Structural Engineering & Statics
where the load goes
Materials

The strength the welder gives back

A 6082-T6 extrusion is twice as strong as a 5083-H111 plate and, welded across, the two are within a few per cent of each other. The heat of the arc anneals the metal for thirty millimetres either side, permanently, and the strength that was bought in a furnace is given back at the first joint.

Assumes The stress at which nothing in particular happens, The stress that was there before the load and The weld that is stronger across than along.

12 min read 7 figures Geometry beats materialWhich failure arrives firstThe load must go somewhere

Aluminium’s strength is not a property of aluminium. Pure aluminium has a proof stress of about 20 N/mm² and is useless as a structural material; the alloys used in structures reach ten or fifteen times that, and every bit of the difference comes from something done to the metal after it was made.

Two things are done. Precipitation hardening dissolves alloying elements at high temperature, quenches them into solution and then ages the metal so that they come out as fine particles that obstruct dislocation motion. Work hardening deforms the metal cold so that the dislocations obstruct each other.

Both are undone by heat, and a weld is heat.

The strength was bought in a furnace and the welder gives it back. Proof stress as delivered and beside a weld, for four aluminium alloys. The heat-treated alloys lose half of it: the strength of a 6xxx extrusion is in precipitates formed by an ageing treatment, and the arc dissolves them for 32 mm either side of the weld, permanently. The work-hardened tempers lose nearly as much, because the heat undoes exactly the work. The annealed ones lose nothing at all, because there is nothing left in them to anneal. The consequence is the crossover: 5083-H22 is 1.04 times 6061-T6 as delivered and 0.92 times it once welded, so the stronger alloy is the weaker member. The 240 mm member drawn, with two longitudinal welds, keeps 87% of its parent capacity — a weld along a member softens a strip and leaves a section, and the same weld across it softens the whole of one.
Fig. 1 Proof stress as delivered and beside a weld, for four aluminium alloys. The heat-treated ones lose half of it, the work-hardened one loses nearly as much, and the annealed one loses nothing because there is nothing left in it to anneal.

Which free body produced the number

None. This is a materials essay and the mechanism is metallurgical, but there is a free body in the consequence and it is worth being precise about where.

The heat-affected zone is a strip of softened metal, twenty-five to forty millimetres wide on each side of the weld, running along the weld’s length. Whether that matters to a member depends entirely on how the strip is oriented relative to the force.

Cut the member across the weld and the free body’s whole section is in the softened zone. The capacity is ρhazAfo\rho_{haz}Af_o — the whole area at the reduced strength.

Cut it across a longitudinal weld and only part of the section is softened. The capacity is (A−Ahaz)fo+Ahazρfo(A - A_{haz})f_o + A_{haz}\rho f_o, and the softened part is a fixed width whatever the member is.

So the same weld costs a narrow member nearly everything and a wide one very little, and the design variable is a ratio of the heat-affected width to the member’s own.

The net section, and the path the tear takes. A 240 mm plate with two holes staggered by 45 mm at a gauge of 70 mm. The straight path through one hole leaves 218 mm; the diagonal path through both leaves 203.23 mm after the s²/4g correction adds 7.23 mm back. The shorter of the two decides, at 84.68% of the gross section.
Fig. 2 The same arithmetic in steel, where the reduction is a hole rather than a softened strip. In both cases a fixed loss on a variable section means the penalty is a proportion rather than a quantity.

There is a further consequence of the strip’s geometry that is not obvious from either formula. A member with a longitudinal weld has a stress distribution across its section that no longer matches its shape: the middle of it is softer than the edges, or the reverse, depending on where the weld ran. So the member does not yield uniformly — it yields in the strip first, redistributes onto the parent metal beside it, and reaches its capacity with part of the section already plastic.

That is not a problem for strength, because aluminium is ductile enough to redistribute. It is a problem for stability: a member yielding in a strip has a tangent stiffness that has fallen locally, and a slender member whose heat-affected zone is at the point of maximum compression buckles at a load the parent alloy’s curve does not predict. The column that yielded before it was loaded is the same interaction with a residual stress instead of a softened zone, and the arithmetic is the same: the effective modulus at the critical fibre is what a column curve is really about.

The crossover, which is the whole essay

Put the alloys side by side and something happens that nothing in a materials table prepares anybody for.

as delivered beside a weld
6082-T6 260 130
6061-T6 240 120
5083-H22 250 110
5083-H111 125 125

5083-H22 is twice as strong as 5083-H111 as delivered and weaker than it once welded. Same alloy, different temper, and the temper that was bought is the temper the arc removes.

And 6082-T6, the workhorse extrusion alloy, is twice the strength of 5083-H111 as delivered and four per cent above it beside a weld.

That has a design consequence which is easy to state and frequently missed: for a welded structure whose members are governed by their welds, the choice of alloy is nearly irrelevant. The 6082 costs more, extrudes into better shapes, and is stronger everywhere except at the joints — and the joints are where the capacity is decided.

Where the alloy does earn its price is in members whose welds are longitudinal, or which are bolted, or where the weld is at a location of low stress. The design decision is therefore not “which alloy” but “where are the welds relative to the force”, which is a geometry question rather than a materials one.

What the alloy was chosen for in the first place

It is worth asking why anybody uses aluminium in a structure at all, because the answer decides how much the softening matters.

It is not strength. Structural steel starts at 275 N/mm² and goes to 690; the best structural aluminium is at 260 and loses half of that at a weld. On strength alone the material is not competitive.

It is strength per unit weight, and there aluminium is genuinely ahead: a third of the density for most of the strength, so a member of the same capacity weighs half as much. That matters where the structure carries mostly itself — a long-span roof, a moving bridge, a mast, anything transported or lifted — and it matters not at all where the structure carries something else.

What a beam of given stiffness is worth, against mild steel. The performance index for a beam of given stiffness, as a multiple of mild steel's. The index is E^½/ρ, and the exponent is not a fudge — it falls out of eliminating the free dimension between the mass and the constraint. Timber wins at 4.28× and mild steel is last at 1.00×. Neither ranking survives a change of load case, which is what the other views in this family are about.
Fig. 3 Why the material is chosen. A strength-per-weight index favours aluminium and a stiffness-per-weight index favours it less, because the modulus is a third of steel’s and the density is a third too — so the two cancel exactly and aluminium is neither better nor worse per kilogram in stiffness.

The ranking belongs to the load case is the general argument, and the specific consequence here is that the weld’s fifty per cent has to be set against a starting advantage that was never fifty per cent to begin with. A welded aluminium member is often no lighter than the steel one it replaced, which is why the material’s structural uses are so concentrated in the cases where corrosion, transport or extrusion — rather than weight — is the reason.

Where the weld can be

Once the mechanism is clear, four moves are available and all of them are about position.

Put the weld where the force is not. A transverse weld at a point of contraflexure costs nothing; the same weld at midspan costs half the section. That is the cheapest of the four and it is a drawing decision.

Make the weld longitudinal. A member fabricated from plates welded along their length has its heat-affected zone as strips rather than as a full section, and a wide member barely notices.

Bolt instead. The metal between the holes is a different reduction with a different arithmetic, and for aluminium it is very often the smaller one: a bolted connection removes 15 to 25 per cent of a section as holes, against 50 per cent as heat.

Or heat-treat afterwards. Possible, expensive, and rules out anything large or already assembled. Solution treatment and ageing needs a furnace the whole component fits in and a quench that does not distort it, which for a structural member is usually the end of the argument.

The load did not move; the section did. A lipped channel 200 by 80 mm at 3 mm thick, drawn twice on top of itself: the outline as fabricated, and the part of it still working once the plates have buckled. The web is held on both edges, so it loses its middle; the flanges are held at the web, so an unlipped one would lose its free edge. What survives is not symmetric with what was drawn, so the centroid moves 4.0 mm — and a load applied along the axis it was designed to arrives 4.0 mm off the section that has to carry it. At the 242 kN this section will take, that is 0.97 kNm of bending nobody applied.
Fig. 4 The general operation: a section reduced to the part of it that is still fully effective. Local buckling removes material for a different reason, and the arithmetic afterwards is the same.

The number to design a member on

Putting the two arithmetics together gives a working rule that is short enough to remember and is the practical content of the whole essay.

For a member with a transverse weld, the capacity is ρAfo\rho A f_o and the alloy hardly matters: every heat-treated alloy lands between 110 and 135 N/mm², and so does the annealed 5xxx that started at half the price.

For a member with longitudinal welds only, the capacity is fo(A−(1−ρ)Ahaz)f_o(A - (1-\rho)A_{haz}) and the alloy matters a great deal, because most of the section is at its full strength. A 400 mm deep welded plate girder in 6082-T6 keeps about 94 per cent of its parent capacity; the same girder in 5083-H111 keeps all of a much smaller number.

And for a member with no welds at all — extruded to length, bolted at its ends — the alloy is worth its full advantage.

Those three cases are three different design problems using the same table, and the thing that selects between them is a drawing decision that is usually made after the member has been sized. The connection is not a point makes the same argument for steel connections: the detail is not a consequence of the member, it is one of its inputs.

The zone has a width, and the width is not a material property

The 25 to 40 mm is not a constant. It depends on the heat input per unit length, on the thickness, on whether the joint is welded from one side or two, on how many passes, on the interpass temperature, and on whether the member was preheated.

That makes it a fabrication variable, and it is the reason aluminium design codes contain clauses about welding procedure that a steel code has no equivalent of. A fabricator who runs hotter to get a better profile widens the softened zone and reduces the member — and there is no inspection that finds it afterwards, because the metal looks identical.

There is a further complication with a name: the softening is time-dependent. A 6xxx alloy welded and left at room temperature partially re-ages over weeks, recovering some of the loss; one welded and then artificially aged recovers more. So a member tested a week after fabrication and one tested a year after are different members.

The stress that leaks away. A restrained shrinkage strain of 300 microstrain in concrete of modulus 32000 N/mm². Ignoring creep it produces 9.60 N/mm², which is above the tensile strength of 3.5 and predicts that every restrained concrete member ever cast has cracked. Counting creep by the superposition integral leaves 2.11 N/mm² after 27 years, and the one-line age-adjusted shortcut at the usually quoted ageing coefficient of 0.8 leaves 3.59. The two disagree — this creep function implies an ageing coefficient of 1.70, not 0.8 — and both are below the tensile strength, so the conclusion turns on counting creep at all rather than on how it is counted.
Fig. 5 A different time-dependent process, drawn for comparison. What natural ageing does to a heat-affected zone is the same shape of curve running the other way — a property recovering rather than a stress decaying.

Why steel does not have this problem, and where it starts to

Steel’s yield stress comes from its microstructure — grain size, carbon content, the products of its rolling and cooling — and ordinary structural steel is welded without measurable loss. That is the whole reason steel fabrication is as free as it is.

Two exceptions are worth naming.

Quenched and tempered high-strength steels do lose strength in the heat-affected zone, by five to fifteen per cent, and they are welded under procedural controls that ordinary grades are not.

And the heat-affected zone in steel can be harder than the parent, which is a different problem: a fast-cooled zone forms martensite, which is strong and brittle, and the failure mode moves from yielding to cracking. The flaw that sets the strength is what governs then, and the design response is preheat rather than a strength reduction.

The hour that is really a temperature. The retention factors for carbon steel against temperature: the yield stress and the elastic modulus. The modulus falls away first — at 500°C the steel has kept 78% of its strength and 60% of its stiffness — so a member's failure mode can change during a fire. A member working at 45% of its cold capacity runs out of strength at 608°C, and out of the stiffness for the same ratio at 552°C, 57 degrees earlier. There is nothing about time in any of it: a fire rating is a temperature the member must not reach, converted into the minutes a particular fire takes to get it there.
Fig. 6 What heat does to steel while it is hot, which is a separate story from what it does after it has cooled. The first is recoverable and the second is not.

The contrast is worth holding on to, because it is the reason the two materials are detailed so differently. In steel a weld is a way of making a continuous member from pieces. In aluminium a weld is a defect with a known size, placed deliberately, and the design is arranged around where the defects are.

Where the model stops

Only the proof stress was considered. The ultimate strength falls much less than the proof stress does, so a heat-affected zone is weaker and considerably more ductile than the parent — which means a member fails there in a way that gives warning, and which is the one favourable thing about the whole effect.

The zone was taken as uniform. It is not: the softening varies across it, from full loss next to the fusion boundary to none at the outer edge, and the design idealisation of a uniform strip of a stated width is a rectangular fit to a gradient.

Nothing here is about local buckling. Aluminium’s modulus is a third of steel’s, so a plate of the same proportions buckles at a third of the stress, and aluminium sections are consequently much stockier or much more heavily stiffened than steel ones. The softened zone interacts with that: a strip of lower yield stress in a compression element lowers the stress at which the element becomes non-compact, so the same weld that halves the strength can also change the section’s classification.

Where the class limits come from. The width-to-thickness ratio at which two kinds of plate reaches its own elastic critical stress at the yield stress, for three steel grades. A flange outstand (buckling coefficient 0.43) derives to 25.1, 20.2, 17.7 at 130, 200, 260 N/mm², against quoted limits of 18.8, 15.2, 13.3; A web, in bending (buckling coefficient 4) derives to 76.4, 61.6, 54.0 at 130, 200, 260 N/mm², against quoted limits of 56.5, 45.5, 39.9. The derived number is the larger every time, and by the same factor at every grade — flange outstand 1.33, web, in bending 1.35 — because both the derivation and the quoted limit go as one over the root of the yield stress. A constant ratio is what a fixed knockdown looks like: the derivation is for a perfect plate and the quoted limit is for a rolled one, carrying residual stress and not quite flat.
Fig. 7 The classification the softening moves. A section that reaches its full strength at the parent’s yield may not reach the reduced one, and a weld can move a section from one class to another without changing a dimension.

Nothing here is about fatigue. A welded aluminium detail’s fatigue strength is decided by the weld’s geometry and not by the parent alloy at all, in exactly the way the load that never came near failing anything describes for steel — so an alloy chosen for strength buys nothing on a fatigue-governed member either.

The strength was taken as the only property affected. The modulus is not: aluminium’s stiffness is 70,000 N/mm² in every alloy and every temper, welded or not, so a weld halves a member’s strength and changes its stiffness by nothing at all. The one number a stronger steel does not change makes the same point about steel grades, and it has a consequence here: an aluminium structure governed by deflection is completely indifferent to where its welds are, and one governed by strength is not.

And residual stresses were ignored. A weld cools and shrinks against restraint, leaving a tension at yield along its own line — the stress that was there before the load — and in aluminium the yield it reaches is the softened one, which is one of the few places where the loss of strength is a small mercy.

The generalisation

The habit is to ask, of any material property, what process produced it and what undoes that process.

A strength that came from a heat treatment is undone by heat. A strength that came from cold work is undone by heat. A strength that came from a coating is undone by abrasion. A strength that came from prestress is undone by relaxation. In every case the property is not a property of the substance; it is a property of the substance in a state, and the state can be left.

There is a corollary about how a material is specified. A steel specification names a grade and the grade is what arrives. An aluminium specification names an alloy and a temper, and the temper is a state that the fabrication will partly destroy — so the number that goes on the drawing is not the number the member will have, and the difference is decided by somebody who is not the designer. The nearest steel equivalent is a preheat requirement, and the difference in how seriously the two are treated is out of proportion to the difference in what they do.

The second reading is the one this collection returns to under geometry beats material, arriving from an unexpected direction. Here the geometry that beats the material is the position of the welds: two members of the same alloy, the same section and the same length differ by a factor of two in capacity according to whether the joints run across them or along them. Nothing was added to either. The fabrication drawing decided it, and the fabrication drawing is usually produced after the member has been sized.

Where this goes next

Three materials pulled until they stop. Three stress-strain curves — mild steel, high-strength steel, aluminium alloy — plotted to a strain of 2.0%. One of them has a plateau, so the stress at which yielding starts is something the specimen does rather than something anyone chooses. The 0.2% offset construction is drawn on the high-strength steel: a line of slope E from a strain of 0.002, cutting the curve at 460 N/mm². The stress at which nothing in particular happens One material in six has a yield point that a specimen actually does something at. For all the others the yield stress is a construction — a line drawn at an arbitrary offset — and every calculation on this site depends on it. A I-section at 80% of its plastic moment. The same I-section drawn three ways: the shape, the strain across its depth, and the stress that strain produces in mild steel. The strain diagram is a straight line, because plane sections stay plane whatever the material is doing. The stress diagram is not: 0% of the area has yielded, working inward from both faces, and the neutral axis sits at 70.9 mm against a centroid at 100.0 mm. The compression resultant is 322.5 kN and the tension resultant 322.5 kN, on a lever arm of 180.1 mm, which multiplies back to the 58.1 kNm the section is carrying. A rolled residual stress pattern of ±30% of yield is locked in before any load arrives. The stress that was there before the load A rolled steel section leaves the mill carrying eighty N/mm² of stress with nothing applied to it, in a pattern that sums to no force and no moment. It is invisible to every calculation and it is the knee in every column curve. A fillet weld is stronger across than along. Capacity of a 4 mm throat over 100 mm, against the angle between the weld's axis and the load. Loaded along its length it carries 116.83 kN; loaded across it, 143.09 kN. The ratio is 1.22, which is √3/√2 exactly, and it comes out of the failure criterion rather than out of a test. The weld that is stronger across than along The same fillet weld, the same size, the same steel, carries twenty-two per cent more when the load runs across it than along it. The factor is exactly the square root of three over the square root of two, and it comes out of the yield criterion rather than out of a test. Four materials pulled until they stop. Four stress-strain curves — mild steel, aluminium alloy, concrete, timber, along the grain — plotted to a strain of 0.6%. One of them has a plateau, so the stress at which yielding starts is something the specimen does rather than something anyone chooses. No offset construction is drawn. The one number a stronger steel does not change Geometry beats material almost everywhere on this site. Stiffness is the exception in the other direction — it cannot be bought at all, because every steel ever made has the same elastic modulus.

Named alongside this one

Essays reaching for the same objects. Nobody chose these; they are what the concept index makes visible.

The objects this essay names

Each one links to every other essay that touches it.

AluminiumAnnealingDuctilityEffective sectionFabricationFatigueHeat affected zoneMaterial selectionNet sectionPrecipitation hardeningProof stressResidual stressStrengthWeldWork hardening