FIGURE 4.2 Frequency distribution of load effect and resistance.

TABLE 4.3 Load Factors and Load Combinations

Notes: D is the dead load, E is the earthquake load, F is the load due to fluids with well-defined pressures and maximum heights, H is the load due to the weight and lateral pressure of soil and water in soil, L is the live load, L is the roof live load, R is the rain load, S is the snow load, T is the self-straining force, and W is the wind load.

The load factor on L in the third, fourth, and fifth load combinations shown above can be set to 0.5 for all occupancies (except for garages or areas occupied as places of public assembly) in which the design live load per square foot of area is less than or equal to 100 psf (4.79 kN/m2). The load factor on H in the sixth and seventh load combinations shall be set to zero if the structural action due to H counteracts that due to W or E.

where f Rn represents the design (or usable) strength and Y1 giQni represents the required strength or load effect for a given load combination. Table 4.3 shows examples of load combinations (ASCE 2002) to be used on the right-hand side of Equation 4.4. For a safe design, all load combinations should be investigated and the design is based on the worst-case scenario.

Tension members are designed to resist tensile forces. Examples of tension members are hangers, truss members, and bracing members that are in tension. Cross-sections that are used most often for tension members are solid and hollow circular rods, bundled bars and cables, rectangular plates, single and double angles, channels, WT- and W-sections, and a variety of built-up shapes.

4.3.1 Tension Member Design

Tension members are to be designed to preclude the following possible failure modes under normal load conditions: yielding in gross section, fracture in effective net section, block shear, shear rupture along

4.3 Tension Members plane through the fasteners, bearing on fastener holes, prying (for lap- or hanger-type joints). In addition, the fasteners' strength must be adequate to prevent failure in the fasteners. Also, except for rods in tension, the slenderness of the tension member obtained by dividing the length of the member by its least radius of gyration should preferably not exceed 300. Allowable Stress Design

The computed tensile stress ft in a tension member shall not exceed the allowable stress for tension, Ft, given by 0.60Fy for yielding on the gross area and by 0.50Fu for fracture on the effective net area. While the gross area is just the nominal cross-sectional area of the member, the effective net area is the smallest cross-sectional area accounting for the presence of fastener holes and the effect of shear lag. It is calculated using the equation

i=1 j=1 . where U is a reduction coefficient given by (Munse and Chesson 1963)

in which l is the length of the connection and X is the larger of the distance measured from the centroid of the cross-section to the contact plane of the connected pieces or to the fastener lines. In the event that the cross-section has two symmetrically located planes of connection, X is measured from the centroid of the nearest one-half the area (Figure 4.3). This reduction coefficient is introduced to account for the shear lag effect that arises when some component elements of the cross-section in a joint are not connected, rendering the connection less effective in transmitting the applied load. The terms in brackets in Equation 4.5 constitute the so-called net section An. The various terms are defined as follows: Ag is the gross cross-sectional area, dn is the nominal diameter of the hole (bolt cutout) taken as the nominal bolt diameter plus 8 in. (3.2 mm), t is the thickness of the component element, s is the longitudinal center-to-center spacing (pitch) of any two consecutive fasteners in a chain of staggered holes, and g is the transverse center-to-center spacing (gage) between two adjacent fasteners gage lines in a chain of staggered holes.

The second term inside the brackets of Equation 4.5 accounts for loss of material due to bolt cutouts; the summation is carried for all bolt cutouts lying on the failure line. The last term inside the brackets of Equation 4.5 indirectly accounts for the effect of the existence of a combined stress state (tensile and shear) along an inclined failure path associated with staggered holes; the summation is carried for all staggered paths along the failure line. This term vanishes if the holes are not staggered. Normally, it is necessary to investigate different failure paths that may occur in a connection; the critical failure path is the one giving the smallest value for Ae.

To prevent block shear failure and shear rupture, the allowable strengths for block shear and shear rupture are specified as follows:

Block shear:

Shear rupture:

where Av is the net area in shear, At is the net area in tension, and Fu is the specified minimum tensile strength.

The tension member should also be designed to possess adequate thickness and the fasteners should be placed within a specific range of spacings and edge distances to prevent failure due to bearing and failure by prying action (see Section 4.11).

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