SERVICE LOAD MOMENTS AND SHEARS

Self-Wt

M(H/2) = Moment at H/2 of section measured from center line of support.

\frac{H}{2} = \frac{(72 + 8.5)}{2} = 40.25 i n = 3.354 f t

M = \frac{w x (1 - x)}{2}

M_{\frac{H}{2}} = \frac{(0.7990 k l f) (3.354 f t) (115.0 f t - 3.354 f t)}{2} = 149.6 k - f t

M_{(M i d s p a n)} = \frac{w l^{2}}{8} = 1320.8 k - f t

V = w (\frac{1}{2} - x)

V_{(\frac{H}{2})} = 0.7990 (\frac{115.0 f t}{2} - 3.354 f t) = 43.3 k

V_{(M i d s p a n)} = 0

DL-Prec

M_{\frac{H}{2}} = \frac{(180 p l f) (3.354 f t) (115.0 f t - 3.354 f t)}{2} = 33.7 k - f t

M_{(M i d s p a n)} = (180 p l f) \frac{{(115.0 f t)}^{2}}{8} = 297.6 k - f t

V_{(\frac{H}{2})} = 180 p l f (\frac{115.0 f t}{2} - 3.354 f t) = 9.7 k

V_{(M i d s p a n)} = 0

Topping

M (\frac{H}{2}) = ({M (\frac{H}{2})}_{G r o s s}) (D L - C o m p T r i b F r a c) = 0.167 \times 275.99 k - f t = 46.1 k - f t

M_{\frac{H}{2}} = (\frac{1670.8 p l f - 799.0 p l f}{1000}) \frac{(3.354 f t) (115.0 f t - 3.354 f t)}{2} = 163.2 k - f t

M_{(M i d s p a n)} = (\frac{1670.8 p l f - 799.0 p l f}{1000}) \frac{{(115.0 f t)}^{2}}{8} = 1411.3 k - f t

V_{(\frac{H}{2})} = (\frac{1670.8 p l f - 799.0 p l f}{2}) (\frac{115.0 f t}{2} - 3.354 f t) = 47.2 k

V_{(M i d s p a n)} = 0

DL-Comp

Moments and shears due to dead load acting on the composite, continuous structure are computed at tenth points of the precast beam length. In the output, under STATIC ANALYSIS, they are referenced with respect to the center lines of piers. Under SERVICE LOAD MOMENTS AND SHEARS, they are referenced with respect to the centerline of the left bearing.

Moments and shears of points which do not fall on these tenth points are computed by parabolic interpolation with respect to adjacent points with known values. Thus, bending moment due to DL-Comp at H/2 is computed as follows:

H/2 = 3.354 ft. from support at final

= 3.354 ft. + 0.50 ft. = 3.854 ft. from left beam end

= 3.854 ft. + 0.50 ft. = 4.354 ft. from left pier center line

Known points are 0.00 ft. and 12.10 ft. Thus,

{M (\frac{H}{2})}_{G r o s s} = \frac{(4.354 f t)}{(12.10 f t)} 767.0 k - f t = 275.99 k - f t

This value appears in the output as 50.5 k-ft., the difference is because, for simplicity in these hand calculations, 46.1 k-ft. was obtained by using straight-line interpolation. The program uses parabolic interpolation (see Full Beam and Half Beam in the Theory section).

M(Midspan) = (0.167)(1597.0 k-ft.) = 266.70 k-ft.

V(Midspan) = (18.2 k)(0.167) = -3.04 k

LL+I (eff)

M+(Midspan)

= (Distribution factor)(1 + Impact factor)(Gross moment)= (0.773)(1.208)(1786.0 k-ft.)

= (0.773)(1.208)(1786.0 k-ft.)= (0.934)(1786.0 k-ft.)= 1667.6 k-ft.

V(Midspan)= (0.934)(39.9 k) = 37.3 k

M-(Midspan)= (0.934)(-408.2 k-ft.) = -381.1 k-ft.

V(Midspan)= (0.934)(7.0 k) = 6.5 k

Vmx(Midspan)= (0.934)(45.9 k) = 42.9 k

M(Midspan)= (0.934)(1737.6 k-ft.) = 1622.4 k-ft.