H2. UNSYMMETRIC MEMBERS AND MEMBERS UNDER TORSION AND COMBINED TORSION, FLEXURE, SHEAR, AND/OR AXIAL FORCE

H2. UNSYMMETRIC MEMBERS AND MEMBERS UNDER TORSION AND COMBINED TORSION, FLEXURE, SHEAR, AND/OR AXIAL FORCE

This section deals with types of cross sections and loadings not covered in Section H1, especially where torsion is a consideration. For such cases it is recommended to perform an elastic analysis based on the theoretical numerical methods available from the literature for the determination of the maximum normal and shear stresses, or for the elastic buckling stresses. In the buckling calculations an equivalent slen- derness parameter is determined for use in Equation E2-2 or E2-3, as follows:

where F e is the elastic buckling stress determined from a stability analysis. This procedure is similar to that of Appendix E3.

For the analysis of members with open sections under torsion refer to Seaburg and Rev. Carter (1997).

FLEXURAL MEMBERS

[Comm. I3.

S eff = S s + ( S Q n / C f ) ( S tr - S s )

(C-I3-7)

where S s = section modulus for the structural steel section, referred to the tension

flange, in. 3 (mm 3 )

S tr = section modulus for the fully composite uncracked transformed section, referred to the tension flange of the steel section, in. 3 (mm 3 )

Equations C-I3-6 and C-I3-7 should not be used for ratios SQ n /C f less than 0.25.

This restriction is to prevent excessive slip, as well as substantial loss in beam stiff- ness. Studies indicate that Equations C-I3-6 and C-I3-7 adequately reflect the reduction in beam stiffness and strength, respectively, when fewer connectors are used than required for full composite action (Grant, Fisher, and Slutter, 1977).

It is not practical to make accurate deflection calculations of composite flexural sections in the design office. Careful comparisons to short-term deflection tests indicate that the effective moment of inertia, I eff , is 15 to 30 percent lower than that calculated based on linear elastic theory. Therefore, for realistic deflection calcula- tions, I eff should be taken as 0.80 I eff or 0.75 I eff . As an alternative, it has been shown that one may use lower bound moment of inertia, I lb , as defined below:

I lb = I x + AY s ( ENA d - 2 3 ) +S ( Q n / F y )(2 d 3 +- d Y ENA ) 1 2 (C-I3-8)

where

d 1 = distance from the centroid of the longitudinal slab reinforcement to the top of the steel section, in. (mm)

d 3 = distance from P yc to the top of the steel section, in. (mm)

I lb = lower bound moment of inertia, in. 3 (mm 3 )

Y Rev.

ENA =[ ( A s d 3 +( SQ n /F y ) (2d 3 +d 1 ) ) / ( A s +( SQ n /F y ) ) ]

Calculations for long-term deformations due to creep and shrinkage may also be carried out. Because the basic properties of the concrete are not known to the designer, simplified models such as those proposed by Viest, Fountain, and Single- ton (1958), Branson (1964), Chien and Ritchie (1984), and Viest, Colaco, Furlong, Griffis, Leon, and Wyllie (1997) can be used.

Negative Flexural Design Strength . The flexural strength in the negative moment region is the strength of the steel beam alone or the plastic strength of the composite section made up of the longitudinal slab reinforcement and the steel section.

Plastic Stress Distribution for Negative Moment . When an adequately braced com- pact steel section and adequately developed longitudinal reinforcing bars act com- positely in the negative moment region, the nominal flexural strength is determined from the plastic stress distributions as shown in Figure C-I3.2. The tensile force T in

Comm. J3.]

BOLTS AND THREADED PARTS

There are practical cases in the design of structures where slip of the connection is desirable in order to allow for expansion and contraction of a joint in a controlled manner. Regardless of whether force transfer is required in the directions normal to the slip direction, the nuts should be hand-tightened with a spud wrench and then backed off one-quarter turn. Furthermore, it is advisable to deform the bolt threads or use a locking nut or jamb nut to insure that the nut does not back off under service conditions. Thread deformation is commonly accomplished with a cold chisel and hammer applied at one location. Note that tack-welding of the nut to the bolt threads is discouraged.

2. Size and Use of Holes

To provide some latitude for adjustment in plumbing up a frame during erection, three types of enlarged holes are permitted, subject to the approval of the designer. The nominal maximum sizes of these holes are given in Table J3.3 or J3.3M. The use of these enlarged holes is restricted to connections assembled with bolts and is subject to the provisions of Sections J3.3 and J3.4.

3. Minimum Spacing

The maximum factored strength R n at a bolt or rivet hole in bearing requires that the distance between the centerline of the first fastener and the edge of a plate toward

which the force is directed should not be less than 1 1 2 d where d is the fastener diam- eter (Kulak et al., 1987). By similar reasoning the distance measured in the line of force, from the centerline of any fastener to the nearest edge of an adjacent hole, should not be less than 3d, to ensure maximum design strength in bearing. Plotting of numerous test results indicates that the critical bearing strength is directly pro- portional to the above defined distances up to a maximum value of 3d, above which no additional bearing strength is achieved (Kulak et al., 1987). Table J3.7 lists the

Rev.

increments that must be added to adjust the spacing upward to compensate for an

increase in hole dimension parallel to the line of force. Section J3.10 gives the bear- ing strength criteria as a function of spacing.

4. Minimum Edge Distance

Critical bearing stress is a function of the material tensile strength, the spacing of

F crft ,F cry ,F crz Flexural-torsional buckling stresses for double-angle and tee-shaped compression members, ksi

F e Elastic buckling stress, ksi

F ex Elastic flexural buckling stress about the major axis, ksi

F ey Elastic flexural buckling stress about the minor axis, ksi

F ez Elastic torsional buckling stress, ksi

F my Modified yield stress for the design of composite columns, ksi

F n Nominal shear rupture strength, ksi

F n ,F nt Nominal strength of bolt, ksi

F p Nominal bearing stress on fastener, ksi

F r Compressive residual stress in flange [10 ksi for rolled shapes; 16.5 ksi for welded built-up shapes]

F s γ Stress for tapered members defined by LRFD Specification Equation A-F3-

6, ksi

F t Nominal tensile strength of bolt from LRFD Specification Table J3.2, ksi

Specified minimum tensile strength of the type of steel being used, ksi

F v Nominal shear strength of bolt from LRFD Specification Table J3.2, ksi

F w Nominal strength of the weld electrode material, ksi

F w γ Stress for tapered members defined by Equation A-F3-7, ksi

F y Specified minimum yield stress of the type of steel being used, ksi. As used in the LRFD Specification, “yield stress” denotes either the specified minimum yield point (for steels that have a yield point) or specified yield strength (for steels that do not have a yield point)

F y ′′′

The theoretical maximum yield stress (ksi) based on the web depth- thickness ratio (h / t w ) above which the web of a column is considered a slender element (See LRFD Specification Table B5.1)

Rev. 2

ht / w Note: In the tables, — indicates F y ′′′ > 65 ksi.

F yb F y of a beam, ksi

F yc F y of a column, ksi

F yf Specified minimum yield stress of the flange, ksi

F yr Specified minimum yield stress of reinforcing bars, ksi

F y st Specified minimum yield stress of the stiffener material, ksi

F yw Specified minimum yield stress of the web, ksi

G Shear modulus of elasticity of steel (G = 11,200 ksi)

G Ratio of the total column stiffness framing into a joint to that of the stiffening members framing into the same joint

H Horizontal force, kips

H Flexural constant

H Average story height

H Height of bolt head or nut, in.

H Theoretical thread height, in. (see Table 7-4)

H s Length of shear stud connector after welding, in.

H 1 Height of bolt head, in. (see Tables 7-3)

H 2 Maximum bolt shank extension based on one standard hardened washer, in. (see Tables 7-3)

I Moment of inertia, in. 4

4 LB

Lower bound moment of inertia for composite section, in.

Effective section modulus about major axis, in. eff 3 S net

Net elastic section modulus, in. 3 S

Warping statical moment at a point on the cross section, in. w 4 S

Elastic section modulus about major axis, in. x 3 S x ′

Elastic section modulus of larger end of tapered member about its major axis, in. 3

S xt ,S xc

Elastic section modulus referred to tension and compression flanges, respectively, in. 3

SRF

Stiffness reduction factors (Table 4-1), for use with the alignment charts (LRFD Specification Figure C-C2.2) in the determination of effective length factors K for columns

T Distance between web toes of fillets at top and at bottom of web, in. = d - 2k T

Tension force due to service loads, kips T

Thickness of flat circular washer or mean thickness of square or rectangular beveled washer, in.

Unfactored tensile force on slip-critical connections designed at service loads, kips

T b ,T m Specified pretension load in high-strength bolt (LRFD Specification Table J3.1), kips

T stl Tensile force in steel in a composite beam, kips T Tot

Sum of tensile forces in a composite beam, kips T u

Required tensile strength due to factored loads, kips U

Reduction coefficient, used in calculating effective net area

V Shear force, kips

V b Shear force component, kips

V h Total horizontal force transferred by the shear connections, kips

V n Nominal shear strength, kips

V u Required shear strength, kips W

Wind load W

Uniformly distributed load, kips W

Weight, lbs or kips, as indicated W

Width across flats of nut, in. W c Uniform load constant for beams, kip-ft

W no Normalized warping function at a point at the flange edge, in. 2 W u

Total factored uniformly distributed load, kips Workable Gage Gage for fasteners in flange (Part 1) that provides for entering and tightening clearances and edge distance and spacing requirements, in. When the listed value is shaded, the actual size, combination and orientation of fastener components should be compared with the geometry of the cross-section to ensure compatibility. Other gages that provide for entering and tightening clearances and edge distance and spacing requirements can also be used.

X 1 Beam buckling factor defined by LRFD Specification Equation F1-8

X 2 Beam buckling factor defined by LRFD Specification Equation F1-9 Y ENA

Distance from bottom of steel beam to elastic neutral axis, in. Y con

Distance from top of steel beam to top of concrete, in. Y1

Distance from top of steel beam to the plastic neutral axis, in.

Errata

Y2 Distance from top of steel beam to the concrete flange force in a composite 11/1/02 beam, in.

Z Plastic section modulus, in. 3 Z ′

Additional plastic section modulus corresponding to 1 / -inch increase in