Beams

Validation and design examples for wood columns per NDS 2018. Note that values will vary slightly (+/- 1%) due to round-off errors.

Example 1 - Sawn Lumber Column using ASD and LRFD

Reference: Abi Aghayere and Jason Vigil, Structural Wood Design, 2nd Edition, 2017, Taylor & Francis, Example 5.6, p. 299

Inputs

Parameter	Value
Column Size & Grade	6x6 D.Fir-L No. 1
Column Unbraced Lengths	$L_x = L_y =$ 12'
Service Conditions	Dry, normal temperature
Axial Loads	$D$ = 6,800 lb, $S$ = 10,200 lb, Self-weight not considered, No eccentricity

Outputs

Result	Example (ASD/LRFD)	ClearCalcs (ASD/LRFD)
Design Load	17,000 lb / 24,500 lb	17,000 lb / 24,500 lb
Buckling Stress $F_{cE}$	695 psi / 1,042 psi	696 psi / 1040 psi
Column Stability Factor $C_p$	0.502 / 0.502	0.503 / 0.501
Allowable Column Capacity*	17,463 lb / 26,300 lb	17,497 lb / 26,205 lb

Example 2 - Exterior Stud Wall Using ASD

Reference: Abi Aghayere and Jason Vigil, Structural Wood Design, 2nd Edition, 2017, Taylor & Francis, Example 5.9, p. 313

Inputs

Parameter	Value
Column Size & Grade	2x6 D.Fir-L No. 2 @ 2' o.c.
Column Unbraced Lengths	$L_x$ = 10', $L_y =$ 0' (braced by sheathing for Y-axis buckling and lateral-torsional buckling)
Service Conditions	Dry, normal temperature, repeating member
Axial Loads	$D$ = 1,440 lb, $L$ = 640 lb, $S$ = 1,440 lb, Self-weight not considered, No Eccentricity
Lateral Loads	$W$ = 25 psf (specified as $0.6W$ = 15 psf in the example)

Outputs

The example splits into 4 main design checks (the first one is ignored as it checks for net section bearing stress which is irrelevant in this case)

Design Check 2 - Pure Axial Loading and Bearing

Result	Example	ClearCalcs
Governing Load Case	D + 0.75(L + S)	D + 0.75(L + S)
Governing Axial Load	3,000 lb	3,000 lb
Column Stability Factor $C_p$	0.492	0.491
Allowable Compression Stress	840 psi	839 psi
Allowable Bearing Stress	625 psi	625 psi
Utilization Ratio *	43.3%	43.3%

*Since the example deals with stresses and ClearCalcs deals with loads, we compare the utilization ratio to show that the results are exactly the same.

Design Check 3 - Pure Bending

Result	Example	ClearCalcs
Governing Load Case	D + 0.6W	D + 0.6W
Governing Moment	4,500 in-lb = 375 lb-ft	375 lb-ft
Allowable Bending Stress	2,153 psi	2,153 psi
Utilization Ratio *	27.6%	27.6%

*Since the example deals with stresses and ClearCalcs deals with loads, we compare the utilization ratio to show that the results are exactly the same.

Design Check 4 - Combined Loading

Result	Example	ClearCalcs
Governing Load Case	D + 0.75(L + S + 0.6W)	D + 0.75(L + S + 0.6W)
Governing Axial Load	3,000 lb	3,000 lb
Governing Moment	3,375 lb-in = 281.25 lb-ft	281.25 lb-ft
Allowable Bending Stress	2,153 psi	2,153 psi
Column Stability Factor $C_p$	0.377	0.376
Allowable Compression Stress	896 psi	894 psi
Interaction Equation	0.49	0.49