306 Reserve Strength

While the elastic behavior of tubular joints is well predicted by shell theory and finite element analysis, there is considerable reserve strength beyond theoretical yielding due to triaxiality, plasticity, large deflection effects, and load redistribution. Practical design criteria make use of this reserve strength, placing considerable demands on the notch toughness of joint can materials. Through joint classification (API) or an ovalizing parameter (AWS), they incorporate elements of general collapse as well as local failure. The resulting criteria may be compared against the supporting database of test results to ferret out bias and uncertainty as measures of structural reliability. Data for K, T/Y, and X joints in compression show a bias on the safe side of 1.35, beyond the nominal safety factor of 1.8, as shown in Figure 30.4. Tension joints appear to show a larger bias of 2.85; however, this reduces to 2.05 for joints over 0.12 in. thick and 1.22 for joints over 0.5 in., suggesting a thickness effect for tests that end in fracture.

For overload analysis of tubular structures (e.g., earthquake), we need not only ultimate strength but also the load-deflection behavior. Early tests showed ultimate deflections of 0.03 to 0.07 chord diameters, giving a typical ductility of 0.10 diameters for a brace with weak joints at both ends. As more different types of joints were tested, a wider variety of load-deflection behaviors emerged, making such generalizations tenuous.

Cyclic overload raises additional considerations. One issue is whether the joint will experience a ratcheting or progressive collapse failure or will achieve stable behavior with plasticity contained at local hotshots, a process called ''shakedown'' (as in shakedown cruise). Tubular connections have withstood 60 to several hundred repetitions of plastic strain at loads in excess of their nominal capacity. A conservative analytical treatment is to extend the hot spot S-N design curve into the low-cycle range as strain.

When tubular joints and members are incorporated into a space frame, the question arises as to whether computed bending moments are primary (i.e., necessary for structural stability, as in a sidesway portal situation, and must be designed for) or secondary (i.e., an unwanted side effect of deflection, which may be safely ignored or reduced). When proportional loading is imposed, with both axial load and bending moment being maintained regardless of deflection, the joint simply fails when it reaches its failure envelope. However, when moments are due to imposed lateral deflection, and then axial load is imposed, the load path skirts along the failure envelope, shedding the moment and sustaining further increases in axial load.

Another area of interaction between joint behavior and frame action is the influence of brace bending or rotation on the strength of gap K connections. If rotation is prevented, bending moments develop that permit the gap region to transfer additional load. If the loads remain strictly axial, brace end rotation occurs in the absence ofrestraining moments, and a lower joint capacity is found. These problems arise for circular tubes as well as box connections, and a recent trend has been to conduct joint-in-frame tests to achieve a realistic balance between the two limiting conditions. Loads that maintain their original direction

1 test" allowable

FIGURE 30.4 Comparison of AWS design criteria with the WRC database.

1 test" allowable

FIGURE 30.4 Comparison of AWS design criteria with the WRC database.

(as in an inelastic finite element analysis) or, worse yet, follow the deflection (as in testing arrangements with a two-hinge jack) result in a plastic instability of the compression brace stub as a column, which grossly understates the actual joint strength. Existing databases may need to be screened for this problem.

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