Shear Design

Concrete Shear Capacity

The shear capacity of the concrete portion of the column is calculated using one of the following:

For members subject to shear and flexure only:

V_{c} = 2 \sqrt{{f^{'}}_{c}} b_{w} d

Equation ACI 11-3

For members subject to axial compression:

V_{c} = 2 (1 + \frac{N_{u}}{2, 000 A_{g}}) \sqrt{{f^{'}}_{c}} b d

Equation ACI 11-4

where

N_u

=

taken as the factored axial load on the column that acts simultaneously with V_u and does not account for effects due to creep and shrinkage.

For members subject to axial tension:

V_c = 0

If lightweight concrete is specified and f_ct is defined, f_ct/6.7 will be used instead of $\sqrt{{f^{'}}_{c}}$ as long as f_ct/6.7≤ $\sqrt{{f^{'}}_{c}}$ per ACI 11.2.1.1. When f_ct is not specified then 0.75 $\sqrt{{f^{'}}_{c}}$ is used instead of $\sqrt{{f^{'}}_{c}}$ per ACI 11.2.1.2

Reinforcement Shear Capacity

The shear capacity is checked along the column in both the major and minor directions. Shear reinforcement is provided for columns at all locations where:

V_{u} > \frac{ϕ_{s} V_{c}}{2}

ACI 11.5.5.1

Shear reinforcement is taken to be provided by reinforcement ties with a user-defined number of legs in both directions.

Shear reinforcement capacity is calculated as:

V_{s} = \frac{A_{v} f_{y} d}{s}

Equation ACI 11-15

Which is limited by:

V_{s} = 8 \sqrt{{f^{'}}_{c}} b d

ACI 11.5.6.9

The shear capacity ratio in each direction is taken as:

Ld/Cap = V_u/ϕ_sV_n

From ACI-10.9.1

Minimum Shear Reinforcement

The minimum shear reinforcement area for ACI 318-99 is:

A_{v, min} = 50 \frac{b_{w} s}{f_{y}}

Equation ACI 11-13

The minimum shear reinforcement area for ACI 318-02 is:

A_{v, min} = 0.75 \sqrt{{f^{'}}_{c}} \frac{b_{w} s}{f_{y}}

Equation ACI 11-13

But shall not be less than:

A_{v, min} = 50 \frac{b_{w} s}{f_{y}}

Shear Reinforcement Spacing Limits

Spiral Reinforcement

Shear reinforcement center-to-center spacing limits for spirals:

s ≤ 3 in. + d_bTrans

ACI 7.10.4.3

The maximum center-to-center spacing of spirals is also checked using ACI-318 99, Eq 10-6 in section 10.9.3, which is reformulated to calculate the maximum spacing using PCA Notes on ACI 318-99, Ex 11.4 page 11-26:

s = \frac{A_{s} π (D_{c} - D_{s})}{A_{c} ρ_{s}}

where

ρ_s	=	$0.45 (\frac{A_{g}}{A_{c}} - 1) \frac{{f^{'}}_{c}}{f_{y}}$ ACI-318 99 Eq. 10-6
A_s	=	Spiral reinforcement area
A_c	=	Column core area enclosed by outside diameter of spiral
D_c	=	Core diameter = column diameter - 2 x spiral diameter
D_s	=	Spiral reinforcement diameter

Tie Reinforcement

Shear reinforcement center-to-center spacing limits for ties:

s ≤ 16d_bLong

ACI 7.10.5.2

s ≤ 48d_bTrans

s ≤ Minimum Column Dimension

Design of Circular Ties

The ACI code makes a distinction between rectangular or circular ties and spiral reinforcement. In some cases circular ties follow the requirements for rectangular ties and in other cases they follow the requirements of spiral reinforcement.

All of the design requirements for circular ties have been outlined in other parts of the RAM Concrete Column Design manual. Where the ACI code does not specifically mention circular ties, the circular ties will be controlled by the provisions of rectangular ties.

Calculation of Actual Bar Spacing

Bar spacing is checked to make sure it is within the code limits. For the transverse bar sets along the length of the column the spacing is taken as:

s = \frac{Bar Set Length}{Total Number of Bars}

Equation 4-10

Transverse Bar Size

The minimum size of bars used as transverse reinforcement is limited as follows:

For spiral reinforcing, d_b≥ 3/8in

ACI-7.10.4.2

For tie reinforcing,

d_b≥0.375 in. for #10 and smaller diameter long bars

ACI-7.10.5.1

d_b≥0.50 in. for #11 and larger diameter long bars

When the transverse bar diameter is smaller than the code limit a design warning will notify the user.

Transverse Bar

Per ACI-11.11.2, for all lateral columns and gravity columns that do not have beams of the same depth framing into all sides of the column, an additional transverse reinforcement segment will be created. This transverse segment will be the same size as the deepest beam and rounded to the user defined Transverse Segment Spacing Increment that is entered in the Design Criteria dialog. The reinforcement for this top segment must be no less than that prescribed by Equation ACI-11.13.