Minimum Shear Wall Thickness - ACI318 or IS456? - A Study from Fundamentals

Introduction 

The Indian Concrete code IS 456-2000 recommends a minimum shear wall thickness of h/30, while the American concrete code ACI318 places it at h/25. 

Which one is correct? Which approach could be more prudent.

Let us discuss from fundamentals.

Problem Visualization

A shear wall is expected to have a lot of strength in its one plane. It's out of plane resistance is negligible compared to its in-plane resistance. This is due to its huge in-plane stiffness compared to its out of plane stiffness.

Its out of plane behavior is more or like that of a slab.

But low out of plane resistance does not mean we can have a thin concrete sheet with minimum cover to the rebar as our shear wall.

Let us analyze from first principles which approach could be good.

Mathematical Modeling

For a compression member's load at buckling failure, we have the following Euler's formula:q

P=p²EI/l²

Where P is the critical load at buckling

E is the modulus of elasticity

I is the modulus of elasticity of the section

l is the effective length of the section

For a shear wall, the effective length is its height h, or 0.75h, depending on the end conditions.

When it reaches the state of buckling, let us assume it loses its rotational restraint at its ends. The the effective length l = height h.

Then the above equation becomes

P=p²EI/h²

Then the critical buckling stress becomes:

P=p²EI/Ah²

Where p=critical compressive stress at buckling

A=cross-section area of the shear wall

This critical buckling stress needs to be more than the design compressive strength of the section.

From IS:456-2000, the Indian Concrete Code, treating the shear wall as a compression member, the maximum compressive strength in limit state design is 0.4f_ck.

If the critical buckling occurs before reaching the design compressive strength, it will escape the design check as the software does not do any buckling analysis of the wall element and at the most checks the code specified height to thickness ratio.

The term EI needs to be multiplied by a stiffness modifier in the above equation.

IS 16700 suggests a modifier of 0.7 under factor loads and 0.9 under un-factored loads. This may be OK for an in-plane moment causing some tension and cracking.

For out of plane, it will be more like a slab action, but the element will still be primarily under compression.

ACI 318-14 suggests a stiffness modifier of 0.35 for a cracked wall and 0.7 for an un-cracked wall under ultimate conditions. Under service conditions this can be enhanced 1.4 times.

Buckling being an extreme case, let us use the serviceability modifier. This means a cracked stiffness modifier of 0.49. 

This means, instead of EI in the above formula 0.49EI will be used.

Results

Considering a unit height of 1m or 1000mm, the thickness of the wall is h/30=33.33mm or h/25=1000/25=40mm.

For any height, same ratio of height by thickness continues and the results will be the same.

Below are the critical buckling stress results vs critical compressive stress for various grades of concrete and for a wall thickness of h/30 and h/25.

Graphically, they can be shown as below:

Inference

• For grades above M30, the buckling strength of the wall is less than its compressive strength for a thickness of h/30, leading to the possibility of a buckling failure before compression failure.

• From M25 thru M60,  the buckling strength of the wall is much higher than its compressive strength for a thickness of h/25, avoiding a failure in the wall before the failure in compression for which it is designed.

Recommendations

• Based on this study, it is recommended to limit the thickness of planar shear walls to not less than h/25.
• When it is difficult to keep the thickness above h/25, it is recommended to at least have the boundary element thickness greater than h/25 with the remaining wall thickness greater than h/30. A buckling analysis maybe performed on such walls.
• For shear walls having return walls in the perpendicular direction, h/30 may be maintained. Their buckling strength may be ascertained from a buckling analysis.