Free Steel Frame Analysis Calculator — 2nd Order

Q: What is the direct analysis method (DAM)?

The direct analysis method (AISC 360 Chapter C) accounts for second-order effects directly without separate K-factor calculations. It applies 0.8 EI reduction for residual stresses and notional loads of 0.002 times gravity load. DAM is the preferred method.

Q: When must P-Delta effects be considered?

AISC 360 requires P-Delta effects when the stability coefficient theta exceeds 0.10. Between 0.10 and 0.33, use B1/B2 amplification. Above 0.33, the frame must be stiffened. ASCE 7 limits theta to 0.5/(beta*Cd) for seismic.

Q: What is the B1 vs B2 moment amplification?

B1 amplifies moments from member curvature between braced points (P-delta). B2 amplifies moments from frame lateral translation (P-Delta). Total amplified moment Mu = B1*Mnt + B2*Mlt per AISC 360 Eq C2-1.

Q: Is this frame analysis calculator free?

Yes, completely free with unlimited calculations. No registration required.

Perform second-order analysis of steel frames using the direct analysis method (DAM). The calculator determines P-Delta effects, notional loads, stability coefficients, effective length factors (K), and moment amplification factors (B1 and B2) per AISC 360-22 Chapter C, AS 4100 Section 4, EN 1993-1-1 Section 5, and CSA S16 Section 8.

Frame types: unbraced (moment-resisting), braced (with lateral bracing), and partially-braced frames. Applicable to low-rise through high-rise steel building frames.

How to Use

Define frame geometry: number of stories, bay widths, story heights.
Enter member sections: columns and beams with section properties.
Apply gravity loads: dead, live, snow, and seismic mass.
Apply lateral loads: wind or seismic equivalent lateral forces.
Set analysis method: DAM (direct), ELM (effective length), or first-order.
Review stability checks: B1/B2 ratios, delta-s/delta-delta, K-factors.

Analysis Methods

Method	AISC 360	AS 4100	EN 1993-1-1	CSA S16
Direct Analysis (DAM)	C2 (0.8*EI reduction)	Cl 4.5.2	Cl 5.2.2	Cl 8.4.2
Effective Length (ELM)	C3	Cl 4.6	Cl 5.3	Cl 8.5
First-order analysis	C2.3 (limited)	Cl 4.5.3	Cl 5.2.1	Cl 8.4.3
Notional loads	C2.2 (0.002*Yi)	Cl 4.5.2	Cl 5.3.2	Cl 8.4.2

Step-by-Step Example

Problem: Check a 3-story moment frame for second-order effects. Story height = 12 ft, bay width = 30 ft. Gravity load at base = 2,000 kips, lateral load = 80 kips. First-order drift = 1.5 inches at roof.

Step 1 — Stability coefficient theta: theta = (P _ delta_s) / (H _ h) = (2000 _ 1.5) / (80 _ 144) = 3000 / 11520 = 0.26 Since theta = 0.26 > 0.10, P-Delta effects must be considered.

Step 2 — B2 factor (AISC 360-22 Eq C2-3): B2 = 1 / (1 - theta) = 1 / (1 - 0.26) = 1.35 Second-order displacement = 1.35 * 1.5 = 2.03 inches.

Step 3 — Stability check: thetamax = 0.5 / (beta * Cd) per ASCE 7. Assuming beta = 1.0, Cd = 4.5: thetamax = 0.5 / (1.0 * 4.5) = 0.111. theta = 0.26 > 0.111 — frame is too flexible. Increase member sizes.

Result: Frame requires stiffening. Consider increasing column sections or adding a braced bay.

Frequently Asked Questions

What is the direct analysis method (DAM) in AISC 360? The direct analysis method (AISC 360-22 Chapter C) accounts for second-order effects directly in the structural analysis without requiring separate K-factor calculations. It applies a 0.8 reduction to member flexural stiffness (EI) to account for residual stresses and geometric imperfections, plus notional lateral loads of 0.002 times the gravity load. DAM is the preferred method for steel frame design since it eliminates the need for K-factors.

When must P-Delta effects be considered in steel frame design? AISC 360-22 Section C2.1 requires P-Delta effects when the stability coefficient theta exceeds 0.10. For theta between 0.10 and 0.33, use B1/B2 moment amplification. For theta above 0.33, the frame is too flexible and must be stiffened (Section C2.1c). ASCE 7 Section 12.8.7 limits theta to 0.5/(beta*Cd) for seismic loading.

What is the B1 vs B2 moment amplification? B1 amplifies moments due to member curvature between braced points (P-delta effect within the member), while B2 amplifies moments due to frame lateral translation (P-Delta effect of the whole story). B1 applies to non-sway moments; B2 applies to sway moments. The total amplified moment Mu = B1Mnt + B2Mlt per AISC 360-22 Eq C2-1.

Is this frame analysis calculator free? Yes, completely free with unlimited calculations.

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice. All structural designs must be verified by a licensed Professional Engineer (PE) or Structural Engineer (SE). The site operator disclaims liability for any loss or damage arising from the use of this page.