100 PRACTICAL STRUCTURAL DESIGN 



The increase in amount of lumber is about one-fourth, while 

 the increased carrying capacity is one-third, so it will be better 

 to use the 16-in. spacing than to use the 12-in. spacing. Thinner 

 joists than 2-in. are not advisable when it is possible to avoid them, 

 so this is another reason for using the wider spacing. To make the 

 floors stiff and to avoid bending under load, or warping of the 

 joists from any cause, lines of cross bridging should be used at 

 intervals approximately twenty-four times the thickness of the 

 joist. This for 2-in. joists will be 48-in. (4-ft.) centers. 



Beams on a Slope 



Let S = length of beam on slope, 

 L = horizontal span, 



W = total load uniformly distributed on the slope, 

 W = total load beam can carry, 



TT7> WS 



then W = -=r~ 

 Li 



The foregoing applies in the case of stringers supporting stairs 

 and inclined rafters carrying a load on the upper surface. There 

 is a horizontal and a vertical force acting when a beam is inclined 

 and the resultant thrust increases the compression and decreases 

 the tension in the fibers. It is usually unimportant and may be 

 neglected when the slope is less than thirty degrees, but should 

 be investigated in any case. When an inclined member of a truss 

 carries a load on the upper surface in addition to the direct thrust, 

 the member must be designed to take these loadings into account. 

 Let M = bending moment due to the load. 

 / = fiber stress. 



A = area of member in cross section 

 W = direct load along axis of the member. 

 h = depth of the member. 



/ = moment of inertia of member, which is assumed here 

 to be symmetrical. 



, , W Mh 

 then /- + _. _. 



In the above expression the first part gives the average fiber 

 stress due to the direct load acting along the length of the member, 

 that is, the push. The second half is the familiar expression for 

 the fiber stress in a beam bending under load. Use it twice, once 

 with a positive sign and once with a negative sign. The ex- 



