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# ACI 318-05 Section 8.3.3 factors

## ACI 318-05 Section 8.3.3 factors

(OP)
Regarding the approximate factors used to calculate moments and shear listed in ACI 318 Section 8.3.3 (2005 Ed. is in effect for this question)

Two factors are listed for positive moment of an end span.  One for "Discontinuous end unrestrained" and another for "Discontinuous end integral with support"

What is the difference between "unrestrained" & "integral with support"?  (the answer key for the NCEES Structural sample exam indicates that 1/11 factor is used for a beam at an exterior column...wouldn't this be integral with the support?)

Thank you.

### RE: ACI 318-05 Section 8.3.3 factors

MrStohler,
I have been researching this as well, probably for the same reason.  I disagree with the NCEES Structural Sample Exam answer key.  This beam IS restrained by the exterior column to which it is framed.
I have searched for an official definition of restrained vs. unrestrained but haven't found one.
My interpretation of restrained vs. unrestrained is as follows:
-Restrained ends are physically connected to supports that provide rotational restraint.
- Unrestrained ends are resting on a support or connected to a flexible member that does not have the stiffness to develop negative moments in the supported (or connected) member at this joint.

The level of restraint at a joint varies according to the rotational or torsional stiffness of the support.  For example, the table in ACI 318-05 Section 8.3.3 indicates that the negative moment at the interior face of an exterior support requires different factors for a spandrel beam or a column for the purposes of determining the negative moment.  The factor is 1/24 for spandrel beams and 1/16 for columns.  Note also that this same section indicates that these are "members built integrally with the supports", further justifying our conclusions that this beam should be considered integral with the support and the positive moment factor should be 1/14 not 1/11.

Hope the discussion helps.  For reference, I looked on the NCEES website for an eratta for this problem.  None exists, but I'm going to contact NCEES and discuss this with them.

### RE: ACI 318-05 Section 8.3.3 factors

I think I would consider relative stiffness.  If the horizontal element is relatively stiffer than the supporting element, I would design using the unrestrained condition.

If a beam is built integrally with a column as part of a moment-resisting frame, and connected in a manner intended to transfer moment between beam and column, it is restrained.

### RE: ACI 318-05 Section 8.3.3 factors

MrStohler> Ref: Simplified Design of Reinforced Concrete Buildings of moderate size and height - Engineering Bulletin 104 published by PCA.
For positive moments:
Discontinuous end unrestrained - The sketch shows member bearing on a wall with a clear separation shown between the supported member and the supporting member to illustrate simple support.
Discontinuous end integral with support - The sketch shows member continuous with the support.

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