The procedures used to prepare data for metal bar grating load tables
***reference document “MBG534-12” METAL BAR GRATING ENGINEERING DESIGN MANUAL”
a = length of partially distributed uniform load or vehicular load, parallel with bearing bars, in.
b = thickness of rectangular bearing bar, in.
c = width of partially distributed uniform load or vehicular load, perpendicular to bearing bars, in.
d = depth of rectangular bearing bar, in.
Ac = distance center to center of main bars, riveted grating, in.
Ar = face to face distance between bearing bars in riveted grating, in.
Aw = center to center distance between bearing bars in welded and pressure locked gratings, in.
C = concentrated load at midspan, pfw
Dc = deflection under concentrated load, in.
Du = deflection under uniform load, in.
E = modulus of elasticity, psi
F = allowable stress, psi
I = moment of inertia, in4
IH20 = moment of inertia of grating under H20 loading, in4
Ib = I of bearing bar, in4
Ig = I of grating per foot of width, in4
In = moment of inertia of nosing, in4
K = number of bars per foot of grating width, 12"/Aw
L = clear span of grating, in. (simply supported)
M = bending moment, Ib-in
Mb = maximum M of bearing bar, Ib-in
Mg = maximum M of grating per foot of width, Ib-in
N = number of bearing bars in grating assumed to carry load
NbH20 = number of main bearing bars under load H20
NcH20 = number of connecting bearing bars under load H20
Pb = load per bar, Ib
Pu = total partially distributed uniform load, Ib
PuH20 = wheel load, H20, Ib
Pw = wheel load, lb
S = section modulus, in3
Sb = S of bearing bar, in3
Sg = S of grating per foot of width, in3
SH20b = section modulus at bottom of grating under H20 loading, in3
Sn = section modulus of nosing, in3
U = uniform load, psf
in. = inch
ft = foot
Ib = pounds
Ib-in = pound-inches
pfw = pounds per foot of grating width
psf = pounds per square foot
psi = pounds per square inch
1. Number of bearing bars per foot of width for welded grating
K = 12/AW
2. Section modulus of rectangular bearing bar
Sb = bd2/6 in3
3. Section modulus of grating per foot of width
Sg = Kbd2/6 in3 = KSb in3
4. Section modulus required for given moment and allowable stress
S = M/F in3
5. Moment of inertia of rectangular bearing bar
Ib = bd3/12 in4 = Sb d/2 in4
6. Moment of inertia of grating per foot of width
Ig = Kbd3/12 in4 = Klb in4
7. Bending moment for given allowable stress and section modulus
M = SF Ib-in
The following formulas are for simply supported beams with maximum moments and deflections occurring at midspan.
8. Maximum bending moment under concentrated load
M = CL/4 Ib-in per foot of grating width
9. Concentrated load to produce maximum bending moment
C = 4M/L Ib per foot of grating width
10. Maximum bending moment under uniform load
M = UL2/(8 x 12) = UL2/96 Ib-in per foot of grating width
11. Uniform load to produce maximum bending moment
U = 96M/L2 psf
12. Maximum bending moment due to partially distributed uniform load
M = Pu (2L - a)/8 Ib-in
13. Maximum deflection under concentrated load
Dc = CL3/48EIg in4.
14. Moment of inertia for given deflection under concentrated load
Ig = CL3/48EDc in4
15. Maximum deflection under uniform load
Du = 5UL4/(384 x 12Elg) = 5UL4/4608EIg in.
16. Moment of inertia for given deflection under uniform load
Ig = 5UL4/4608EDu in4
17. Maximum deflection under partially distributed uniform load
Du = Pu((a/2)3 + L3 - a2 L/2)/48ElbN in.
The concentrated midspan and uniform load bearing capabilities of W-19-4 (1-1/2 x 3/16) welded
A1011 CS Type B carbon steel grating and the corresponding midspan deflections will be calculated.
Allowable stress, F = 18,000 psi
Modulus of elasticity, E = 29,000,000 psi
Span, L = 54 in.
Bearing bar spacing, Aw = 1.1875 in.
Number of bearing bars per foot of width
K = 12/Aw = 12/1.1875 = 10.105
Section modulus of grating per foot of width
Sg = Kbd2/6 = 10.105 x 0.1875 (1.5)2/6 = 0.711 in3
Moment of inertia of grating per foot of width
Ig = Kbd3/12 = 10.105 x 0.1875 (1 .5)3/12 = 0.533 in4
Maximum bending moment for grating per foot of width
Mg = FSg = 18,000 x 0.711 = 12,800 Ib-in
Load, C = 4Mg /L = 4 x 12,800/54 = 948 pfw
Defl, Dc = CL3/48Elg = 948 x (54)3/(48 x 29,000,000 x 0.533) = 0.201 in.
Load, U = 96Mg /L2 = 96 x 12,800/(54)2 = 421 psf
Defl, Du = 5UL4/4608Elg = 5 x 421 x (54)4/(4608 x 29,000,000 x 0.533) = 0.251 in.
Concentrated Mid Span Load per foot of width Uniform Load per square foot