TM 5-809-3/NAVFAC DM-2.9/AFM 88-3, Chap. 3
(1) Design coefficients. In the design of reinforced rectangular sections, the first step is to locate the
neutral axis. This can be accomplished by determining the coefficient, k, which is the ratio of the depth of the
compressive stress block to the total depth from the compression face to the reinforcing steel, d. k is derived
by equating the moment of the transformed steel area about the centroidal axis of the cross section to the
moment of the compression area about the centroidal axis as follows:
kd
kd
' nAs (d & kd)
b(kd)
2
Rearranging;
b(kd)2
& nAs (d & kd) ' 0
2
The steel ratio, p, is determined by:
p = As/bd
(eq 5-8)
Substituting phd for As;
b(kd)2
& npbd(d & kd) ' 0
2
2
Dividing through by bd ;
k2
& pn(1 & k) ' 0
2
From which;
1/2
(np 2 % 2np
k'
& np
(eq 5-9)
The coefficient j, which is the ratio of the distance between the resultant compressive force and the centroid
of the tensile force to the distance d, is determined by--
k
j'1&
(eq 5-10)
3
The balanced steel ratio in the working stress design method, pe, is defined as the reinforcing ratio where the
steel and the masonry reach their maximum allowable stresses for the same applied moment. pe is determined
by the equation 5-11 as follows:
n
pe '
(eq 5-11)
2(Fs/Fm) [n % Fs/Fm)]
Where:
Fs = The allowable tensile stress in the reinforcing steel, psi.
Fm = The allowable flexural compressive stress in the masonry, psi.
(2) Computed working stresses. The working stresses for the steel and the masonry are computed as
follows:
(a) If p < pe, the steel stress, fs, will reach its allowable stress before the masonry and equation 5-12
will control.
M
fs '
(psi)
(eq 5-12)
Asjd
(b) If p > pe, the masonry stress, fm, will reach its allowable stress before the steel and equation 5-13
will control.
2M
fm '
(psi)
(eq 5-13)
2
kjbd
Where:
M = The moment, inch-kips.
b = The width of the member effective in compression as shown in figure 5-2b, inches.
(3) Resisting moments.
(a) The resisting moment for the reinforcement, Mrs, can be determined by substituting the
allowable steel stress, Fs, for the computed steel stress in equation 5-12 and solving for the moment.
FsAsjd
Mrs '
(ft&lb)
(eq 5-14)
12
(b) The resisting moment for masonry, Mrm, can be determined by substituting the allowable
masonry stress, Fm, for the computed masonry stress in equation 5-13 and solving for the moment.
5-6
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