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Understanding the Stability Factor (k12) for Slenderness in Mass Timber Design

By December 18, 2023February 5th, 2024No Comments

In the world of mass timber design, the Stability Factor (k12)  plays a central and coordinating role in ensuring structural integrity in slender bending and axial compression members. As we navigate the complexities of bending and compression through the CLT Toolbox, the stability factor actively manages and brings together different factors, such as material constants and slenderness coefficients for the design of members   

Stability Factor (k12) for Bending Members 

Reference: AS1720.1   

Stocky members do not tend to buckle. The failure is correctly predicted by the material capacity and hence k12 = 1.0. As slenderness increases, a transition is reached, and the failure mode will change from a material failure for stocky members to a buckling failure for slender members. In this transition area, k12 is a little less than 1.0. The failure mode for members with high slenderness will be by buckling, and k12 < 1.0. For very slender members, this will result in a substantial reduction in strength. The formula for the modification of a characteristic value in bending (k12): 

Optimizing material constant: The material constant (ρb) is a function of properties that vary with the grade of the beam and can be calculated using the following equations for seasoned and unseasoned timber. 

a) Beams of seasoned timber 

 

b) Beams of unseasoned timber 

 

Where r = temporary design action effect/total design action effect. This ratio denoted as r, is used to find the material constants, offering insights into the behaviour of the beam under various conditions. For LVL and glulam, a recommended r value of 0.25 is suggested for permanent loads, ensuring stability and conservatism across different load combinations.

Slenderness coefficient for lateral buckling under bending: The slenderness coefficient is essential in predicting lateral stability problems. For beams that bend about only their minor axis for all cases, the slenderness coefficient S2 = 0. Follow the systematic flow chart (Figure 1) and Table 1 for slenderness coefficients for beams that bend about their major axis tailored to load and restraint conditions.

 

Figure 1: Flow chart for finding slenderness of beams

 

Table 1: Slenderness coefficient for beams

 

Stability Factor (k12) for Compression Members

Reference: AS1720.1

Stability factor for compression members under compression:

For compression members, the Stability Factor (k12) utilises material constants (ρc) and slenderness coefficients (S3 and S4). The formula for the modification of a characteristic value in compression (k12): 

 

Optimizing material constant: The material constant (ρc) is calculated from the relationship between characteristic compressive strength and characteristic modulus of elasticity. ρc can be calculated using the following equations:  

a) Columns of seasoned timber 

 

b) Columns of unseasoned timber 

 

Slenderness coefficient for lateral buckling under compression: The slenderness coefficients (S3 and S4) for major and minor axes, respectively perform the final act, and are determined based on restraint conditions. Decode the notation in Figure 2, guiding your understanding of column restraint, and delve into Table 2 for stability against buckling under compression.  

Figure 2: Notation for column restraint

 

Table 2: Slenderness coefficient for compression member

 

Slenderness coefficient of spaced columns  

Reference: AS1720.1 Appendix E 

Spaced columns have individual shafts spaced apart by end and intermediate packing pieces or batten plates. These packing pieces and batten plates shall be fastened by glue, nails, screws, bolts, split ring or shear-plate fasteners. The slenderness coefficient for bending about the x-axis shall be taken to be that of a solid timber column and for bending about y-axis (S5) is given by the following equation:  

 

In the design of CLT toolbox members, CLT walls are considered as spaced columns that are glued together. Due to the glued connection, the shaft spacing (a/ts) is assumed to be zero. Based on this the modification factor g28 for the effective length of CLT walls is assumed to be 1. The stability factor obtained from this slenderness coefficient is used to determine the compressive strength of columns carrying axial compression.  

Stability factor for compression members under bending:

For compression members, it’s vital to recognize that these components not only bear axial loads but may also encounter bending forces. In such scenarios, we seamlessly incorporate the procedural steps typically reserved for bending members, addressing both the major and minor axes of the compression member. It’s crucial to emphasize that, unlike bending members where the minor axis slenderness is fixed at 0, compression members necessitate a certain examination of slenderness for both major and minor axes, following the established procedure for determining slenderness on the major axis. This refined approach ensures a comprehensive evaluation, encompassing the diverse forces that may influence the stability and performance of these elements under a spectrum of conditions.  

Conclusion

As our journey through the Stability Factor (k12) concludes, the harmonious blend of slenderness, material constants, and stability emerges as the key to structural resilience in mass timber design. The CLT Toolbox simplifies this process, allowing designers to craft masterpieces that highlight the transformative power of timber in construction. 

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