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Steel Grating Concentrated Load Calculation

Steel Grating Concentrated Load Example


***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.

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


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

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.


GRATING SELECTION

Example

Required: A welded ASTM A36 steel grating Type W-22-4 to support a concentrated load, C, of 4,000 pounds per foot of width at midspan on a clear span of 8'-0". Deflection, D, is not to exceed the 0.25" recommended for pedestrian comfort.


Allowable stress, F = 20,000 psi

Modulus of elasticity, E = 29,000,000 psi

Span, L = 96in.

Bearing bar spacing, Aw = 1.375 in.     K = 12/Aw = 12 / 1.375 = 8.727


For a span of 8'-0", the minimum size bearing bar to sustain a 4,000 pfw load is:


3 x 3/8


Ig = Klb = 8.727 x 0.8438 = 7.364 in4      Sg = KSb = 4.909 in3

C = 4Mg/L = 4 x F x Sg/96 = 4 x 20,000 x 4.909/96 = 4,091 pfw


Dc = CL3 /48Elg = 4,000 x (96)3 /(48 x 29,000,000 x 7.364) = 0.345 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 = CL3 /48EDc = 4,000 x (96)3 /(48 x 29,000,000 x 0.25) = 10.17 in4

Using the next larger size:


3-1/2 x 3/8


Ig = 8.727 x 1.3398 = 11.693 in4

Sg = 8.727 x 0.7656 = 6.682 in3

C = 4 x 20,000 x 6.682/96 = 5,568 pfw

D = 5,568 x (96)3 /(48 x 29,000,000 x 11.693) = 0.303 in.


Deflection is directly proportional to load:


Dc = 0.303 x 4,000/5,568 = 0.217 in. ≤ 0.25 in. OK


Steel Grating Concentrated Load Calculation



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