WebStructural

Frame Designer

2D frames and trusses with steel or wood members: reactions, moment, shear, axial force and deflection, and a code check of every member.

Joints

Positions in feet; y is up. At a rigid joint the members carry moment from one to the next; at a pinned one each member's end turns freely.

Jointx (ft)y (ft)SupportConnection

Members

Steel or wood members, bending about the shape’s strong axis. Self-weight is included.

MemberStartEndShape typeShape

Joint loads

Forces in kips, + to the right and up. Moments in kip-ft, + counterclockwise.

JointLoad caseFx (k)Fy (k)M (k·ft)
Earthquake loads from the base shear

Works out the earthquake loads by the equivalent lateral force procedure (ASCE 7-22 section 12.8): the base shear V = CsW, with W the frame’s dead load and self-weight, split among its levels by weight and height. Put the dead load for the frame’s share of the building on it first.

Member loads

Kips per foot of member length, varying from the start joint to the end joint. Down is + downward, sideways is + to the right, and perpendicular is + toward the member’s right side going from its start to its end.

MemberLoad caseDirectionStart (k/ft)End (k/ft)

Design checks

Enter each load in its load case (dead, live, roof live, snow, wind or earthquake) and every member is checked under the ASCE 7-22 or 7-16 load combinations, with wind both as entered and reversed, and live load (L) on members also placed on alternate spans and on the spans either side of each joint. Or enter the loads already combined and they’re checked as entered. Steel is checked to AISC 360-22 and wood to NDS 2024.

Use the edition your snow load comes from: 7-22 maps snow at strength level, with lower factors on it.

The second-order analysis includes the extra moments from the loads acting on the frame as it sways (P-Δ), by the AISC direct analysis method: steel at 0.8 of its stiffness, a sideways notional load (N) of 0.3% of the gravity load at each joint, and, for ASD, 1.6 times the loads with the results divided by 1.6. Steel members then take K = 1. Its deflections are for checking strength; deflection limits are checked by a separate analysis under service loads.

Deflection is checked under unfactored loads, first-order and with steel at its full stiffness: live load (L with Lr or S, or 0.7S for ASCE 7-22 snow) against span/360, dead and live load together against span/240, and the sideways drift of columns under 0.6W against height/400. Loads entered already combined are checked as entered, against the total load limit. Leave a limit blank to skip it. Across each member, deflection is measured from the line through its ends; a cantilever’s is measured from its supported end, against twice its length.

Grade sets the steel’s yield strength, or the wood’s species and grade. K is the effective length factor for buckling in the plane of the frame. Brace spacing is the distance between braces against buckling out of the plane and against lateral-torsional buckling: leave it blank when the member is braced only at its ends, or enter 0 when it’s braced all along, by roof or floor sheathing, say. Tick Overstrength for a member ASCE 7-22 requires to be designed for the earthquake load with overstrength, such as a column or beam under a discontinued wall or frame (section 12.3.3.3) or a collector (section 12.10.2.1); it’s also checked with Ω0QE in place of ρQE.

MemberSizeGradeKBrace spacing (ft)Overstrength

How the Frame Designer Works

The frame designer analyzes a two-dimensional frame or truss made of steel or wood members: W shapes, Hollow Structural Sections (HSS), pipes and channels from the AISC shape tables, and sawn lumber, glulam, laminated veneer lumber (LVL) and parallel strand lumber (PSL). Draw the frame by entering joints and the members between them, set the supports, add loads, and it reports the support reactions and the bending moment, shear, axial force and deflection along every member, and checks each member against the steel or wood design code. The drawing updates as you type.

Method and assumptions

  • A linear elastic stiffness (matrix) analysis, solved with the Frame3DD finite element program.
  • Joints between members are rigid unless you set them to pinned. At a rigid joint the members carry moment from one to the next; at a pinned joint each member's end turns freely and carries no moment.
  • Steel with E = 29,000 ksi, and wood with its grade's E. Each member's self-weight comes from the shape's weight per foot (36 lb/ft³ for sawn lumber and glulam, 42 for LVL and 45 for PSL) and is included.
  • A second-order analysis by default: the frame is solved in balance in its deflected shape, so the extra moments from vertical load acting on a frame that sways (P-Δ effects) are included. It follows the AISC 360-22 direct analysis method: steel at 0.8 of its stiffness, a small sideways notional load of 0.3% of the gravity load at each joint, and for allowable stress design 1.6 times the loads with the results divided by 1.6. Steel members then use K = 1. A first-order analysis is there too, for comparison or for frames checked another way.
  • If the loads are past what the frame can carry before it buckles sideways, the second-order analysis says so.
  • Units are feet and kips.

Supports and loads

  • Supports: fixed (holds both directions and rotation), pinned (holds both directions), or a roller that holds one direction. The designer tells you if the supports can't hold the frame still.
  • Connections: rigid, or pinned for a hinge where the members' ends turn freely, like a bolted truss joint or a beam hung from a cantilever. Too many pins make a frame that folds up, and the designer says so.
  • Joint loads: forces in x and y and a moment at a joint.
  • Member loads: uniform or linearly varying loads per foot of member length, acting down, sideways, or perpendicular to the member.
  • Load cases: each load is dead (D), live (L), roof live (Lr), snow (S) or wind (W). The member's self-weight is dead load.

Design checks

  • Load combinations: the frame is analyzed under each ASCE 7-22 combination of the load cases it has, for allowable stress design (ASD, section 2.4.1) or load and resistance factor design (LRFD, section 2.3.1), and each member is checked under the combination that's worst for it. Wind is checked as entered and reversed (−W). In the LRFD combinations with wind, earthquake or roof load, live load takes a factor of 1.0, or 0.5 if you choose it: ASCE 7-22 allows 0.5 (sections 2.3.1 and 2.3.6) where the live load is 100 psf or less, except garages and places of public assembly.
  • Earthquake: enter the horizontal seismic forces (QE) as loads in the earthquake case, with SDS, the design spectral acceleration at short periods, and the redundancy factor ρ. They're combined by ASCE 7-22 sections 2.3.6 and 2.4.5, with Eh = ρQE and the vertical seismic load Ev = 0.2SDSD (section 12.4.2.2) added to the factor on dead load, so 1.2D + Ev + Eh + L + 0.15S shows as 1.4D + 1.3E + L + 0.15S for SDS = 1 and ρ = 1.3. Earthquake is checked both ways, like wind.
  • Earthquake loads from the base shear (ASCE 7-22 section 12.8): under Joint loads, enter SDS, SD1, R and the kind of structure, and the base shear V = CsW is worked out with W the frame's dead load and self-weight. Cs = SDS/(R/Ie), no more than SD1/(TR/Ie) and no less than 0.044SDSIe or 0.01, or 0.5S1/(R/Ie) where S1 is 0.6 or more, with T the approximate period Cthnx (Table 12.8-2). V is split among the levels by weight times height to the power k (section 12.8.3), and each level's force among its joints by their weight. The forces replace the earthquake joint loads when you choose to use them. Put any storage live load, partitions or heavy snow that count toward W (section 12.7.2) in the dead load; periods over TL aren't covered.
  • Overstrength (ASCE 7-22 section 12.4.3): members marked for it, such as columns and beams under a discontinued wall or frame and collectors, are also checked under the same earthquake combinations with Emh = Ω0QE in place of ρQE. They show in the list of combinations, such as “1.4D + 2.5E + L + 0.15S (overstrength)”. Enter Ω0 from Table 12.2-1. Emh isn’t limited to the capacity-limited load (section 12.4.3.1), so the check is on the safe side; drift and deflection don’t use it.
  • Earthquake drift (ASCE 7-22 sections 12.8.6 and 12.12.1): each column's drift under the earthquake forces alone (ρ = 1), times Cd/Ie, against the allowed story drift from Table 12.12-1, such as 0.020 times the story height for Risk Category I or II. For moment frames in Seismic Design Category D to F, the allowed drift is divided by ρ (section 12.12.1.1): choose the smaller limit. Drift is measured at each column, so enter each story's columns as separate members.
  • Earthquake stability (ASCE 7-22 section 12.8.7): each story's stability coefficient θ = Pxδ/(Vxh), with Px the gravity load above the story's mid-height (D + L + 0.15S, no factor over 1.0), Vx the earthquake forces above it, δ its drift under them and h its height. A story is the columns with the same bottom and top. Up to 0.10 nothing more is needed; up to θmax = 0.5/Cd (at most 0.25, with β = 1) the story's earthquake drift is increased by 1/(1 − θ) and the frame needs the second-order analysis for its member forces; past θmax it's unstable.
  • Pattern live load (ASCE 7-22 section 4.3.3): live load (L) on members is also placed on some members and not others in the combination where it's the main load (D + L for ASD, 1.2D + 1.6L for LRFD): on alternate spans, for the largest moments within them, and on the two spans either side of each joint, for the largest moments over it. Each pattern shows in the list of combinations, such as “D + L (L on 1 and 3)”. Live load on joints stays on in every pattern, and roof live load and snow aren’t patterned.
  • To check one combination of your own, choose loads that are already combined and enter them with their factors. With LRFD the self-weight is then factored by 1.2.
  • Steel, to AISC 360-22: compression (chapter E), bending (chapter F, with Cb = 1), shear (chapter G), and axial force with bending (equation H1-1). Moments are amplified for the member's own deflection (B1). Channels aren't checked.
  • Wood, to NDS 2024: compression with the column stability factor, bending with the beam stability factor (and glulam's volume factor), shear, tension, and axial force with bending (section 3.9). Members are checked dry, without the repetitive member factor, and with the load duration factor (ASD) or time effect factor (LRFD) that goes with each combination: for ASD the one for the shortest load in it, from 0.9 for dead load alone to 1.6 with wind.
  • Each member buckles over K times its length in the plane of the frame, and between its braces out of the plane. Leave the brace spacing blank for a member braced only at its ends, or enter 0 for one braced all along by sheathing or a deck.
  • Each check is a ratio of the force to the member's strength, taken at the worst place along it; 1.00 or less works.
  • Deflection: a separate first-order analysis under unfactored loads, with steel at its full stiffness, checks each member's deflection under live load (span/360; ASCE 7-22 snow at 0.7 times, as the 2024 International Building Code allows) and dead plus live load (span/240), and the drift of each column under 0.6 times the wind (height/400), the limits in the International Building Code's Table 1604.3 for floors. Each limit can be changed, or left blank to skip it. Deflection is measured from the line through the member's ends, and a cantilever's from its supported end against twice its length.

Checking a model by hand

Start with something you can check. A 20 ft W14x22 beam, pinned at one end and on a roller at the other, under 1 kip/ft:

  • Each reaction is wL/2 = 1 × 20 / 2 = 10 kips.
  • The largest moment, at midspan, is wL²/8 = 1 × 20² / 8 = 50 kip-ft.
  • Midspan deflection is 5wL⁴/(384EI) = 5 × (1/12 kip/in) × (240 in)⁴ / (384 × 29,000 ksi × 199 in⁴) = 0.62 in, about span/385.

The designer's numbers come out about 2% higher, because the beam's own weight (22 lb/ft) is added to the 1 kip/ft.

Examples to start from

  • Portal frame: two W10x33 columns fixed at the base and a W16x31 beam spanning 30 ft, with dead and live load on the beam and wind at the top.
  • Gable frame: a pinned-base frame with sloped W14x30 rafters, under dead load, snow and wind on one side.
  • King post truss: a 24 ft HSS truss with pinned joints and dead and snow loads at the peak.
  • Wood king post truss: a 24 ft roof truss of Douglas Fir-Larch No.2 lumber with pinned joints, under snow and ceiling loads, braced by the sheathing and ceiling.
  • Pratt, Howe and Warren trusses: the same 36 ft, 6 ft deep steel truss of HSS members with pinned joints, laid out three ways, under 2 kips dead and 4 kips live load at each bottom panel point. The tutorials work each one by hand: Pratt, Howe and Warren.
  • Two-span beam: a continuous W14x22 over three supports, with uniform and varying dead and live loads.
  • Two-story moment frame (earthquake): a steel special moment frame 30 ft wide with W14x68 columns and stories of 14 and 12 ft, under dead, live and snow load and earthquake forces of 8 and 12 kips at the floor and roof (SDS = 1.0, Cd = 5.5, Ω0 = 3). Its columns are checked with overstrength, which governs them, along with earthquake drift and each story's stability.

What it doesn't do

  • It doesn't have rain or other load cases, unbalanced snow, or the earthquake combinations with overstrength (Ω0). For those, enter the loads already combined, one combination at a time.
  • It checks earthquake drift from a first-order analysis, without the stability coefficient check of ASCE 7-22 section 12.8.7.
  • It doesn't model a member bending between its ends in the second-order analysis (P-δ); the steel checks amplify each member's moments for that instead (B1). The column designer checks one column in more detail.
  • It doesn't check connections, add long-term creep to wood deflection, release moment at one end of a member only (a pinned joint releases every member there), or model concrete members.

The results are a design aid. Have a licensed engineer check a design before it's built.

Frequently asked questions

Is the frame designer free?

Yes, the analysis and the member checks are free without an account. Pro adds saved frames and PDF reports.

Can it analyze a truss?

Yes. Model each truss member between joints. Joints start rigid, so the members carry small bending moments as well as axial force, which is closer to how a welded or gusseted truss behaves. Set the joints to pinned for the textbook truss, where loads at the joints give axial force alone. The Pratt, Howe and Warren examples are set up that way, and the Pratt truss tutorial checks them by hand.

How do I find the moment in a portal frame?

Load the portal frame example, change the column and beam sizes, height, span and loads to match yours, and read the moment diagram. Fixed bases attract moment at the base; pinned bases put it all at the beam-to-column corners.