Steel Grating Uniform Load Calculation

***reference document “MBG534-12” METAL BAR GRATING ENGINEERING DESIGN MANUAL”

NOMENCLATURE

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.

A_c = distance center to center of main bars, riveted grating, in.

A_r = face to face distance between bearing bars in riveted grating, in.

A_w = center to center distance between bearing bars in welded and pressure locked gratings, in.

C = concentrated load at midspan, pfw

D_c = deflection under concentrated load, in.

D_u = deflection under uniform load, in.

E = modulus of elasticity, psi

F = allowable stress, psi

I = moment of inertia, in⁴

I_H20 = moment of inertia of grating under H20 loading, in⁴

I_b = I of bearing bar, in⁴

I_g = I of grating per foot of width, in⁴

I_n = moment of inertia of nosing, in⁴

K = number of bars per foot of grating width, 12"/A_w

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

ABBREVIATIONS

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

FORMULAS

1. Number of bearing bars per foot of width for welded grating

K = 12/AW

2. Section modulus of rectangular bearing bar

S_b = bd²/6 in³

3. Section modulus of grating per foot of width

S_g = Kbd²/6 in³ = KS_b in³

4. Section modulus required for given moment and allowable stress

S = M/F in³

5. Moment of inertia of rectangular bearing bar

I_b = bd³/12 in⁴ = S_b d/2 in⁴

6. Moment of inertia of grating per foot of width

I_g = Kbd³/12 in⁴ = Kl_b 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 = P_u (2L - a)/8 Ib-in

13. Maximum deflection under concentrated load

D_c = CL³/48EI_g in⁴.

14. Moment of inertia for given deflection under concentrated load

Ig = CL3/48EDc in4

15. Maximum deflection under uniform load

D_u = 5UL4/(384 x 12El_g) = 5UL4/4608EI_g in.

16. Moment of inertia for given deflection under uniform load

Ig = 5UL⁴/4608EDu in⁴

17. Maximum deflection under partially distributed uniform load

D_u = P_u((a/2)³ + L³ - a² L/2)/48El_bN in.

GRATING SELECTION

Example

Required: A 6063-T6 aluminum grating Type P-19-4 to support a uniform load, U, of 300 pounds

per square foot on a clear span of 5'-0". Deflection, D, is not to exceed the 0.25" recommended for

pedestrian comfort.

Allowable stress, F = 12,000 psi

Modulus of elasticity, E = 10,000,000 psi

Span, L = 60 in.

Bearing bar spacing, Aw = 1.1875 in.   K = 12/Aw = 1211.1875 = 10.105

For a span of 5’-0”, the minimum size bearing bar to sustain a 300 psf load is:

1-3/4x3/16

Ig = Klb = 10.105 x 0.0837 = 0.846 in⁴

Sg = KSb = 10.105 x 0.0957 = 0.967 in³

U = 96Mg/L2 = 96 x F x Sg/(60)² = 96 x 12,000 x 0.967/(60)² = 309 psf

Du = 5UL⁴/4608Elg = 5 x 309 x (60)⁴ /(4608 x 10,000,000 x 0.846) = 0.514 in.

Deflection is directly proportional to load:

Du = 0.514 x 300/309 = 0.499 in.

Since this exceeds the recommended limitation, a grating with a larger moment of inertia is needed to keep the deflection less than 0.25 in.

Ig = 5UL⁴ /4608EDu = 5 x 300(60)⁴ /(4608 x 10 x 10⁶ x 0.25) = 1.6875 in⁴

Using a larger size:

2-1/4 x 3/16 Ig =1.798 in⁴  U=512 psf  D = 0.400 in.

Du = 0.400 x 300/512 = 0.234 in. ≤ 0.25 in. OK

Note: Uniform loads in these examples and in the standard load tables do not include the weight of the gratings. In designing for uniform live loads the weight of the grating, as well as any other dead load, must be added

Uniform Load per square foot