PROBLEMS IN DESIGN OF BEAMS 89 



3. Neglecting deflection, what is the greatest permissible spacing 

 of joists for the following loads per square foot (including the weight 

 of the flooring) : 42 Ibs. ; 78 Ibs. ; 103 Ibs. ; 129 Ibs.? 



Flooring extends over several supports, so we may assume a 

 condition of restraint and use the formula 



M = - jr-, in foot pounds. 

 iz 



The load is given in pounds per square foot, so the span should 

 be in feet. The formula then becomes 



, , . 



M = in. Ibs. 



\.JL 



which reduces to M = wL 2 in. Ibs. 



o- -i i e \f wL?l2 . ., 

 Similarly, for M = 5 in. Ibs. 



o 



we obtain M = \.bwL? in. Ibs. 



Another condition sometimes met with in wood and steel design 

 and frequently used in reinforced concrete design is a partially 

 restrained condition in which the beam rests freely on one end 

 support and is fully restrained at the other support. For this con- 

 dition the coefficient is 10 and 



,.. wL*l2 . ., 



M = in. Ibs., or M - 1.2teXA 



Using the expression M = w>L 2 , the spans for the various floor 

 thicknesses are found as follows: 



M t /M 



U = , or L = i/ 

 w V w 



Using the resisting moments in inch pounds obtained for each 

 thickness, 



f-in. flooring: L - \J^j - 3.85 ft. 



f - 2.83 ft. 



The rest of the examples are left to the student as a useful 

 exercise. 



4. A floor is constructed of 2-in. (1.75-in.) planking laid over 

 beams spaced 4 ft. 6 ins. center to center, the span of the beam from 

 wall to girder being 18 ft. Find size of beam when the total load 



