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05-17-2010, 04:52 PM   #1
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load bearing formula

I have three supports. One at "A", "B" and "C". The distance between A & B and B & C is identical at 84". If the load is equally distributed from points A, B, & C, how can I determine the amount of load in lbs at each of A, B, & C?
Thanks.

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05-17-2010, 05:16 PM   #2
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The load on each column depends on the specific method of attachment of the beam across each column. The simplest case is if there are effectively two beams, one from A to B, and the other from B to C. This would occur if the beam from A to C is NOT continuous, and is effectively pinned at B. Such a connection would occur if you nailed each beam into B. This case is called a simple beam.

Assuming you have the simple beam case, and your load is uniformly distributed, to compute the load on each column you multiply the load per foot by the span, in this case 7 feet (84 inches) from A to B, to calculate the total load carried by A and B. Assuming 100 lbs/ft, the total load would be 700 lbs, which would be equally distributed between A and B, or 350 lbs each. The same logic applies between B and C. Therefore, A and C end up carrying 350 lbs each, and B carries 700 lbs.

Total load is 1400 lbs, easily checked because 14 feet times 100 lbs/foot equals 1400 lbs. Of course, you load per foot depends on the specific loading of your structure.

CAUTION: This analysis does not apply if the load is not equally distributed, and does not apply if the beam across the top of B is continuous.

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05-17-2010, 06:15 PM   #3
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Quote:
 Originally Posted by Daniel Holzman CAUTION: This analysis does not apply if the load is not equally distributed, and does not apply if the beam across the top of B is continuous.
Without solving
http://en.wikipedia.org/wiki/Theorem_of_three_moments
can we at least say that B carries less than 700# if the beam is solid?

Last edited by Yoyizit; 05-17-2010 at 07:17 PM.

 05-17-2010, 07:12 PM #4 Member   Join Date: Jul 2007 Posts: 2,045 Rewards Points: 1,910 Does the beam on top of the posts extend beyond the end posts A and C?
 05-17-2010, 08:29 PM #5 Member   Join Date: Oct 2007 Posts: 126 Rewards Points: 113 Thanks for the help. However, the beam is continuous. I didn't think to include that. jogr---No. The ends of the beam are at A & C.
 05-17-2010, 09:45 PM #6 Civil Engineer   Join Date: Mar 2009 Location: Boston Posts: 5,640 Rewards Points: 4,860 OK, continuous beam problem, somewhat more complex. The following solution only applies if the beam is IDENTICAL over all three supports. Assuming it is identical, if the distance between supports A and B is L feet, and the distance between B and C is L feet, and the load per foot is w pounds, the total load is 2wL pounds. Support A and support C carry 3wL/8 pounds, and support B carries 10wL/8 pounds. Maximum positive moment occurs at 3L/8 feet from support A (and B). The maximum positive moment is 9wL^2/128 ft-lbs. The maximum negative moment occurs over the middle support (B), and is wL^2/8 ft-lbs. You MUST design this beam to carry the maximum positive and negative moment, the supports must be properly designed to carry the beam, and you have to be very careful about designing the beam for eccentric loading conditions such as point loads one one side of the center support but not the other. Continuous beams require much more careful analysis, design, fabrication, support and installation than simple beams, so please make sure you FULLY understand all possible loading conditions that may occur, both static and dynamic, before you install this beam.
05-18-2010, 07:29 AM   #7
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load bearing formula

Thanks for your help.

 05-18-2010, 09:22 AM #8 Member   Join Date: Jan 2008 Location: Alabama Posts: 608 Rewards Points: 500 If the load is equally distributed accross the beam, and the beam is of reasonably equal stiffness across its length, and if supports A, B and C are mainly counter-acting gravity (i.e. we're not talking about any horizontal loads, just vertical) then... ...drop the complex of positive and negative moment arms and a detailed analysis using mechanics of solids. With the given assumptions, this is a simple strait forward Statics or Physics 101 problem that can be simplified as two point loads centered between A&B and B&C. As such, a reasonable estimate can be made (solid beam or not) that supports A & B carry half the load, supports B & C carry the other half of the load, therefore support A carries 1/4th of the load, B carries 2/4th (1/2) of the load, and C carries 1/4th of the load. Now if you add POINT loads or a beam that has changing values of elasticity across its length, or if the loads are such that the beam might break, then we can get into moment arms and mechanics of solids. But that's not what was asked.
 05-18-2010, 11:44 AM #9 Civil Engineer   Join Date: Mar 2009 Location: Boston Posts: 5,640 Rewards Points: 4,860 HooKoo, I suggest you reread all the posts. Your analysis is correct ONLY for the simple beam case I discussed earlier. It is dangerously INCORRECT for the continous beam case described by the OPS. A continuous beam over three supports MUST be analyzed as such, it cannot be approximated as two simple beams. I don't know what causes you to believe you can substitute two simple beams for a continuous beam, you can't. I suggest you consult a book on mechanics of solids if you don't believe the results I posted above.
05-18-2010, 02:33 PM   #10
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Quote:
 Originally Posted by HooKooDooKu I think using the equations for simple beams will get us the type of answer we need.
No.
Read #9.
Otherwise, Darwin Award.
Somebody took the trouble of coming up with these equations because they are necessary.
And even those equations are an approximation but at least if you follow them you have shown 'due diligence'.

BTW, L is the span in inches and w is the weight in pounds per linear inch.

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Last edited by Yoyizit; 05-18-2010 at 02:48 PM.

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