86 STRESSES IN A TRANSVERSE BENT 



L = C U cos n (29) 



In calculating the corresponding stresses on the windward side, 

 the wind components acting at the points (a), (b) and (c) must be 

 subtracted from H, B and C. 



The shear in the leeward column is equal to H 1 below and C above 

 the foot of the knee brace, (d) Fig. 51. 



The moment in the column is shown in (e), Fig. 51, and is a max- 

 imum at the foot of the knee brace and is, M = H 1 d. 



The maximum fibre stress due to wind moment and direct loading 

 in the columns will occur at the foot of the knee brace in the leeward 

 column, and will be compression on the inside and tension on the out- 

 side fibres, and is given by the 'formula* 



p _i_ 



~ h* (30) 



10 E 



where / t = maximum fibre stress due to flexure; 

 / 2 = fibre stress due to direct load P; 

 A = area of cross-section of column in square inches; 

 M = bending moment in inch-pounds = H 1 d; 

 y = distance from neutral axis to extreme fibre of column in 



inches ; 

 7 = Moment of Inertia of column about an axis at right angles 



to the direction of the wind ; 

 P = direct compression in the column in pounds ; 

 h = length of the column in inches ; 



H = the modulus of elasticity of steel = 28,000,000 ; 



P h* 



IQ~ is minus when P is compression and plus when P is tension. 



The maximum compressive wind stress is added to the direct dead 

 and minimum snow load compression and governs the design of the 

 column. 



*This formula was first deduced by Prof. J. B. Johnson. For deduction 

 of the formula see Chapter XV, or "Modern Framed Structures" by Johnson, 

 Bryan and Turneaure. 



