AS 3600 Punching Shear Design

The AS 3600 Punching Shear Model

The critical section for punching shear is assumed to be at d_om/2 from the face of the loaded area or support, where d_om represents the mean value of d_o, averaged around the critical perimeter. Based on the derivation of the code equations, d_om is not meant to include the thickness of beams. RAM Concept uses a heuristic method for determining the critical section thickness in regions of differing slab/beam thicknesses around the punching check. The critical section thicknesses can be inspected by turning them on using "visible objects".

The AS 3600 model for punching shear assumes that the shear force V* is distributed evenly around the critical section creating a uniform average shear stress of ν = V*/ud_om. The unbalanced moment, M_v* is resisted by a 3-component mechanism:

Difference in yield moments at the front and back faces of the slab strips.
Eccentricity of the uniform shear stresses ν from the centroid of the support or load.
Torsional moment on the side faces (torsion strips).

In the model, the torsional moment in #3 is resolved into a maximum shear stress and added to the uniform average shear stress ν. The proportion of M_v* contributing to the torsional moment in #3 is actually variable, but is assumed to be constant to simplify the model. The value of M_v* is taken at the centre of the column/support.

Design Equations

The resulting shear capacity V_uo where M_v* is zero (as well as on slab strip faces) is calculated per AS 3600 clause 9.3.3a:

V_{u o} = u d_{o m} (f_{c v} + 0.3 σ_{c p})

Rearranged to view in terms of limiting stress, this equation becomes:

\frac{V *}{u d_{o m}} \leq f_{c v} + 0.3 σ_{c p}

Where M_v* is not zero, the model results in the following design equation in AS 3600 clause 9.3.4a when there are no closed ties in the torsion strips and no spandrel beams:

V_{u} = \frac{V_{u o}}{[1 + (\frac{u M_{v}^{*}}{8 V^{*} a d_{o m}})]}

This expression sets an upper limit on the combination of M_v* and V* that can be resisted by the concrete. This equation can be rearranged to view in terms of limiting stresses:

\frac{M_{v}^{*}}{8 a d_{o m}^{2}} + \frac{V^{*}}{u d_{o m}} \leq f_{c v} + 0.3 σ_{c p}

The code allows for increasing the punching capacity by placing a minimum quantity of closed ties in the torsion strips. RAM Concept provides check box items to include calculation based upon the presence of these minimum closed ties in accordance with AS 3600 clause 9.3.4b. RAM Concept does not calculate the quantities of minimum ties required by this clause, which must be calculated and included by the Engineer.

When the minimum quantity of closed ties is present in the torsion strips, the equation in clause 9.3.4b is used:

V_{u} = \frac{1.2 V_{u o}}{[1 + (\frac{u M_{v}^{*}}{2 V^{*} a^{2}})]}

This expression can also be re-arranged to view in terms of limiting stresses:

\frac{M_{v}^{*}}{2.4 a^{2} d_{o m}} + \frac{V^{*}}{1.2 u d_{o m}} \leq f_{c v} + 0.3 σ_{c p}

In scenarios where the shear to moment ratio is small and/or torsion strip width to effective depth is small, it is possible for the AS 3600 equations to calculate a lower strength with ties than without.

RAM Concept does not calculate shear capacity using the beam provisions of clause 9.3.4c and 9.3.4d.

Calculation of Maximum and Allowable Shear Stress and Corresponding Stress Ratio

The allowable shear stress calculated is: f_cv + .3σ_cp, where

f_{c v} = 0.17 (1 + \frac{2}{β_{h}}) \sqrt{{f^{'}}_{c}} \leq 0.34 \sqrt{{f^{'}}_{c}}

and σ _cp is the average prestress in the punching check region. If σ_cp results in tension it reduces the allowable stress. The reported allowable shear stresses are multiplied by φ = 0.7.

For each set of enveloped force reactions, a maximum unreinforced shear stress is calculated as follows:

The maximum unreinforced shear stress on the slab strip face is calculated.
The maximum unreinforced shear stress on the torsion strip due to combined shear and bending is calculated for bending about the r-axis, using the closed ties provisions if selected by the user.
The maximum unreinforced shear stress on the torsion strip due to combined shear and bending is calculated for bending about the s-axis, using the closed ties provisions if selected by the user.

The absolute maximum shear stress from above is reported as the maximum unreinforced shear stress for that force envelope. The unreinforced stress ratio for each force envelope is the maximum unreinforced stress/allowable stress.

Calculation of Punching Resistance with SSR

The SSR is used to resist direct shear stresses, but not torsion stresses. Where SSR is provided the punching resistance is calculated as follows:

The following operations are performed individually on each face:
A minimum number of rails are installed based upon a maximum transverse rail spacing of 2d_om. The rails are installed at the allowable maximum spacing. The length of each rail is a minimum of 2.5d.
The number of strips used for strength is calculated, up to a total of 4 (2 slab and 2 torsion strips). This is accomplished by determining how many faces contain parts of the critical section. If there is no part of the critical section on a particular face, this face will not be used for strength design but will get rails placed, if possible, using the maximum transverse spacing requirement.
The perimeter length of the face is calculated both as a slab strip and a torsion strip. The length of the torsion strip is simply the appropriate width of the critical section. The length of the slab strip is calculated as the length remaining after any torsion strip lengths have been deducted. If the torsion strip is broken up with holes/openings, it is possible that the slab strip length will be less than or equal to zero. In this event no design will be reported and the status will be reported as "Failed".
The average effective depth of the slabs containing the existing rails is calculated.
The number of additional rails required is calculated and added, if necessary, and step 4 and 5 are repeated until a satisfactory solution is found.

The strength equations used in the calculation of SSR are as follows:

For slab strips:

V_{u} = V_{u o} (1 + K_{s})

where

K_s	=	$\frac{1}{V_{u o}} A_{v s} f_{v y} (\frac{d}{s}) (\frac{u}{b})$
A_vs	=	cross sectional area of one peripheral line of studs in the strip
b	=	width of the strip
f_vy	=	yield stress of the studs in the strip
d	=	average effective depth of the slab containing the shear stud rails
u	=	perimeter length of the critical section

For torsion strips:

V_{u} = \frac{V_{u o}}{\frac{1}{1 + K_{t}} + \frac{u M_{v}^{*}}{8 V^{*} a d_{o m}}}

where

K_t	=	$\frac{1}{V_{u o}} A_{v t} f_{v y} (\frac{d}{s}) (\frac{u}{a})$
a	=	width of the strip

The maximum punching shear force which can be transferred to the column is taken as the smaller of these two values of φv_u:

V ≤ ΦV_u

Φ = 0.7

Maximum Reinforced Strength

The maximum strength of the reinforced slab/column connection is given as:

V_umax = 0.2fc’ud_om

thus giving the following 2 conditions that must be satisfied:

In the slab strip,

V_uo (1+K_t) ≤ 0.2ud_om f_c’

In the torsion strip,

V_uo (1+K_s) ≤ 0.2ud_om f_c’

Miscellaneous Provisions

The spacing to the first stud is calculated as 0.35 d. This spacing is rounded down to the nearest 5 mm for metric units (or 1/8 inch for US units).

The maximum typical stud spacing is 0.75 d. In seismic applications, the Engineer can limit the typical spacing to a smaller value by specifying the typical stud spacing directly.

When SSR reinforcement is required, a minimum quantity of reinforcement is provided on all strength strips as follows:

A_{s v} = \frac{0.35 b_{w} s}{f_{v y}}

(for AS 3600-2001)

A_{s v} = \frac{0.06 \sqrt{{f^{'}}_{c}} b_{w} s}{f_{s y, f}} \geq \frac{0.35 b_{w} s}{f_{s y, f}}

(for AS 3600-2009)

A_{s v} = \frac{0.08 \sqrt{{f^{'}}_{c}} b_{w} s}{f_{s y, f}}

(for AS 3600-2018)