Transverse reinforcement (columns seismic: ACI 318)
Joint shear strength
The calculation of joint shear strength is a requirement of ACI 318 for joints of Special Moment Frames and it is obtained by considering both the free body diagram of the column and of the joint. The stress in the beam's tensile reinforcement at the joint's face is assumed as at least η *fy by considering the probable moment strengths of framing beams.
The calculation is performed on the following basis:
- Probable Moment Strengths are obtained from beams in the same direction as the column's considered direction
- Whether beams in the column SFRS Direction are included in the SFRS or not
- At the top region of stack only
- For both sway right and sway left cases
- Beams with pinned connection are ignored
- Axial stress in beams is assumed to be zero
- Contribution of the slab longitudinal reinforcement in the beam effective flange width is recommended to be considered, but remains beyond scope in the current release.
Design shear force
The Design Shear Force of a member subjected to flexure as well as axial loading part of a Moment Resisting Frame is checked taking into consideration the shear from the moment strengths of the connected flexural members due to reverse curvature bending.
- Shear design for columns is done for the entire stack as a single region and checked for the minimum requirements from the design code.
- The design is performed independently for both the orthogonal directions.
Minimum area of transverse reinforcement
For columns that are part of Special Moment Frames, the minimum area of transverse reinforcement required in confinement regions of a column is obtained as below:
Note: For Special Moment Frames the amount of confinement reinforcement in joints with
beams on all 4 sides wider than ¾ of the column width is allowed to be reduced to
half and the spacing to be relaxed within the depth of the shallowest member - this
is beyond scope in the current release of Tekla Structural Designer.
Note: Non-reversing plastic hinge regions along the span have the same requirements as
support regions - Non-reversing plastic hinge regions are beyond scope in the
current release of Tekla Structural Designer.
For circular columns:
| ρs | = | MAX[ 0.12 * (f’c / fyt) , 0.45 * [(Ag / Ach)-1] * (f’c / fyt)] |
| where | ||
| ρs | = | ratio of volume of circular reinforcement to total volume of confined concrete core. |
| f’c | = | Specified compressive strength of concrete. |
| fyt | = | Specified yield strength of transverse reinforcement. |
| Ag | = | Gross area of concrete section. |
| Ach | = | Area of concrete member section measured to the outside of the transverse reinforcement. |
|
For other supported column geometries
| ACI 318-11 | ||
| Ash | = | MAX[0.3 * s * bc * (f’c / fyt) * [(Ag / Ach)-1] , 0.09 * s * bc * (f’c / fyt)] |
| ACI 318-14 | ||
| Ash | = |
MAX[0.3 * s * bc * (f’c / fyt) * [(Ag / Ach)-1] , 0.09 * s * bc * (f’c / fyt), 0.2 * kf * kn * (Pu /(MIN[fyt , 700MPa] * Ach)] |
| where | ||
| Ash | = | total cross-section of transverse reinforcement, including cross-ties, within spacing s and perpendicular to dimension bc. |
| s | = | Center to center spacing of transverse reinforcement along the region's height. |
| bc | = | Cross section dimension of the member core measured to the outside of the transverse reinforcement and in the direction perpendicular to the considered reinforcement link legs. |
| Ag | = | Gross area of concrete section. |
| Ach | = | Area of concrete member section measured to the outside of the transverse reinforcement. |
|
Support regions of columns belonging to any other Moment Resisting Frame type have the minimum area of transverse reinforcement as per conventional design requirements.
Maximum allowed center hoop spacing
The maximum allowed horizontal center spacing of hoops in confinement regions of columns part of Moment Resisting Frames is limited as below.
If SFRS Type = Ordinary Moment Frame:
• No spacing requirement applies to support regions when designing for seismic provisions.
If SFRS Type = Special Moment Frame and the region is a support region:
| scr,max,sup | = | MIN[6*db,smallest, 0.25*MIN(c1, c2), 100 mm ≤ 100+((350 – hx)/3) ≤ 150 mm] | metric units |
| scr,max,sup | = | MIN[6*db,smallest, 0.25*MIN(c1, c2), 4 in. ≤ 4+((14 - hx)/3) ≤ 6 in.] | US units |
| where | |||
| db,smallest | = | Smallest longitudinal reinforcement bar diameter | |
| c1 | = | Rectangular or equivalent rectangular column dimension in the direction of the span for which moments are being considered | |
| c2 | = | Dimension of the column perpendicular to c1 | |
| hx | = | Maximum center-to-center horizontal spacing of crossties at any face of the column | |
|
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If SFRS Type = Special Moment Frame and the region is not a support region:
| scr,max,span | = | MIN[6 * db,smallest, 150 mm] | metric units |
| scr,max,span | = | MIN[6 * db,smallest, 6 in.] | US units |
|
If SFRS Type = Intermediate Moment Frame and the region is a support region:
| scr,max,sup | = | MIN[8*db,smallest, 24 *db,w , 1/2 * MIN(c1, c2), 300 mm] | metric units |
| scr,max,sup | = | MIN[8*db,smallest, 24 **db,w , 1/2 * MIN(c1, c2), 12 in.] | US units |
| where | |||
| db,w | = | = Link (hoop) diameter | |
|
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If SFRS Type = Intermediate Moment Frame and the region is not a support region:
- No spacing requirement applies beyond the conventional design requirements.