the week

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But you should get 0.179 — there has to be an error somewhere.
Yes.. instead of 49.05N for the friction force I wrote 45.05 when I took the natural log...that did it... I do get 0.179...whew....gotta watch out for these simple mistakes on the exam...thanks !

 
Last one before the big day next Friday. Good luck to all!!!!

An external point load of 3 kip is applied at point C on the steel bar shown. The bar is supported by two springs at its ends A and B. Each spring has the same stiffness and is originally un-stretched. You may assume the weight of the bar is negligible, and that Young's modulus is E=29,000 ksi. For the bar, I=12 in^4. The vertical displacement at the point of application of the load shall not exceed 1.51 inches. Under these conditions, the stiffness (kip/ft) of each spring is most nearly:

(A) 15

(B) 20

(C) 25

(D) 30

Screen Shot 2018-04-04 at 9.56.55 PM.png

 
Is this question set up right? Deflections at the ends will be zero. Maybe I'm missing something?

 
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Is this question set up right? Deflections at the ends will be zero. Maybe I'm missing something?
Deflections at the ends are not zero, because the supports are compression springs which will be shortened upon the application of the load.

But, even if they were zero at the ends... the deflection at the point of application of the load is non-zero and is given as 1.51 inches.

What the problem is asking for is the spring stiffness, k.

 
Last edited by a moderator:
I come up with (A)..  15kip/ft

Found the deflection of the beam at the point load.  Then subtracted the deflection from the total deflection.  Created a slope intercept form equation for the slope of the beam due to the uneven deflections of the springs.   

 
I get A as well. Took me a bit too long though. about 12 min because I didn't have any beam tables readily accessible (at work) and had to search through my bookmarked resources online

Same way as Mikeglass describes above.

 
I get A as well.  Maybe it's just me, but I found it to be a challenging problem, but a good one.

 
A is the correct answer for the beam deflection problem. Use the principle of superposition to add the displacement of the load application point assuming rigid supports with an elastic beam plus the displacement of the load application point assuming a rigid beam but elastic supports.

 
A is the correct answer for the beam deflection problem. Use the principle of superposition to add the displacement of the load application point assuming rigid supports with an elastic beam plus the displacement of the load application point assuming a rigid beam but elastic supports.
Please do you guys mind sharing your calculation? Thanks.

 

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