 # D1.G.2 Allowable Stress per AITC Code

Explanation of terms and symbols used in this section

Table 1. Timber design nomenclature
Symbols Description
fa Actual compression or tension stress (in PSI). For tension, the axial load is divided by net sectional area (i.e, NSF x X-area).
FA Allowable design value for compression or tension (in PSI) modified with applicable modifiers or calculated based on slenderness in case of compression.

fbz

fby

Actual bending stresses about local Z and Y axis (in PSI).

FBZ

FBY

Allowable design values for bending stresses about local Z and Y axis (in PSI) modified by the applicable modifiers.

JZ

JY

Modifier for P-DELTA effect about the Z and Y axis respectively as explained in formula 5-18 of TCM.

fvz

fvy

Actual horizontal shear stresses.

FVZ

FVY

Allowable horizontal shear stresses.

VZ

VY

Shear in local Z and local Y direction.

ZD

YD

Depth of section in local Z and Y axis.

EZ

EY

Minimum eccentricity along Z and Y axis.

CFZ

CFY

Values of the size factors in the z-axis and y-axis, respectively.

CLZ

CLY

Represent the factors of lateral stability for beams about the z-axis and y-axis, respectively.
RATIO Permissible ratio of stresses. The default value is 1.0.

## D1.G.2.1 Combined Bending and Axial Tension

The following interaction formulae are checked :

fa/FA + fbz/(FBZ x CFZ) + fby/(FBY x CFY) ≤ RATIO

Lateral stability check with Net compressive stress:

fa/FA + fbz/(FBZ x CLZ) + fby/(FBY x CLY) ≤ RATIO

## D1.G.2.2 Combined Bending and Axial Compression

fa/FA + fbz/(FBZ-JZ x fa) + fby/(FBY-JY x fa) ≤ RATIO

Applicability of the size factor:

1. When CF < 1.00,

if fa > FBZ x (1-CFZ), FBZ is not modified with CFZ. if fa > FBY x (1-CFY), FBY is not modified with CFY.

if fa < FBZ x (1-CFZ) FBZ is taken as FBZ x CFZ + fa but shall not exceed FBZ x CLZ

if fa < FBY x (1-CFY) FBY is taken as FBY x CFY + fa but shall not exceed FBY x CLY

2. When CF ≥ 1.00, the effect of CF and CL are cumulative FBZ is taken as FBZ x CFZ x CLZ FBY is taken as FBY x CFY x CLY

## D1.G.2.3 Minimum Eccentricity

The program checks against min. eccentricity in following cases:

1. The member is a FRAME member and not a truss member and under compression.
2. The value of actual axial compressive stress does not exceed 30% of the allowable compressive stress.
3. The actual moments about both axes are less than moments that would be caused due to min. eccentricity. In this approach, the moment due to min. eccentricity is taken as the compressive load times an eccentricity of 1 in. or 0.1 x depth whichever is larger.

In case of min. eccentricity,

 fbz = fa x (6+1.5 x JZ)/(EZ/ZD)

 fby = fa x (6+1.5 x JY)/ (EY/YD)

the following conditions are checked :

 fa/FA + fbz/(FBZ-JZ x fa) ≤ RATIO

 fa/FA + fby/(FBY-JY x fa) ≤ RATIO

## D1.G.2.4 Shear Stresses

Horizontal stresses are calculated and checked against allowable values:

fvz = 3 x VY /(2 x Area x NSF) ≤ FVZ

fvy = 3 x VZ /(2 x Area x NSF) ≤ FVY