Unbraced Length in RAM SBeam

Unless specified otherwise by the user, the program determines unbraced lengths and sizes the members accordingly. The user may specify a number of parameters related to unbraced length considerations. These criteria are found in the **Design Defaults** tab of the **Criteria - Design **command. The user may suppress entirely the checking of unbraced length by de-selecting the **Check Unbraced Length **option. In this case, all beams are designed as if the compression flange is continuously braced for the full length of the beam. This speeds up the design process but may result in unconservative results, and is not generally recommended.

The user may indicate whether or not the deck braces the top flange for non-composite and precomposite design. For non-composite beams this is specified in the **Beam - Span Definition **command; for precomposite beams this is done on the **Design Defaults** tab of the **Criteria - Design** command. The effect of deck oriented parallel to the beam may be specified independently of that of deck oriented perpendicular to the beam. See Section
4.3.2 for a discussion of perpendicular versus parallel deck. For composite beams the deck is always assumed to brace the top (compression) flange in the positive moment region, except in the precomposite state the flange bracing is based on the parameters specified by the user. The program assumes that the deck does not brace the compression flange of cantilevers and beams in the negative moment region.

For cantilevers, the program assumes that the ends are fully braced against twist.

One of the criteria available is an option to **Consider Point of Inflection**. Selecting this option does not mean that the point of inflection will necessarily be considered a brace point; rather, it affects the way the program looks at brace points of the flanges on either side of the point of inflection when determining the unbraced length. This is further explained below.

In the program, one flange brace point list is created for the top flange and another is created for the bottom flange. These brace points are determined in the following way:

- Beams are assumed to be braced at supports on both the top and the bottom flange.
- Cantilever ends are assumed to be braced on both the top and the bottom flange.
- User-assigned brace points, specified by the user with the
**Layout - Beams - Brace Points**command, brace the specified flange. - For composite beams in the composite state, the deck is assumed to brace the top flange in the positive moment region.
- For the precomposite state of composite beams the deck is assumed to brace the top flange according to the criteria specified for Unbraced Length in
**Design Defaults**tab of the**Criteria - Design**command. The user may indicate whether or not the deck braces the top flange when the deck is oriented parallel to the beam and when it is oriented perpendicular (or at an angle) to the beam. - For non-composite beams the top flange is braced or not according to the option specified in the
**Beam - Span Definition**command.

When determining the moment capacity associated with a moment at a given point, if the moment causes compression in the top flange and the top flange is braced by the deck, the unbraced length is set to 0.0.

Note that the calculation of the unbraced length is affected by whether or not the **Consider Point of Inflection** option is selected. If the option is not selected, the unbraced segment length is the distance between physical brace points along the flange under consideration. For example, in Figure 4 2 below, **L _{u2}** would be the unbraced length for the Moment at the left support. This would be used even though the bottom flange is only in compression between the left support and the point of inflection; it is in tension from the point of inflection to the right support.

**L**is the distance between bottom flange physical bracing, which in this example is the entire beam span. This is consistent with the recent work by Joseph A. Yura of the University of Texas, Austin.

_{u2}If the

**Consider Point of Inflection**option is selected, the unbraced length is the distance between points where the compression flange (whichever flange is in compression at any particular point) is braced, not the distance along a given flange where that flange is braced. For example, in Figure 4 2 below,

**L**would be the unbraced length for the Moment at the left support because at the left support the bottom flange is in compression but at the point of inflection the top flange becomes the compression flange, and that flange is braced at the second top flange brace point.

_{u1}**L**is the distance between compression flange bracing. This is consistent with what has been long-standing practice; see, for example, the publication "Cantilever Roof Framing Using Rolled Beams" published by AISC.

_{u1}
Points of inflection are not of themselves considered brace points. However, if the top flange is specified as continuously braced, the point at which the continuous bracing of the compression flange begins or ends coincides with the point of inflection. In Figure 4 2, if the top flange is continuously braced and the **Consider Point of Inflection** option is *not *selected, the unbraced length would still be **L _{u2}**

_{ }as shown. However, if the top flange is continuously braced and the

**Consider Point of Inflection**option is selected, the unbraced length would be the distance between the left support and the point of inflection (not

**L**). Thus, although the point of inflection appears to be acting as a brace point in that case, it is actually the continuous bracing that is acting as the brace ‘point'.

_{u1}

**Figure 4-2: Points of inflection.**

Based on these criteria and the geometry of the model, the program automatically determines the braced condition for each member.

Unbraced length is taken as the distance between brace points. At supporting columns, it is taken to column centerline, not column face.

The program checks each unbraced segment to determine the controlling condition of moment and unbraced length, and selects the beam size accordingly.

## ASD and LRFD

When calculating the allowable stress (ASD) or moment capacity (LRFD) of an unbraced segment, the program calculates Cb based on the end moments of the segment. Although not required by Code the user may conservatively specify that Cb be set equal to 1.0 for all simple span non-composite beams. The user may also specify that Cb be set equal to

1.0 for all cantilevers, as recommended by the Codes and other sources. Otherwise, the program will calculate and use the values of Cb as allowed by the appropriate Code.

The output shows the values of stress/capacity, unbraced length, and Cb at the points of maximum and minimum moments as well as the controlling condition. Note that the controlling condition may not correspond to any of the maximum or minimum moment conditions; this indicates that the controlling condition occurs in a segment with a lesser moment but greater unbraced length

## CAN/CSA-S16-01

The effective length of a beam can be controlled by setting the criteria from the **Design Defaults** tab of the **Criteria - Design** command. The specifications of CAN/CSA-S16-01 have been implemented with the following modifications according to the Structural Stability Research Council (SSRC), "Guide to stability Design Criteria for Metal Structures", Galambos, 1998.

For cantilever beams the effective length is taken as 1.5 times the unbraced length. This assumes the cantilever tip is restrained against torsion. Omega 2 (w2) is taken as 1.0 for cantilevers.

## BS 5950

The effective length of a beam can be controlled by setting the criteria from the **Design Defaults** tab of the **Criteria - Design** command. The effective length (Le) of the unbraced segment depends on the end conditions of the segment. The following assumptions are made by the program unless overridden in the **Design Defaults** tab of the **Criteria - Design** command. Loads are assumed to be normal loads (applied at the shear center). For a segment continuous through brace points, Le is equal to the unbraced length. Where a beam is continuous through a column or supporting girder an effective length factor of 0.7 is assigned to that end of the segment. This is indicative of the column providing the beam a measure of restraint for bending about the minor axis. Where a beam is pinned at a support, or where a cantilever tip occurs, the effective length factor is taken as the value provided by the engineer in the **Design Defaults** tab of the **Criteria - Design** command. The effective length factor for an entire segment is taken as the average of the factors at the segment ends.

## Eurocode

Within each unbraced segment the points of maximum moment and shear and the segment end points are all checked against the segment capacity.

When calculating the member capacity for an unbraced segment the lateral torsional buckling must be considered. In these cases it is necessary to calculate the elastic critical moment (Mcr). The program calculates the elastic critical moment using the procedures outlined in Annex F (Specifically Equation F2) of the Eurocode specification. The program assumes that the factors k and kw are equal to 1.0. The following procedures are implemented to calculate the C factors, depending on the beam major axis loading in the segment being checked:

End Moments Only:

C1 = 1.88 - 1.40ψ + 0.52ψ

^{2}< 2.70 (Eq F.3)

C2 = 0.0

C3 = 0.5(1.0 + ψ)C1

Uniform Load Only: Based on the procedure detailed in the French Journal, Rubrique du Praticien, "Abaques De Deversement Pour Profiles Lamines", Construction Metallique no 1 - Mars 1981.

C1 = C

_{1}^{0}|Mmax/M|

C2 = 4/π^{2}*|μ|*C_{1}^{0}

C3 = 0.525 if ends pinned, 0.753 if ends fixed, 0.64 for one end pinned, other fixed.

*where:*

γ = 4μ + β - 1

f = Uniform Load,

M = Maximum End Moment.

L = Member Length.

Uniform loading, with negative end moments and a positive moment within the span of the beam: Per Table F.1.2 of ENV 1993-1-1:1992 (for k=1.0).

C1 = 1.285

C2 = 1.562

C3 = 0.753.

General Loading Pinned Ends - C1 is an adaptation of the British Code equation for the moment modification factor α_{m}.

C1 =

C2 = 4/π^{2}*C1

C3 = 1.0

*where:
*

Mmax is maximum moment in the span.

M_{2}, M_{4}are quarter point moments.

M_{3}is mid span moment.

General Loading Fixed Ends: No generic formula could be determined which would adequately handle all cases of loading.

C1 = 1.0

C2 = 1.0

C3 = 1.0

Note that C values for cantilevers are calculated as for all other members as the program assumes the ends of a cantilever to be laterally braced.

The output shows the values of: class, the design shear and moments at the indicated beam location, the segment unbraced length (Lb), the type of moment that controls the member capacity (Mb = buckling, Mc = plastic capacity, Mv = is shear reduced capacity) and the member capacity. Note that the controlling condition may not correspond to any of the maximum or minimum moment conditions; this indicates that the controlling condition occurs in a segment with a lesser moment but greater unbraced length.

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