The Cheapest Member on the Schedule, and Three Sheets of Details
A braced bay is almost free in tonnage and expensive in drawing time. The diagonal is usually the smallest thing on the material list — a 25 mm rod, a pair of 90 mm angles, a modest square hollow section — while the plate it dies into, the bolt pattern through that plate, the clearance around the beam flange, the pin at the clevis and the note telling the erector not to release it until the deck is welded down will run across several sheets and generate most of the connection RFIs on the job. That imbalance is the subject of this page. Sizing the member takes a few minutes. Landing it takes the rest of the week.
Two questions do most of the work. The first is geometric and gets asked long before analysis is finished: how long is the diagonal, and what does it weigh, because a rod that arrives 40 mm short of its clevis is a crane day nobody planned for and a bay left unbraced overnight. The second is the one an engineer loses sleep over: with a story shear of whatever it is, does the rod give way first, or does a chunk of the gusset tear out around the bolt group and leave the diagonal hanging with a piece of plate still bolted to it.
The order below follows those two questions and what sits between them. Bay geometry first, because the angle sets every force downstream of it. Then what kind of diagonal you are allowed to use, then what the diagonal is actually worth, then the four separate ways a gusset refuses. Then where the force was assumed to arrive, the clearance a seismic brace needs to fold, and the short list of things that get quietly changed after the steel is standing.
What lands at the corner of a braced bay
- Diagonal rod — priced and shipped by its own length, which is the hypotenuse of the bay rather than either dimension anybody quoted Steel Bracing Rod Diagonal Length & Weight Calculator
- Clevis and pin — the fitting that turns an axial rod into a hinge, and the reason the rod is ordered to a pin-to-pin dimension and not a member length
- Gusset plate — the element with four separate failure lines through it, any one of which can arrive before the diagonal has reached its own capacity Steel Plate Block Shear and Net Section Calculator
- Bolt group — checked for shear, bearing and tearout at each hole, on limit states entirely separate from the ones running through the plate body Bolt Group Shear, Bearing and Tearout Calculator
- Beam and column steel — carries the horizontal and vertical components of the brace force away as axial load in members drawn for bending Structural Steel Tonnage Aggregator
Angle Is the Only Free Variable You Have
The bay's proportions are fixed by the architecture before anyone asks. Column grid gives the width, floor-to-floor gives the height, and the brace has to fit between them. What that geometry decides, and what a lot of otherwise careful sizing overlooks, is how much bigger the brace force is than the shear it resists. The horizontal component of the diagonal force is what the floor hands over; the diagonal itself carries that divided by the cosine of its angle to horizontal. Nothing else in the frame amplifies a load simply for being at an angle.
Numbers make the point faster than the ratio does. Put a brace across a bay 7.5 m wide and 4.5 m high and the diagonal is 8.75 m long, its cosine is 0.858, and the brace carries 1.17 times the story shear. Squeeze the same brace into a 3 m wide bay at the same 4.5 m height — because a stair got wider, or a duct riser claimed the middle bay — and the diagonal is 5.41 m, the cosine drops to 0.555, and the brace now carries 1.80 times the shear. The story force has not moved. The member, the bolt count, the plate thickness and the anchor rods below all have to grow by half again because a bay got narrower.
The same right triangle also gives you the two numbers procurement wants. Diagonal length is what a rod is cut to and what a hollow section is ordered at, and it is neither of the dimensions on the framing plan; the length times the section's linear weight is what the piece weighs, which decides whether a bay's worth of bracing goes up by hand, on a telehandler, or on the crane that is already booked for something else. Round bar is easy arithmetic once you have the diameter — a 25 mm rod runs about 3.85 kg/m at 7,850 kg/m³, a 30 mm rod about 5.55 kg/m — but for angles, channels and hollow sections take the linear weight from the section tables rather than deriving it, because the corner radii and the wall tolerances make a real difference over an eight metre piece.
One caution on the length. A rod system is ordered pin to pin, not member end to member end, so the fabricated bar is shorter than the geometric diagonal by whatever the clevis, the pin centre and the turnbuckle body consume at each end. Those allowances come from the supplier's system literature — Macalloy tension bar systems and the Halfen/Leviat Detan range both publish them as assembly dimensions — and they are why the geometric diagonal is a check dimension for the drawing rather than a cutting list.
The bay dimensions are on the plan and the diagonal is not, so this is the number that has to be worked out before a rod is ordered or a lift is planned — length from the two bay dimensions, weight from the section's own linear rate.
The horizontal distance across the braced bay.
The vertical distance across the braced bay.
The linear weight of the rod or cable, from its diameter/section table.
Bracing rod weight
60.63 lb
- Diagonal length
- 23.44 ft
They open the calculator with your figures already in it
Steel Bracing Rod Diagonal Length & Weight Calculator: 60.63 lb — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
Estimated cost — your price
This site holds no price list for this material — local prices vary too much to publish honestly. Enter your supplier's price and the result is costed with it.
What this calculation does not cover
- The diagonal is measured corner to corner of the bay, which is the work line and not a cut length. A rod brace is an assembly — threaded ends, a turnbuckle or coupler, clevises or pins — and that hardware commonly takes 300 to 600 mm (24 in) out of the run, so the rod ordered is shorter than the figure here while the installed assembly is exactly this long. Cut the rod to the diagonal and there is no thread left to tension it.
- One rod is counted. Rods and cables carry tension only and go slack the instant the load reverses, so a braced bay is normally cross-braced with a pair working in opposite directions, and a frame braced in two directions doubles again. Take this weight straight into a bill of materials and the brace steel comes in at half.
Something That Pulls, Something That Pushes, and What the Code Lets You Choose
A diagonal that can only pull is a different structure from one that can also push. Rods and cables buckle at any load at all, so they only work in crossed pairs: one leg of the X takes the whole story shear in tension while the other goes slack and does nothing, and the pair swaps roles when the wind comes from the other side. Every force in the bay is therefore sized on one leg alone, and the slack leg is not a reserve. Angles, channels and hollow sections can take compression, so a single diagonal can serve both directions — at the price of a compression capacity that depends on unbraced length and on the connection at each end being able to develop it.
AISC 360, Specification for Structural Steel Buildings, keeps a slenderness advisory for members designed on the basis of tension and explicitly exempts rods and hangers from it, which is the code's way of saying a rod is expected to be slender and that its sag is a serviceability matter rather than a strength one. Sag is still a matter. A long horizontal-ish rod hangs visibly, rattles in wind, and a bay full of rods that were never drawn up will pick up load later than the frame expects, so pretension is installed through the turnbuckle to take the slack out. How much is a system question, not a code question: the tension rod suppliers publish installation forces and turnbuckle rotations for their own bars, and inventing a figure for somebody else's hardware is exactly the way to yield a rod during erection.
Where seismic provisions apply, the choice narrows sharply. AISC 341, Seismic Provisions for Structural Steel Buildings, imposes width-to-thickness, slenderness and connection requirements on the braces of concentrically braced frames, and tension-only rod bracing does not meet the requirements for a special concentrically braced frame — the system is expected to yield and buckle its braces repeatedly and to detail the connections for that behaviour. Whether a bay is being detailed as part of a seismic force-resisting system or as ordinary wind bracing is a question to settle before any of the geometry below, because it changes what the connection has to develop from the force in the analysis to the expected strength of the member.
In a metal building the whole question is answered differently again. Rod and cable bracing in the roof plane and in the sidewalls is standard practice there, sized by the manufacturer against the MBMA Metal Building Systems Manual and delivered as a kit; the engineer's problem shifts to the interface — whether the endwall column, the base condition and the foundation are receiving the forces that kit produces, which are not the forces a designer sketching an equivalent braced frame would have assumed.
What the Diagonal Is Actually Worth
A tension member has two capacities and the smaller one wins. Yielding runs across the gross area at the specified yield strength and is checked with the higher resistance factor, because a member that yields along its length gives warning and redistributes; rupture runs across the effective net area at the tensile strength and gets the lower factor, because it does not. Both are in Chapter D of AISC 360, and the pattern repeats through the plate checks further down the page: the yielding limit states get the generous factor and the rupture limit states get the strict one, so the lowest nominal capacity in a list is not necessarily the one that governs the design.
Threaded rod has a wrinkle worth knowing. AISC 360 handles threaded parts in the section covering tension and shear strength of bolts and threaded parts, and takes the tensile strength on the gross area of the rod with a reduction that already accounts for the thread — so the number to use is the shank area with the code's factor, not a root area computed from a thread table. Upset-end rods, where the bar is enlarged before the thread is rolled, exist specifically so the threaded end is not the weak point at all; the supplier's own literature states the capacity of that assembly, and it is normally a larger number than the plain bar of the same nominal diameter would give.
Then look past the rod. A clevis pin is in double shear and bears against the eye of the fitting and the plate between the prongs, a turnbuckle body has its own rated capacity, and a cable termination — a swaged fitting or a poured socket to the strand manufacturer's specification — has an efficiency well below the strand's breaking strength. The weakest link in a tension-only bay is very rarely the piece of steel everyone calls the brace. It is the small forged part between the brace and the plate, bought on a catalogue page nobody re-read after the loads went up in the second issue.
Four Ways a Gusset Says No
Now to the plate, and to the question the bay actually turns on. A gusset with a bolt group in it does not have one capacity; it has four independent ones, each running along a different line through the same lump of steel, and they respond to different dimensions. Draw them by hand on the detail before you compute anything. A straight line across the bolt lines is the net section. A U around the group — shear down the two sides, tension across the end — is the block. A fan opening out from the first row of bolts to the last is the Whitmore section. The plate's full width, away from any hole at all, is gross yielding.
Net section rupture takes every hole out of the width in one line, and AISC 360 Section B4.3 requires that the width deducted for a hole is larger than the hole itself, to account for the material damaged in punching — a 20 mm bolt sits in a 22 mm standard hole and is deducted at 24 mm, a 3/4 in bolt sits in a 13/16 in hole and is deducted at 7/8 in. Section J4.1 also caps the effective net area of a connecting element at 0.85 of its gross area, whatever the pattern happens to leave, which means a gusset with generous edge distances stops being rewarded for them at that ceiling. Block shear rupture is AISC 360 Section J4.3: the tension plane across the end of the group plus the two shear planes down its sides, taken as the lesser of shear rupture and shear yielding on those planes, with the tension term scaled by whether the tension stress on the block is uniform. For a gusset pulled along its own axis it is uniform. For a coped beam web with two lines of bolts, which is not this detail but is the case people copy the input from, it is not, and the tension term is halved.
The Whitmore section is the one that is genuinely a gusset check rather than a general plate check, and it comes from R. E. Whitmore, Experimental Investigation of Stresses in Gusset Plates, University of Tennessee Engineering Experiment Station Bulletin No. 16 (1952). The effective width is measured by spreading thirty degrees from the outer fasteners of the first row out to the last row, and the yielding check runs on that width alone. It is also where the fan routinely opens out past the edges of the plate, and when it does there is no steel out there to yield — the check has to be truncated at the material that exists, and a geometric width larger than the plate is a signal that the plate is too narrow for the pattern rather than a capacity you may claim.
The four move in different directions, which is what makes the choice of remedy non-obvious. Widening the gauge or the edge distance buys gross section and net section at once. Lengthening the pitch or the end distance buys block shear and the Whitmore width at once, and buys the net section nothing whatever, since a straight row of holes takes the same area out of the width regardless of what sits behind it. Thickening the plate scales all four in step and is the answer when the pattern is already as generous as the geometry allows.
Two things this list does not cover, and both of them bite. It is the plate only: bolt shear, bearing and tearout at each hole are separate checks in Chapter J and frequently arrive first, so a plate that passes here can still fail at the first bolt. And it is all tension: a gusset carrying a compression brace buckles over the Whitmore width, and that needs an unbraced length and an effective length factor taken off the detail geometry, which no bolt pattern by itself can supply.
| Failure line | Where it runs | Dimensions that help it | Dimensions that do nothing for it |
|---|---|---|---|
| Gross section yielding | Full plate width, clear of the holes | Gauge, edge distance, thickness | Pitch, end distance |
| Net section rupture | Straight across the line of holes | Gauge, edge distance, thickness, smaller holes | Pitch, end distance, more bolts along the line |
| Block shear rupture | Tension across the end, shear down both sides | Pitch, end distance, gauge, thickness | Widening beyond the outer bolt lines |
| Whitmore section yielding | A thirty-degree fan from the first bolt row to the last | Pitch, more bolts along each line, plate width to contain the fan | Extra plate outside the fan |
All four lines run through the same bolt pattern, so the only useful answer is which of them arrives first — that is what decides whether the next revision gets a thicker plate, a wider one, or another bolt in each line.
The thickness of the connecting plate or gusset on the failure line.
The specified minimum yield strength of the plate steel.
The specified minimum tensile strength of the plate steel.
The hole width to take out of the section, which is wider than the hole itself.
How many lines of bolts sit side by side across the plate, perpendicular to the force.
How many bolts sit one behind another in a single line, along the direction of the force.
The spacing between adjacent bolt lines, measured across the plate.
The spacing between adjacent bolts within one line, along the force.
From the centre of an outer bolt line to the nearer long edge of the plate.
From the centre of the end bolt to the free end of the plate, along the force.
Whether tension is spread evenly across the block's tension plane, or concentrated at one end.
Governing design strength
81.33 kips
The governing limit state is net section tension rupture. The thirty-degree spread reaches past both plate edges, so the Whitmore section has been truncated at the plate's own width — there is no material out there to yield.
- Net section tension rupture
- 81.33 kips
- Block shear rupture
- 162.65 kips
- Yielding on the Whitmore section
- 105.38 kips
- Gross section tension yielding
- 105.38 kips
- Nominal strength at the governing limit state
- 108.43 kips
- Allowable strength at the governing limit state
- 54.22 kips
- Whitmore effective width from the thirty-degree spread
- 9.93 in
- Gross plate width across the bolt group
- 6 in
- Area remaining on the rupture line
- 1.66 in²
- Area remaining on the two shear planes
- 4.15 in²
They open the calculator with your figures already in it
Steel Plate Block Shear and Net Section Calculator: 81.33 kips — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
Add the equipment this sizes
This result is a specification — 81.33 kips — not a quantity. Put the thing it sizes into your project: how many, what you call it, and your supplier’s price.
What this calculation does not cover
- Checks the PLATE only. Bolt shear, bearing and tearout at each hole are Section J3 checks that frequently govern before any of the four run here, and a plate that passes on this page can still fail at the first bolt.
- Does not check the gusset in compression. Buckling on the Whitmore section needs an unbraced length and an effective length factor taken from the detail geometry, and both are outside what a bolt pattern alone can tell you.
- Assumes holes in line, not staggered. A staggered pattern earns back net width through the s²/4g term in AISC 360 Section B4.3, which is not applied here.
- Assumes a flat plate carrying axial force. An angle leg, a tee stem or a coped beam web has different geometry, and the coped web also belongs at Ubs = 0.5.
The pattern entered holds 6 bolts, in 2 lines of 3, and which of the four failure lines arrives first is named in the note beside the result. That one is the only one worth spending steel on. Widening the gauge or the edge distance buys net section and gross section together; lengthening the pitch or the end distance buys block shear and the Whitmore width together, and buys the net section nothing at all. Where the remaining area looks thin, that is the whole choice — and it is why another bolt row usually answers better than a bigger bolt.
The Work Point, and the Beam That Turns Into a Strut
Every force above was resolved about a work point: the intersection of the centrelines of the brace, the beam and the column. Put the work point there and the three members meet without eccentricity, and the moments in the joint are the ones the analysis assumed. Move it — to shorten a gusset, to clear a slab edge, to keep the plate off a façade bracket — and a moment appears at the joint that no member was sized for, carried by whichever of the three is least able to argue.
Getting the brace force out of the gusset and into the beam and the column is the other half of it. The Uniform Force Method, set out in Part 13 of the AISC Steel Construction Manual, is the standard way to proportion the gusset so the interfaces to the beam and to the column carry axial force without moment, and it turns the gusset's own dimensions into design variables rather than into whatever fits. Detail the plate first and compute afterwards and you will find the interfaces carrying moments you then have to weld for.
The consequence that gets missed sits along the beam. The horizontal component of the brace force does not vanish into the connection; it travels along the beam as axial load, out to wherever the floor diaphragm hands it over. A beam drawn on the framing plan as a simple span carrying its share of the slab is, in a braced bay, also a strut or a tie carrying a substantial axial force, and it needs to be checked as such — combined axial and bending, with the connections at both ends able to deliver that axial force into the columns. Chasing this one line item is worth more than most of the fine tuning on the plate, because a beam sized for bending alone in a narrow bay at 1.80 times the story shear is a real problem rather than a conservatism.
Clearance for a Brace That Is Supposed to Buckle
In a seismic braced frame the brace is expected to buckle, and the gusset has to let it. A brace buckling out of plane forms a hinge in the plate somewhere off the end of the member, and the plate needs a strip of free material for that hinge to form in without tearing the welds to the beam and column. The convention drawn on most details is a linear clearance of twice the plate thickness, measured from the end of the brace to a fold line across the gusset; it is presented that way in the AISC Seismic Design Manual, along with an elliptical clearance model developed in later full-scale brace-frame testing, which produces more compact gussets by letting the fold line curve around the end of the brace instead of running straight across.
Everything else in that assembly then follows from the brace's expected strength rather than the analysis force. Connections in a special concentrically braced frame are designed to develop the expected yield strength of the brace in tension and its expected post-buckling strength in compression, both of them larger than what the load combinations delivered; the protected zone around the brace end and its connection allows no attachments, no burnt holes, no tack-welded hangers. A conduit clip welded into that zone by a trade with no reason to know it is there removes the qualification the detail was drawn under, and no calculation on this page or any other recovers it.
What Changes After the Steel Is Standing
The braced bay is also an erection item, and an unusual one: it is the part of the frame that has to be complete and tight before much else can go up, and the part most likely to be released early so a delivery can get through. Responsibility for temporary supports and for when permanent bracing may be relied upon is set out in AISC 303, Code of Standard Practice for Steel Buildings and Bridges, and in the United States the erection sequence itself is governed by OSHA's steel erection standard at 29 CFR 1926 Subpart R. Neither of those is the erector's judgement to override on the day, and a bay slackened off to swing a beam through is a decision that belongs to whoever wrote the erection scheme.
The changes that matter afterwards are small and dimensional, and they all happen to the plate rather than to the member. A fitter trims a gusset corner by 20 mm to clear a duct hanger and takes gross width, net width and Whitmore width in the same cut. A hole is reamed a size up because the pattern will not line through, and the deduction on the rupture line grows with it. A turnbuckle is run down until the rod sings, which on a long bar can be a substantial fraction of its capacity spent before any wind arrives. Each of these is invisible on the as-built photograph and each moves a limit state that was checked once.
So the walk-round at handover is short and specific. Measure the plate that exists rather than the plate that was drawn: hole to hole, hole to edge, end bolt to plate end. Confirm the diagonal is the member on the schedule and not a substitution that happened at the mill. Check that turnbuckles carry the lock nuts or the tell-tale the supplier requires, that clevis pins have their retainers, and that the beam in the braced bay has the end connections its axial force needs, not the shear tabs its bending would have justified. Then write down what you measured, because the next engineer to look at this bay will have the drawing and nothing else.
- Re-measure the gusset that exists: gross width across the bolt group, edge distance to each long edge, and end distance past the last bolt.
- Compare the hole size in the steel to the size the net area was computed on, and re-run the rupture line if it was reamed.
- Confirm the work point still falls where the analysis put it, and note any gusset that was shifted to clear services.
- Record the pretension actually installed in each rod against the supplier's stated installation force, not against a target somebody remembered.
- Check the beam end connections in the braced bay for axial capacity, not only for the shear reaction on the framing plan.
- Photograph any welding, drilling or clipping found inside a seismic protected zone and raise it as a non-conformance rather than a query.
Take the bay into the workspace
Six things to settle before the connection drawing goes out, in the order they stop being optional. Take them with the framing plan, the section tables and the connection detail as issued for construction, and record the dimension you measured beside the one that was drawn.
- Diagonal length, pin to pin — The hypotenuse of the bay is the check dimension; the ordered bar is shorter by whatever the clevis, pin centre and turnbuckle body take up at each end, per the supplier's assembly dimensions.
- Brace force divided by the cosine of its angle — A narrower bay at the same floor height raises the brace force, the bolt count and the plate thickness together — check the ratio before sizing anything, not after.
- Rod or section weight per bay — Length times linear weight decides the lift method. Round bar can be computed from the diameter; angles, channels and hollow sections come off the section tables.
- Hole size, gauge, pitch, edge and end distance — Five dimensions that drive four separate limit states in the plate. Measure them on the steel where the bay already exists, and take the deduction width from the hole type rather than the bolt size.
- Work point location and gusset interface forces — Confirm the brace, beam and column centrelines still meet where the analysis assumed, and proportion the plate to the Uniform Force Method rather than to what fits.
- Axial force in the braced-bay beam — The horizontal component runs along the beam to the diaphragm. Check that member and both its end connections for axial load combined with bending.
Opens the calculators above on one screen with the dimensions from this article already filled in. Quantities only — this site publishes no price list, because local prices vary too much to publish honestly.