Brackets and Corbels

50.9 Brackets and Corbels

Brackets and corbels are cantilevers having shear span to depth ratio, a/d, not greater than unity. The shear span a is the distance from the point of load to the face of support, and the distance d shall be measured at face of support (see Fig. 50.14 ).

The corbel shown in Fig. 50.14 may fail by shearing along the interface between the column and the corbel, by yielding of the tension tie, by crushing or splitting of the compression strut, or by localized bearing or shearing failure under the loading plate.

The depth of a bracket or corbel at its outer edge should be less than one-half of the required depth

d at the support. Reinforcement should consist of main tension bars with area A s and shear reinforcement with area A h (see Fig. 50.15 for notation). The area of primary tension reinforcement A s should be made equal to the greater of (A f +A n ) or (2A vf /3 + A n ), where A f is the flexural reinforcement required to resist moment [V u a+N uc (h – d)], A n is the reinforcement required to resist tensile force N uc , and A vf is the shear-friction reinforcement required to resist shear V u :

In the above equations, f y is the reinforcement yield strength;

f is 0.9 for Eq. (50.119) and 0.85 for Eqs. (50.120) and (50.121). In Eq. (50.119), the lever arm jd can be approximated for all practical purposes in most cases as 0.85d. Tensile force N uc in Eq. (50.120) should not be taken less than 0.2V u unless special provisions are made to avoid tensile forces. Tensile force N uc should be regarded as a live load even when tension results from creep, shrinkage, or temperature change. In Eq. (50.121), V i / f(= V n ) should not be

taken greater than 0.2f c ¢ b w d nor 800b w d in pounds in normal-weight concrete. For “all-lightweight” or “sand-lightweight” concrete, shear strength V n should not be taken greater than (0.2 – 0.07a/d)f c ¢ b w d nor (800 – 280a/d)b w d in pounds. The coefficient of friction m in Eq. (50.121) should be 1.4l for concrete placed monolithically, 1.0 l for concrete placed against hardened concrete with surface intentionally roughened, 0.6 l for concrete placed against hardened concrete not intentionally roughened, and 0.7l for concrete anchored to as-rolled structural steel by headed studs or by reinforcing bars, where l is 1.0 for normal weight concrete, 0.85 for “sand-lightweight” concrete, and 0.75 for “all-lightweight” concrete. Linear interpolation of l is permitted when partial sand replacement is used.

The total area of closed stirrups or ties A h parallel to A s should not be less than 0.5(A s –A n ) and should

be uniformly distributed within two-thirds of the depth of the bracket adjacent to A s . At front face of bracket or corbel, primary tension thermal A s should be anchored in one of the following ways: (a) by a structural weld to a transverse bar of at least equal size; weld to be designed to develop specified yield strength f y of A s bars; (b) by bending primary tension bars A s back to form a horizontal loop, or (c) by some other means of positive anchorage. Also, to ensure development of the yield strength of the reinforcement A s near the load, bearing area of load on bracket or corbel should not project beyond straight portion of primary tension bars A s , nor project beyond interior face of transverse anchor bar (if one is provided). When corbels are designed to resist horizontal forces, the bearing plate should be welded to the tension reinforcement A s .