84 PRACTICAL STRUCTURAL DESIGN 



ins. would have a resisting moment of only 137,000 ins. Ibs. Allow- 

 able deflection = 0.667 ins. Actual deflection 



20 x20 



= 0.6675 ins. 



44 x 13.5 



The deflection in the formulas presented is dependent upon 

 the stress, so the deflection found is that produced when the beam 

 is fully stressed, that is, when the full resisting moment of 167,500 

 in. Ibs. is developed. Under the load found for the 20-ft. span the 

 moment is only 143,500 in. Ibs., so the deflection will be less than 

 that given. 



This case may be dealt with as follows if it is desired to find the 

 actual deflection. The divisor for the span squared is 41 for a 

 fiber stress of 1300 Ibs. per square inch, 44 for a fiber stress of 1000 

 Ibs. per square inch, and 46 for a fiber stress of 800 Ibs. per square 

 inch. The divisor is seen to alter by 1 for each 100 Ibs. change in 

 unit fiber stress. Find the maximum fiber stress for the bending 

 moment developed and then applying the proper divisor ascertain 

 the actual deflection. 



, 143,500 6 x 143,500 



/ = ~bhT '- 5.5 x 13.5* = 859 ' 2 lbs ' P" Square mch ' 

 6 



The divisor for all practical purposes is 45.6. 



L 2 20x20 



= 4K6l - 45.6 X 13.5 = 



The load this beam can carry on a 20-ft. span with a deflection 

 equal to 0.6675 in. is 



167,500 _ 

 - 12L 1.5 x 20 ' 



All the computations have been made with a slide rule, so in 

 some cases the terminal figures in the results may differ slightly 

 from those found by arithmetical computations, but when deal- 

 ing with large quantities small differences in the units place make 

 no material difference in results. 



The calculations for deflection in wooden beams can never 

 give exact results, for woods vary in texture throughout and the 

 amount of moisture and seasoning also act to increase or decrease 

 deflection. 



