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

A_x , A_y , A_z , I_x , I_y , and I_z , b, h	=	are user-specified. Refer to TR.20.2 Prismatic Property Specification.
b	=	ZD
h	=	YD
C_w	=	$\frac{1}{24} \frac{b}{2} \frac{{(h - b)}^{2}}{h + b} h^{2} b^{2}$ , ref.NS app C3.

General Stress Calculation

σ = σ_{x} + σ_{b y} + σ_{b z} = \frac{F_{x}}{A_{x}} + \frac{M_{y}}{I_{y}} z + \frac{M_{z}}{I_{z}} y

τ = τ_{x} + τ_{y} + τ_{z} = τ_{x, \max} {(\frac{c}{b})}^{2} + \frac{V_{y}}{A_{y}} + \frac{V_{z}}{A_{z}}

τ_{x, \max} = \frac{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	σ_x	σ_by	σ_bz	τ_x	τ_y	τ_z
1	$\frac{F_{x}}{A_{x}}$	$\frac{M_{y}}{I_{y}} \frac{b}{2}$	$\frac{M_{z}}{I_{z}} \frac{h}{2}$	$τ_{x, \max} \frac{b^{2}}{b^{2} + h^{2}}$	0	0
2	"	$\frac{M_{y}}{I_{y}} \frac{b}{2}$	0	$τ_{x, \max}$	$\frac{F_{y}}{A_{y}}$	0
3	"	0	$\frac{M_{z}}{I_{z}} \frac{h}{2}$	$τ_{x, \max} \frac{b^{2}}{h^{2}}$	0	$\frac{F_{z}}{A_{z}}$