ACI 318-19: Moment Magnification - Sway Frames (Cl. 6.6.4.6)

About this ACI 318-19: Moment Magnification - Sway Frames (Cl. 6.6.4.6) Calculator

This calculator applies the moment magnification method for sway frames per ACI 318-19 Cl. 6.6.4.6. It computes the sway magnifier δs using one of three code-permitted approaches — the Q method, the sum of P concept, or second-order elastic analysis — then combines it with the nonsway and sway moment components to produce magnified end moments M₁ and M₂.

• Structural engineer — apply the moment magnification method to sway-frame columns during design, select the appropriate δs method, and confirm magnified end moments without manual iteration.
• RC detailing engineer — verify that the Q method restriction is satisfied before finalising column reinforcement, and switch to the sum of P concept where δs exceeds the code limit.
• Checking engineer — audit the sway magnifier calculation and traced end moment outputs against ACI 318-19 equations in a single structured page.

This is an engineering-grade calculator built on CalcTree, covering all three code-permitted methods for δs with a built-in code compliance check for the Q method restriction.

More info on ACI 318-19: Moment Magnification - Sway Frames (Cl. 6.6.4.6)

Inputs

The calculator takes two categories of input. The first is the end moment decomposition: each column end requires a nonsway moment component and a sway moment component, entered separately for end 1 and end 2. This separation is fundamental to the method, as ACI 318-19 magnifies only the sway portion of the moment.

The second category depends on the chosen method for computing δs. For the Q method, the story stability index Q is required. For the sum of P concept, the sum of factored vertical loads in the story and the sum of critical buckling loads for all sway-resisting columns in the story are entered. If second-order elastic analysis has already been performed, the resulting magnifier is entered directly and used without further modification beyond enforcing the minimum value of 1.0.

Methods for Computing the Sway Magnifier

ACI 318-19 Cl. 6.6.4.6.2 permits three methods for determining δs, and this calculator supports all three via a selector input. The Q method uses the story stability index to compute δs from Eq. (6.6.4.6.2a). The sum of P concept uses the ratio of total factored vertical load to total critical buckling load, scaled by 0.75, per Eq. (6.6.4.6.2b). The third option accepts a δs value obtained directly from a second-order elastic analysis per Cl. 6.6.4.6.2(c). In all cases, δs is enforced to be no less than 1.0.

Magnified End Moments

Once δs is determined, the calculator applies ACI 318-19 Eqs. (6.6.4.6.1a) and (6.6.4.6.1b) to compute the magnified end moments. M₁ is the sum of the nonsway moment at end 1 and δs multiplied by the sway moment at end 1. M₂ follows the same form at end 2. These magnified moments are the values to be used in the design of the column cross-section.

Design Checks

The calculator enforces the code restriction in Cl. 6.6.4.6.2: if δs exceeds 1.5 and the Q method has been selected, the check flags a failure. This is because the Q method is only permitted by ACI 318-19 when δs is at or below 1.5. When this limit is exceeded, the code requires the use of the sum of P concept or second-order elastic analysis instead. The check result is displayed as a traffic light in the summary, providing an immediate and unambiguous status for the selected method.

Common Calculation Errors to Avoid

• Failing to decompose moments into sway and nonsway components — the method requires each end moment to be split into its sway and nonsway parts before magnification; applying δs to the total moment overstates the amplification.
• Using the Q method when δs exceeds 1.5 — ACI 318-19 Cl. 6.6.4.6.2 prohibits this; switch to the sum of P concept or second-order elastic analysis when the magnifier is large.
• Confusing the story-level sums with individual column values — ΣPu and ΣPc in Eq. (6.6.4.6.2b) are summed across all columns in the story, not taken for a single column.
• Omitting the 0.75 factor on ΣPc — ACI 318-19 explicitly includes the 0.75 stiffness reduction in the denominator of the sum of P formula; leaving it out unconservatively reduces the computed δs.
• Accepting a δs below 1.0 — the code requires δs to be no less than 1.0; raw formula results can fall below this when loads are very low, and the minimum must be enforced.
• Applying a single δs from one story to the whole structure — δs is story-specific; columns in different stories may have different stability indices and critical load sums and must be evaluated separately.

FAQs

What is the moment magnification method for sway frames, and why does it exist?

Second-order effects in laterally flexible (sway) frames cause column moments to exceed first-order predictions. Rather than requiring a full geometric nonlinear analysis every time, ACI 318-19 Cl. 6.6.4.6 provides the moment magnification method as an approved simplified approach. A sway magnifier δs is computed from story-level stability data and applied directly to the sway moment components, giving magnified end moments M1 and M2 that account for P-delta effects at the story level.

What are the three methods for computing δs, and when should I use each?

ACI 318-19 Cl. 6.6.4.6.2 permits three approaches. The Q method (Eq. 6.6.4.6.2a) uses the story stability index Q and is the quickest to apply, but is restricted to cases where δs ≤ 1.5. The sum of Pu/Pc method (Eq. 6.6.4.6.2b) uses story-level factored loads and critical buckling loads and is required when δs > 1.5. Second-order elastic analysis (Cl. 6.6.4.6.2c) takes δs directly from software output and is appropriate when a full second-order model is already available. Use the Q method for quick checks on stable frames, and switch to the sum of P or second-order method for slender or heavily loaded stories.

Why is the Q method not permitted when δs exceeds 1.5?

At higher magnification levels, the Q method linearization becomes insufficiently accurate. ACI 318-19 Cl. 6.6.4.6.2 explicitly restricts the Q method to δs ≤ 1.5; beyond that threshold, the code requires the sum of Pu/Pc method or second-order elastic analysis, both of which capture the nonlinear amplification more reliably. The template flags this automatically with a pass/fail check in the results summary.

How do I separate the sway and nonsway moment components for each column end?

Run two first-order load cases: one with gravity loads only (no lateral), and one with lateral loads only. The nonsway components M1,ns and M2,ns come from the gravity-only case; the sway components M1,s and M2,s come from the lateral-only case. These are superimposed by the magnification equations, with δs applied only to the sway components. If your analysis combines both effects in a single run, you need to disaggregate them before entering inputs here.

What inputs are needed if I switch to the sum of P method in this template?

Select "Sum of Pu/Pc (Eq. 6.6.4.6.2b)" from the method dropdown. Then enter ΣPu, the total factored vertical load on all columns in the story, and ΣPc, the sum of critical buckling loads for all sway-resisting columns in that story. The 0.75 factor in the denominator is built into the equation per ACI 318-19 and does not need to be manually applied.

What happens if δs comes out less than 1.0?

Both methods enforce a lower bound of δs ≥ 1.0 per ACI 318-19, meaning sway effects cannot reduce design moments below first-order values. The template applies this minimum automatically regardless of which method is selected, so if your raw computed value is below 1.0, the template clips it to 1.0 before applying it to M1 and M2.