ACI 318-19

ACI 318-19 Section 6.5 | Approximate Moment & Shear Coefficients

For regular continuous beams and one-way slabs where adjacent spans do not differ by more than 20% and live load does not exceed 3 times dead load, ACI 318-19 Section 6.5 permits engineers to use envelope moment coefficients (wu ln² / C) that automatically account for pattern live load placement.

Code Equation

Governing Formula

M_u = \frac{w_u \ell_n^2}{C_m}, \qquad V_u = 1.15 \frac{w_u \ell_n}{2} \; (\text{ first interior support })

Standard: ACI 318-19Dual US Customary & SI Metric

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Notation & Variables

w_u

Factored distributed line load per unit length

kip/ft or kN/m

\ell_n

Clear span for positive moment; average of adjacent clear spans for negative moment

ft or m

C_m

ACI Table 6.5.2 denominator (14 or 16 for positive; 9, 10, 11, 16, or 24 for negative)

unitless

Worked Example

Verify applicability limits

Check that spans are roughly equal (longer ≤ 1.20 × shorter) and L ≤ 3D.

Evaluate end span positive moment

For an end span discontinuous at an integral beam support, Cm = 14: Mu+ = wu ln² / 14.

Evaluate first interior negative moment

For more than two spans, Cm = 10 at the first interior support: Mu- = wu ln,avg² / 10.

Governing Criteria

When does this govern?

Provides fast, conservative design envelopes for multi-span floor beams, joists, and one-way slabs.

Common Pitfall

Common Mistake

Forgetting the 1.15 continuity multiplier on shear at the exterior face of the first interior support.

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