# D12.A.6.7 Rectangular massive box (prismatic)

Code check of the general purpose prismatic cross section defined in the STAAD.Pro analysis package is not available. The prismatic section is assumed to be a rectangular massive box and the von Mises stress is checked at 3 locations as shown in figure below.

Note: Note that "b" may not be much greater than "h". If that is the case, define the member with h > b and beta angle 90° instead.

## Section Properties

where
 Ax , Ay , Az , Ix , Iy , and Iz , b, h = are user-specified. Refer to TR.20.2 Prismatic Property Specification. b = ZD h = YD Cw = $1 24 b 2 ( h − b ) 2 h + b h 2 b 2$, ref.NS app C3.

## General Stress Calculation

$σ = σ x + σ b y + σ b z = F x A x + M y I y z + M z I z y$
$τ = τ x + τ y + τ z = τ x , max ⁡ ( c b ) 2 + V y A y + V z A z$
$τ x , max ⁡ = M x ( 1.5 h + 0.9 b ) 0.5 h 2 b 2$

ref. [4] tab. 20, case 4 at midpoint the largest (i.e, point 2)

## Stress calculation at selected stress points

Point No σx σby σbz τx τy τz
1 $F x A x$ $M y I y b 2$ $M z I z h 2$ $τ x , max ⁡ b 2 b 2 + h 2$ 0 0
2 " $M y I y b 2$ 0 $τ x , max ⁡$ $F y A y$ 0
3 " 0 $M z I z h 2$ $τ x , max ⁡ b 2 h 2$ 0 $F z A z$