# D1.F.4.6.1 Cracked Moment of Inertia - ACI Beam Design

When beam design is done per ACI 318, STAAD will report the moment of inertia of the cracked section at the location where the design is performed. The cracked section properties are calculated in accordance with the equations shown below.

## Rectangular Sections

### Gross section (A) and cracked transform section (B) for rectangular shapes

Without compression steel

n = Es/Ec

$B = b n A I$
$I g = b × h 3 12$
$k d = 2 d × B + 1 − 1 B$
$I c r = b ( k d ) 3 3 + n A s ( d − k d ) 2$

## Tee Shaped Sections

### Gross and cracked transform sections for tee shapes without compression steel

Without compression steel

$C = b w n A s$
$f = h f ( b − b w ) n A s$
$y = h − 1 2 ( b − b w ) × h f 2 + b w × h 2 ( b − b w ) × h f + b w × h$
$k d = C ( 2 d + h f × f ) + ( 1 + f ) 2 − ( 1 + f ) C$
$I c r = ( b − b w ) × h f 3 12 + b w ( k d ) 3 3 + ( b − b w ) × h f × ( k d − h f 2 ) 2 + n A s × ( d − k d ) 2$

See D1.F.4.5 Beam Design Output for an example of output including the calculated cracked moment of inertia.