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A GRAPHICAL COMPUTATOR FOR DETERMINING THE MOST 

 ECONOMICAL BEAM TO CARRY A GIVEN LOAD. 



By Prof. K. W. Chapman, M.A., B.C.E. 



[Read October 10, 1918.] 



An ordinary rectangular beam, designed to carry a given 

 load, will have its cross section of minimum area when it is 

 so proportioned that it is just as likely to fail by horizontal 

 shearing along the neutral axis as to fail by rupture in the 

 ordinary way. For a beam of breadth b and depth d, carry- 

 ing a uniformly distributed load W over a span Z, the con- 

 ditions that this may be the case can be readily expressed in 

 the form : — 



log 6 + log d = \og IF — log | s (1) 



log d = log I — log — (2) 



s 



where 6- is the maximum resistance of the timber to shearing 

 in pounds per square inch and / is the modulus of rupture. 



The computing apparatus illustrated is designed to facili- 

 tate the determination of the proper size of beam required to 

 satisfy these two equations. Standing up at right angles to 

 the base line are two fixed logarithmic scales for the breadth 

 and depth of the beam in inches. Midway between is another 

 parallel scale, so that if a straight edge be placed between 

 two points representing b and d, the intercept on the middle 

 scale will be \ (log b -flog d). This middle scale is graduated 

 bo that the distance from the base line to the graduation 

 marked W = J (log W — log |- s). As the value of s depends 

 on the nature of the timber, the middle scale is made to 

 slide to different positions corresponding to different woods. 

 Thus if a straight edge be placed across the three scales, the 

 three quantities b, d, and W then in line satisfy the condi- 

 tion (1). Alongside the scale of depths is another sliding 

 scale for the span, so graduated that when set to any par- 

 ticular timber it satisfies the condition (2). 



Thus if we wish to find the minimum beam to carry a. 

 given load, we first set the two sliding scales to the marks 

 indicated for that particular timber. Then corresponding to 

 the given span we at once read off the proper depth of the 



