Building

For greatest resistance to bending, as much of a plate girder cross section as practicable should be concentrated in the flanges, at the greatest distance from the neutral axis. This might require, however, a web so thin that the girder would fail by web buckling before it reached its bending capacity.

To preclude this, the AISC specification limits h/t.

For an unstiffened web, this ratio should not exceed.

where F_y = yield strength of compression flange,ksi (MPa).

Larger values of h/t may be used, however, if the web is stiffened at appropriate intervals.
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In building construction, allowable bearing stress for milled surfaces, including bearing stiffeners, and pins in reamed, drilled, or bored holes, is F_p= 0.90F_y, where F_y is the yield strength of the steel, ksi (MPa)

For expansion rollers and rockers, the allowable bearing stress, kip/linear in (kN/mm), is

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The area A₁, in²(mm²), required for a base plate under a column supported by concrete should be taken as the larger of the values calculated from the equation cited earlier, with R taken as the total column load, kip (kN), or

A₁=R /0.70f^‘_c

Unless the projections of the plate beyond the column are small, the plate may be designed as a cantilever assumed to be fixed at the edges of a rectangle with sides equal to 0.80b and 0.95d, where b is the column flange width, in (mm), and d is the column depth, in (mm).

To minimize material requirements, the plate projections should be nearly equal. For this purpose, the plate length N, in (mm) (in the direction of d), may be taken as
N=(A₁)^½+0.5(0.95d–0.8b)
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To resist a beam reaction, the minimum bearing length N in the direction of the beam span for a bearing plate is deter- mined by equations for prevention of local web yielding and web crippling. A larger N is generally desirable but is limited by the available wall thickness.

When the plate covers the full area of a concrete support, the area, in ² (mm ² ), required by the bearing plate is

A ₁= R/0.35f^‘_c
Where
R=beam reaction, kip (kN),
f ^‘_c= specified compressive strength of the concrete, ksi (MPa).
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Results of membrane and bending theories are expressed in terms of unit forces and unit moments, acting per unit of length over the thickness of the shell. To compute the unit stresses from these forces and moments, usual practice is to assume normal forces and shears to be uniformly distributed over the shell thickness and bending stresses to be linearly distributed. Then, normal stresses can be computed from equations of the form:

where
z=distance from middle surface
t=shell thickness

M_x= unit bending moment about an axis parallel to direction of unit normal force N_x

Similarly, shearing stresses produced by central shears T and twisting moments D may be calculated from equations of the form:

Normal shearing stresses may be computed on the assumption of a parabolic stress distribution over the shell thickness:
where V=unit shear force normal to middle surface.