18 



Table VII. — Giving length of grip <il end bearing required for uniformly loaded longleqf- 

 pine ( Pinus palustris) beams of varying heights and lengths of span. 



Formula: 



where 



°— o a 1 or for given species c=K-r- 



c = required length of grip in inches. 



R = safe modulus of rupture. (See Table IV. ) 



S = safe crushing strength across the grain. (See Table IV.) 



// = height of beam in inches. 



I = length of span in inches. 



K = a constant, depending upon the material used. 



For longleaf pine K=4.8: shortleaf, 4.0; white pine, 4.0; Norway pine, 5.0; Douglas fir, 5.28; bald 

 cypress, 5.55. 



To obtain the tabular values for other species multiply the value for the longleaf pine given in the 



, , , . K' (for the species) 



table by the ratio of K (for i ongIea f pine I ' 



For beams under concentrated loads, such as trestle stringers, add 30 per cent to above values. 

 For single concentrated load in middle of beam divide these values by 2. 



Table VII gives the length of grip at end bearing required for uni- 

 formly loaded longleaf-pine beams of varying heights and lengths of 

 span. 



2 R A 2 

 The formula c — o u/ has been obtained in the following manner: 



S = 



w 



7^-j or W'= 2 Scb (see Table VII for definition of quantities) 



A T? * •* 1 A 3W "^ TXT,, 4RSA 2 . 



and K tor uniform load = , 7 ,., or W"= — o~? — 



4 I) ft /> I 



Where W = total load on beam at time the end bearing has its proof 



load. 



W" = total load on beam at time the extreme fiber has its 



proof load. 



