## 452e

The variables used in the above equations are defined in the following, where h is the clear distance between flanges less the fillet or corner radius, tw is the web thickness, Fyw is the yield stress of web, Aw = dt„, and d is the overall depth of the section.

### 4.5.1.2.3 Criteria for Concentrated Loads

When concentrated loads are applied normal to the flanges in planes parallel to the webs of flexural members, the flanges and webs must be checked to ensure that they have sufficient strengths f Rn to withstand the concentrated forces Ru, that is fRn > Ru

The design strengths for a variety of limit states are given below.

4.5.1.2.3.1 Local Flange Bending — The design strength for local flange bending is given by fRn > 0.90[6.25ff2Fyf]

where tf is the flange thickness of the loaded flange and Fyf is the flange yield stress.

The design strength in Equation 4.53 is applicable only if the length of load across the member flange exceeds 0.15 b, where b is the member flange width. If the length of load is less than 0.15 b, the limit state of local flange bending need not be checked. Also, Equation 4.53 shall be reduced by a factor of half if the concentrated force is applied less than 10tf from the beam end.

4.5.1.2.3.2 Local Web Yielding — The design strength for yielding of the beam web at the toe of the fillet under tensile or compressive loads acting on one or both flanges are

If the load acts at a distance from the beam end which exceeds the depth of the member f Rn = 1.00[(5k + N)Fywiw] (4.54)

If the load acts at a distance from the beam end which does not exceed the depth of the member fRn = 1.00[(2.5k + N)Fyw tw] (4.55)

where k is the distance from the outer face of the flange to the web toe of the fillet, N is the length of bearing on the beam flange, Fyw is the web yield stress, and tw is the web thickness.

4.5.1.2.3.3 Web Crippling — The design strength for crippling of beam web under compressive loads acting on one or both flanges are

If the load acts at a distance from the beam end which exceeds half the depth of the beam fRn = 0.75 < 0.80t;

EFyw f tw

If the load acts at a distance from the beam end which does not exceed half the depth of the beam and ifN/d < 0.2

EFyw f tw

If the load acts at a distance from the beam end which does not exceed half the depth of the beam and ifN/d > 0.2

EFyw f tw

where d is the overall depth of the section, tf is the flange thickness, and the other variables are the same as those defined in Equations 4.54 and 4.55.

4.5.1.2.3.4 Sideways Web Buckling — Sideways web buckling may occur in the web of a member if a compressive concentrated load is applied to a flange not restrained against relative movement by stif-feners or lateral bracings. The sideways web buckling design strength for the member is If the loaded flange is restrained against rotation about the longitudinal member axis and (h/tw)(l/bf) is less than 2.3

If the loaded flange is not restrained against rotation about the longitudinal member axis and (dc/ tw)(l= bf) is less than 1.7

ÇrtWtf h2

Khf'

where tf is the flange thickness (in.), tw is the web thickness (in.), h is the clear distance between flanges less the fillet or corner radius for rolled shapes; distance between adjacent lines of fasteners or clear distance between flanges when welds are used for built-up shapes (in.), bf is the flange width (in.), l is the largest laterally unbraced length along either flange at the point ofload (in.), Cr = 960,000 ksi if Mu/My < 1 at the point of load and Cr = 480,000 ksi if Mu/My > 1 at the point of load, and My is the yield moment.

4.5.1.2.3.5 Compression Buckling of the Web — This limit state may occur in members with unstiffened webs when both flanges are subjected to compressive forces. The design strength for this limit state is fRn = 0.90

This design strength shall be reduced by a factor of half if the concentrated forces are acting at a distance less than half the beam depth from the beam end. The variables in Equation 4.61 are the same as those defined in Equation 4.58 to 4.60.

Stiffeners shall be provided in pairs if any one of the above strength criteria is violated. If the local flange bending or the local web yielding criterion is violated, the stiffener pair to be provided to carry the excess Ru need not extend more than one-half the web depth. The stiffeners shall be welded to the loaded flange if the applied force is tensile. They shall either bear on or be welded to the loaded flange if the applied force is compressive. Ifthe web crippling or the compression web buckling criterion is violated, the stiffener pair to be provided shall extend the full height of the web. They shall be designed as axially loaded compression members (see Section 4.4) with an effective length factor K = 0.75, a cross-section Ag composed of the cross-sectional areas of the stiffeners plus 25tw for interior stiffeners and 12t^ for stiffeners at member ends.

### 4.5.1.2.4 Deflection Criterion

The deflection criterion is the same as that for ASD. Since deflection is a serviceability limit state, service (rather than factored) loads are used in deflection computations.

### 4.5.2 Continuous Beams

Continuous beams shall be designed in accordance with the criteria for flexural members given in the preceding section. However, a 10% reduction in negative moments due to gravity loads is permitted at the supports provided that

• The maximum positive moment between supports is increased by the average of the negative moments at the supports.

• The section is compact.

• The lateral unbraced length does not exceed Lc (for ASD) or Lpd (for LRFD) where Lc is as defined in Equation 4.26 and Lpd is given by

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