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WORKING STRESS DESIGN EQUATIONS - T SECTIONS





In the design of reinforced T-sections, as in the design of rectangular sections, the first step is to locate the neutral axis. As with rectangular sections, this can be accomplished by determining the coefficient k . k is derived by assuming that the compressive force in the flange, C, is equal to the tension force in the reinforcement. The contribution of the portion of the web in compression is small and can be neglected, therefore if;

T = C
Then
pbdf_s = f_m (2k_Td - t_s / 2k_Td) bt_s
Where: t_s = The thickness of the face shell of the unit, inches.

From the strain compatibility relationship it can be determined that;

k_t = n / (n + (f_s/f_m))
Rearranging the equation and solving for f_m yields:

f_m = (f_s) k_T/ (n(1-k_T))
Substituting this equation for f_m into the equation above yields;

k_T = np + 1/2(t_s/d)² / [np + (t_s/d) ]
The coefficient, j_T , can be determined by the relationship,

j_T d = d - z
Where: z = The distance from the extreme compressive fiber to the center of compression and is determined as follows:

z = [ 3k_Td - 2t_s/ (2k_Td - t_s) ] [ t_s/3 ]
From the above equations j_T can be determined by:

j_T =[ 6 - 6(t_s/d) + 2(t_s/d)² + (t_s/d)³ [1/2pn)] ]/ (6 - 3(t_s/d))
The resisting moments of the steel and masonry are equal to the product of the moment arm, j_T d, and the tension or compression force, respectively, therefore:

M_rs = F_sA_sjd/12 (ft-lb)
And

M_m = F_mkjbd²/12 [ 1 - ts/ 2k_Td ] (ft-lb)

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