Total cross-sectional area of rectangular hoop reinforcement for confinement Ash shall not be less than that given by the following two equations:

Transverse reinforcement shall be provided by either single or overlapping hoops. Crossties of the same bar size and spacing as the hoops are permitted, with each end of the crosstie engaging a peripheral longitudinal reinforcing bar. Consecutive crossties shall be alternated end for end along the longitudinal reinforcement.

Eqs. (21.3) and (10.6) need not be satisfied if the design strength of the member core satisfies the requirement of the design loading combinations, including the earthquake effects.

If the thickness of the concrete outside of the confining transverse reinforcement >4 in., additional transverse reinforcement shall be provided at a spacing <12 in. Concrete cover on the additional reinforcement < 4 in. Transverse reinforcement shall be spaced at distances not exceeding

• Minimum member dimension/4.

• 6 x longitudinal bar diameter.

14 - h where 4 in. < s* = 4 +-- <6 in. (21.5)

Crossties or legs of overlapping hoops shall not be spaced more than 14 in. on center in the direction perpendicular to the longitudinal axis of the structural member. Vertical bars shall not be farther than 6 in. clear from a laterally supported bar.

Where transverse reinforcement as required in Sections is no longer required, the remainder of the column shall contain spiral or hoop reinforcement spaced at distances not to exceed

• 6 x longitudinal bar diameter.

Transverse reinforcement must also be proportioned to resist the design shear forces.

Columns supporting reactions from discontinued stiff members, such as walls, shall have transverse reinforcement as specified in Sections over their full height, if the factored axial compressive force related to earthquake effects > Af/10. This transverse reinforcement shall extend into the discontinued member for at least the development length of the largest longitudinal reinforcement in the column in accordance with Section 21.5.4.

• If the lower end of the column terminates on a wall, transverse reinforcement per Sections shall extend into the wall for at least the development length of the largest longitudinal bar in the column at the point of termination.

• If the column terminates on a footing or mat, transverse reinforcement per Sections shall extend at least 12 in. into the footing or mat.

Schematic details of reinforcement for a ductile frame are shown in Fig. 4.31. Transverse Reinforcement: Joints

Transverse reinforcement requirements for joints of SMRFs given in Sections through are as follows:

• Transverse hoop reinforcement required for column ends per Section 21.4.4 shall be provided within a joint, unless structural members confine the joint as specified in Section

• Where members frame into all four sides of a joint and each member width is at least 3/4 the column width, the transverse reinforcement within the depth of the shallowest member may be reduced to V2 of the amount required by Section The spacing of the transverse reinforcement required in Section shall not exceed 6 in. at these locations.

• Transverse reinforcement per Section 21.4.4 shall be provided through the joint to confine longitudinal beam reinforcement outside the column core if a beam framing into the joint does not provide such confinement.

Figure 4.31 shows reinforcement schematics for a ductile frame: Shear Strength of Joint

Shear strength requirements for joints in special moment-resisting frames (SMRFs) given in Sections and, are summarized as follows:

• For normal weight concrete, the nominal shear strength of the joint shall not exceed the following forces:

• For joints confined on all four faces 20^¡f Aj

• For joints confined on three faces or on two opposite faces 15^/fAj

• For other joints 12*JfC Aj where Aj = effective cross-sectional area within a joint in a plane parallel to the plane of the reinforcement generating shear in the joint. The overall depth shall be the overall depth of the column. Where a beam frames into a support of larger width, the effective width of the joint shall not exceed the smaller of

1. Beam width plus the joint depth.

2. Twice the smaller perpendicular distance from the longitudinal axis of the beam to the column side.

• A joint is considered confined if the confining members frame into all faces of the joint. A member is considered to provide confinement at the joint if the framing member covers at least 3/4 of the joint face.

• For lightweight aggregate concrete, the nominal shear strength of the joint shall not exceed 3/4 of the limits given in Section

Renewable Energy 101

Renewable Energy 101

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