Transverse reinforcement (beams seismic: ACI 318)

Seismic requirements relating to transverse reinforcement take into account properties, strengths and outcomes which are shear related ignoring any reinforcement intended to deal with torsional effects.

Design shear force

The design shear force for members subjected to earthquake effects is obtained by consideration of the minimum required shear strength of the member. The required nominal shear strength of a flexural member part of a Moment Resisting Frame is checked considering the sum of shears resultant from the moment strengths due to reverse curvature bending acting at each end of the beam and from the tributary factored gravity loads.

Beams are checked for shear in three regions:

Left region, S1;
Central region, S2;
Right region, S3.

Shear design is performed considering the Major axis shear force only. Shear Force in the minor axis is checked against the ignorable threshold.

If SFRS Type = Ordinary Moment Frame, then no shear seismic check applies.

If SFRS Type = Intermediate Moment Frame


V_e	=	ɸMIN(V_e,Mn+V_e,gravity,V_e,2E)
where
ɸ	=	Strength reduction factor = 1.0
V_e	=	Minimum design shear force for load combinations including earthquake effects
V_e,gravity	=	Shear due to factored gravity loads from seismic combinations (including vertical earthquake effects) retaining the sign from analysis
V_e,2E	=	Maximum shear resultant from seismic combinations, with doubled earthquake effect [i.e.: V_{e.non-seismic} + V_e.E x 2]
V_e,Mn	=	Maximum shear associated with the development of reversed curvature bending due to nominal resisting moments at both ends of the member, considering both the clockwise and counter-clockwise cases

If SFRS Type = Special Moment Frame


V_e	=	ɸ(V_e,Mpr+V_e,gravity)
where
ɸ	=	Strength reduction factor = 1.0
V_e	=	Minimum design shear force for load combinations including earthquake effects
V_e,gravity	=	Shear due to factored gravity loads from seismic combinations (including vertical earthquake effects) retaining the sign from analysis
V_e,Mpr	=	Maximum shear associated with the development of reversed curvature bending due to the probable flexural moment strength for both the clockwise and counter-clockwise situations, at both ends of the member

Maximum hoop spacing

The maximum allowed horizontal center spacing of hoops in confinement regions of beams is limited by ACI 318 depending on the type of Seismic Force Resisting System considered.

Note: This check is performed for support regions only, it is beyond scope in the current release of Tekla Structural Designer for other confinement regions.

Note: Non-reversing plastic hinge regions along the span have the same requirements as support regions, but these are beyond scope in the current release of Tekla Structural Designer.

For Support Regions:

If SFRS Type = Special Moment Frame

The maximum allowed center hoop spacing in support regions, s_cr,max,sup is calculated as follows:

According to ACI318-08¹:


s_cr,max,sup	=	MIN(d/4, 8 * d_b,smallest, 24 * d_b,w, 300mm)	Metric-units
s_cr,max,sup	=	MIN(d/4, 8 * d_b,smallest, 24 * d_b,w, 12 in.)	US-units

According to ACI318-11¹:


s_cr,max,sup	=	MIN(d/4, 6* d_b,smallest, 150 mm)	Metric units
s_cr,max,sup	=	MIN(d/4, 6 * d_b,smallest, 6 in.)	US units


where
d	=	Distance from extreme compression fiber to centroid of longitudinal tension reinforcement
d_b,smallest	=	Smallest longitudinal reinforcement bar diameter
d_b,w	=	Link (hoop) diameter

If SFRS Type = Intermediate Moment Frame

The maximum allowed center hoop spacing in support regions, s_cr,max,sup is calculated as follows:


s_cr,max,sup	=	MIN(d/4, 8* d_b,smallest, 24 * d_b,w, 300mm)	Metric units
s_cr,max,sup	=	MIN(d/4, 8 * d_b,smallest, 24 * d_b,w, 12 in.)	US units


where
d	=	Distance from extreme compression fiber to centroid of longitudinal tension reinforcement
d_b,smallest	=	Smallest longitudinal reinforcement bar diameter
d_b,w	=	Link (hoop) diameter

For Span Regions:

If SFRS Type = Special Moment Frame, or Intermediate Moment Frame

The maximum allowed hoops spacing outside confinement regions, s_cr,max,span is calculated as follows:


	s_cr,max,span	=	d/2

Maximum allowed lateral link leg spacing

The clear spacing between link legs at right angles to the span is limited in confinement reinforcement regions of members part of Special Moment Frames only.

Note: This check is performed for support regions only, it is beyond scope in the current release of Tekla Structural Designer for other confinement regions.

Footnotes