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3.3.2 - Flexural Design Equations
The calculation of actual bending stress for sawn lumber, glulam and SCL members is given in 3.3.2.2 as
fb = 6M / bd2
where M is the bending moment at the member cross section. The factored bending stress is compared with the factored allowable bending stress.
Refer to NDS 7 - Wood I-Joists for I-Joist bending design and PRG 320 Table A-2 and O86 8.4.3.1 - Bending Moment Resistance for CLT design.
3.3.3-Beam Stability Factor, CL
Points of lateral support can be specified in Beam View or Column View for Beam and Column modes by entering a lateral support spacing, indicating that the member is supported continuously, or that it is supported only at the span ends where there is a point of bearing.
In Beam mode, lateral support is provided for both the top and bottom faces of the beam, and the program determines which to use by whether these faces are loaded in compression or tension. .
In Column mode the value entered in the Lb and Ld fields for the b and d load faces are assumed to be the lateral support spacing for the compression face of a laterally loaded column in the b and d directions.
Concept mode has a more limited set of selections:
- the tops and bottoms of beams and joists are either fully restrained or only restrained at their supports
- the b and d faces of columns and walls are either fully restrained or only restrained at their supports
3.3.3.2 and 3.3.3.3: In Sizer, CL = 1.0 when the compression edge of a beam, joist, column or wall stud is fully restrained. It is the responsibility of the user to satisfy the lateral support requirements of clause 5.4.1 whenever Sizer assumes or applies a fully restrained condition.
3.3.3.4: The unsupported length lu is determined for each span as the smaller of the following distances:
- between the two points of bearing
- the user-input lateral support spacing
- if you have selected to allow this in the Design Settings , the distance between points of zero moment within a span (counter flexure) or the point of bearing or another point.
Background to zero moment option: Since NDS C3.3.3.3 refers to the compression edge of the member, many designers measure Lu only over those distances that the member is in compression, that is, treating points of zero moment as if they were lateral support points. Other analysts question this approach, for example the CSA Handbook of Steel Construction does not allow it based on work done by Schmitke and Kennedy, 1985.
For multi-span systems, if the maximum moment occurs within a span, then lu is taken for the span in which the maximum moment occurs. If the maximum moment occurs at a support, the largest lu from either side of the support is taken.
3.3.3.5: The effective length, le, is conservatively calculated for cantilevers under all loading conditions as:
le= 1.87 lu when lu /d < 7 (d = member depth)
le= 1.44 lu + 3d when lu /d >= 7
For all other members the footnotes of Table 3.3.3 of the NDS apply:
le= 2.06 lu when lu /d < 7
le= 1.63 lu + 3d when 7 <= lu/d < 14.3
le= 1.84 lu when lu /d > 14.3
3.3.3.6: Slenderness Ratio RB : The slenderness ratio is used to compute the lateral stability factor CL in NDS 3.3.3.8, and itself is limited to no more than 50 in 3.3.3.7. If this value is exceeded, a message appears on the screen and moment design is not calculated, showing instead a failure for slenderness ratio.
For multi-ply members, the NDS does not offer guidance on whether to use the full member width or a single ply width, so there is an option in the Design Settings for either to be selected, depending on the judgement of how well the individual members are connected.
Unpublished research has shown that nailed and bolted beams have at most 30% composite action effect in terms of resisting torsional buckling, so it is recommended to use single play width unless there is certainty that the individual members are fastened together such that they act as a unit.
3.3.3.8 Beam Stability factor CL :Where CV > 1, as can occur for SCL materials,, Sizer adjusts Fb* in the term FbE/Fb* by CV prior to calculating CL. Refer to www.awc.org/wood-design/2006/09/application-of-volume-factor-cv-for.html.