A beam that held its load on test day has told you very little. What matters is whether it will hold on the worst day of fifty years: the day a crowd stands in the wrong place, the concrete in that corner was a bit weak, and a storm is blowing. Engineers cannot know that day in advance. What they can do is decide how unlikely they will let it be.
Structural design is the art of doing that with steel and concrete. Structural analysis (34/64) hands you the forces. Design turns them into a real thing: how deep the beam, how many bars of reinforcement and where, how many bolts, and how to arrange it so that if the structure is ever overloaded it gives warning rather than letting go. It is a small number of ideas applied with great care.
Who takes it: civil and structural engineers, usually in the third and fourth years, as two courses: reinforced concrete design and steel design. Architects meet a lighter version. Programmes that follow the ASCE Civil Engineering Body of Knowledge require design in at least one structural material.
What it is for: choosing the size and detail of beams, columns and slabs so that they safely carry the forces from structural analysis, under the rules of a design code.
Comes after: Structural Analysis (34/64) and Materials Science & Manufacturing (34/13).
Leads to: Construction Management (34/70), which has to build what is drawn, and the capstone Systems Engineering (34/22). Foundations in this design rest on Geotechnical Engineering (34/66).
What this piece will and won't give you: you won't be able to design a beam: that needs a code, and every value here is an example, not a design value. You will see why the steel in a concrete beam goes where it does, why codes use safety factors, and why a structure that bends first is safer.
Easier first reads: Mechanics of Materials (34/11), Materials Science & Manufacturing (34/13) and Statics (34/10). The Hyatt Regency walkway collapse is told in Engineering Drawing & CAD (34/18) and not repeated here.
Modern codes design for limit states: conditions beyond which a structure no longer does its job. The ultimate limit state is collapse or loss of stability. The serviceability limit state is the quieter failure: a floor too bouncy to live on, a crack too wide, a beam that sags until the doors jam. For the ultimate limit state, the rule in words is: the design strength of the member must be at least as big as the factored loads.
Read it as: take the nominal strength, shrink it by a factor φ below 1, and make sure it still beats the loads, each stretched by a factor γ above 1. The factors are not superstition. Loads vary (a live load is far more uncertain than a dead load, which is why it gets the bigger factor) and strength varies (one batch of concrete, one steel heat). Treat both as bell curves. The structure fails where the load curve overlaps the strength curve, and the factors are chosen so the overlap is acceptably small. Eurocode EN 1990 puts the target for an ordinary building at a reliability index β of 3.8 over 50 years, which is a probability of failure of about 7 in 100,000.
Notice what the overlap depends on. A member with a mean strength 1.6 times the mean load, with 12% scatter in strength and 20% in load, has β of only 2.2 and a failure chance of about 1.5%. Raise the ratio to 2.2 and β reaches 3.6, about 1 in 7,000. Calibrating φ and γ so that ordinary members land near the target is what code committees spend years on. Older "allowable stress" design instead divided strength by one overall factor and did not know how safe the result was.
Move the average strength above the average load, and change how much each one scatters. The overlap is the chance of failure.
Concrete is very good at being squeezed and poor at being stretched: its tensile strength is only about a tenth of its compressive strength. Steel is good at both. Reinforced concrete puts each where it is needed. Load a simply supported beam and it sags: the top squeezes and the bottom stretches, and between them is a line, the neutral axis, with no stress at all. So the steel goes at the bottom, as far from the neutral axis as the cover allows, where its pull works with the longest lever arm. The two materials expand with temperature at nearly the same rate, and ridges on the bars grip the concrete, which is why the combination works at all. In a cantilever the top is the stretched side, so the bars go in the top.
Read it as: the pull in the steel times the lever arm between the pull and the push in the concrete. Four 20 mm bars (1,257 mm²) of 500 MPa steel, 450 mm below the top of a 300 by 500 mm beam of 30 MPa concrete, make a push zone 82 mm deep and a capacity of 257 kN·m. It also sets how the beam will fail. If the steel is modest, it yields first and the beam bends a long way with wide cracks, which is a warning. If there is too much steel, the concrete crushes first, suddenly. Codes force the first kind by limiting the steel and by cutting φ for the second.
Slide the bars from the bottom to the top of the beam and watch the capacity collapse. Add bars until the failure mode changes.
Cracks let in water and corrosion, and a cracked beam is less stiff. Prestressing avoids them. The engineer stretches steel strands, bolts them against the ends of the beam, and lets them squeeze the concrete before any load arrives. When the load comes and tries to stretch the bottom, the squeeze has to be undone first, and the concrete never goes into tension. The strands are placed low, so that the squeeze itself bends the beam upward and fights the sag.
Read it as: the even squeeze, plus the bending the squeeze causes because it is off-centre, plus the bending from the load. For a 300 by 600 mm section over 10 m, 20 kN/m of load would put 13.9 MPa of tension on the bottom, four times what concrete can take, so it would crack. With 1,000 kN of prestress 200 mm below the centre, the bottom is in 2.8 MPa of compression. The prestressing also lets a floor be thinner for the same span. Eugène Freyssinet was the pioneer of the method in the 1920s and 1930s. The thing to watch is the unloaded stage: the beam may crack on top, because the squeeze pushes it up.
Without prestress, the beam cracks. Add force and lift the strands away from the centre.
Steel is strong, stiff and made in a factory to tight tolerances, so steel members are slim: I-beams, tubes and angles with a high stiffness for their weight (34/11). Slimness is its weakness. A slim column buckles; a slim flange wrinkles (local buckling); a deep beam can twist sideways (lateral-torsional buckling). Much of steel design is deciding how to prevent these, by bracing, by choosing compact sections, and by checking each failure mode with its own formula.
The real work is at the connections. Members are joined with bolts or welds, and the joint must be strong enough in every way it could fail: the bolts shearing, the plate crushing against the bolt, the end tearing out, the plate rupturing through the bolt holes. The idea underneath is a chain. A chain is as strong as its weakest link, so the designer chooses which link is the weakest, and makes it the one that stretches. A tension plate with holes shows it: the whole plate yields at 0.9 × Ag × fy, but through the holes only the net area carries load, and failure there is rupture, at 0.75 × An × fu. A plate 200 by 12 mm with two 22 mm holes yields at 540 kN against rupture at 562 kN, so it yields first, and shows it. With three holes the rupture value is 482 kN. It now breaks without stretching. (The factors shown follow AISC 360; Eurocode 3 uses different partial factors for the same two checks.) A famous connection failure is told in Engineering Drawing & CAD (34/18).
Add holes and make them bigger until the weak link changes from yielding to rupture.
Strength is not the only thing a structure needs. Ductility is the ability to deform a long way past the first yield while still carrying load. A ductile structure announces its distress with visible cracks and sag, and gives people time to leave. A brittle one fails without warning. Mild steel can stretch by a fifth or more of its length before it breaks; concrete crushes at a strain of 0.3%. That is why codes limit the steel in a beam and demand detailing, such as closely spaced ties, that keeps the concrete confined.
Ductility has a second, larger use: earthquakes. Making a building strong enough to stay elastic in the worst earthquake would be absurdly costly. Instead, codes let it yield, because yielding absorbs energy. Seismic codes divide the elastic force by a response modification factor (called R in ASCE 7, with values between about 1.5 and 8, or a behaviour factor q in Eurocode 8) in return for demanding detailing that guarantees the structure can move that far without failing. The rule behind it, the "equal displacement" approximation, says that a yielding structure moves about as far as an elastic one would, so the ductility it needs is about R. If the structure is brittle, the discount is not available.
Divide the earthquake force by a factor R, then give the structure the ductility to match.
The physics is the same everywhere. The codes are not, because each country writes its own, shaped by its climate, earthquakes, materials, history and legal system. Nearly all use limit-state design with factors. Here are the best-known names. These are examples; always use the code in force where the building stands.
| Region | Concrete | Steel | Loads and quakes |
|---|---|---|---|
| Europe (EU and many others) | Eurocode 2 (EN 1992) | Eurocode 3 (EN 1993) | EN 1990, 1991, Eurocode 8 (EN 1998) |
| United States | ACI 318 | AISC 360 | ASCE 7 |
| Mexico | NTC for concrete | NTC for steel | NTC for earthquake design (Mexico City) |
| China | GB 50010 | GB 50017 | GB 50011 (seismic) |
| India | IS 456 | IS 800 | IS 1893 (seismic) |
| Japan | AIJ standards | AIJ standards | Building Standard Law |
| Australia | AS 3600 | AS 4100 | AS 1170 |
| Canada | CSA A23.3 | CSA S16 | National Building Code |
| Brazil | ABNT NBR 6118 | ABNT NBR 8800 | ABNT NBR 6123 (wind) |
Typical factors show the family resemblance: ASCE 7 uses 1.2 D + 1.6 L and ACI 318 a strength factor of 0.90 for a ductile beam; Eurocodes use 1.35 G + 1.5 Q and partial factors of 1.5 on concrete and 1.15 on reinforcing steel. Different numbers, same method. These are examples, not design values.
The code that changed the most was written after a gas leak. At about 5:45 am on 16 May 1968, a resident on the 18th floor of Ronan Point, a 22-storey tower of precast concrete panels in Canning Town, East London, lit a match to light the stove. Leaking gas exploded, and the blast blew out a load-bearing wall panel in the corner of the building. The floors above collapsed and the failure ran down the whole corner of the building. Four people died and 17 were hurt; the toll was low only because most residents were still in their bedrooms. The tower had been completed two months earlier.
The Griffiths inquiry found that the design had met the regulations of the day. The regulations simply did not yet ask for what was missing: the floor-to-wall connections were not designed for sideways loads such as an explosion or wind, nothing gave the load another route when one panel was lost, and later investigation found missing bolts and holes stuffed with rubbish. It recommended that new tall blocks be designed to resist progressive collapse. In 1970, the Fifth Amendment to the UK Building Regulations introduced requirements against disproportionate collapse; many other jurisdictions have since adopted similar rules. The same two ideas run through this whole course: ties that hold the structure together, and spare paths for the load when one is lost (34/64).
A design code is a way of saying how rare a failure must be, turned into factors on loads and strengths. Concrete carries the squeeze and steel carries the stretch, placed where each belongs. Prestress keeps the concrete from stretching at all. In steel, the connection decides, and the weakest link should be the one that yields. Above all, a structure should bend before it breaks, because that is what gives people time, and what lets an earthquake design trade strength for movement.
Try this: look at a concrete beam or bridge soffit and ask where the cracks, if any, would run, and which side the steel must be on. Then look at a steel joint and ask which part would give way first.
Sources. Limit-state design, the reliability index (β = (μR − μS) ÷ √(σR² + σS²), the normal-distribution model used for illustration), the rectangular stress block for reinforced concrete, the prestress stress formula, the net-section tension check and the equal-displacement rule are standard textbook material. Every number in the interactives was computed in node: β = 2.16 (about 1.5%) at 1.6 × / 12% / 20% and 3.62 (about 1 in 7,000) at 2.2 ×; Φ(−3.8) = 7.2×10⁻⁵; Mn = 257 kN·m for four 20 mm bars at d = 450 mm (a = 82 mm, steel strain 1.07%, f′c 30 MPa, fy 500 MPa, β1 = 0.836 from the ACI formula); the prestress example (P/A = 5.56 MPa, Pec/I = 11.11 MPa, Mc/I = 13.89 MPa: bottom −2.78 MPa, top −8.33 MPa); the plate (540 kN yield against 562 kN rupture with two 22 mm holes, 482 kN with three); and the R = 4, μ = 3 example. The strength factors 0.90 and 0.75 follow AISC 360 for yielding and rupture in tension; the flexure factor and the concrete strength relations follow ACI 318 in simplified form, and the moment-capacity routine solves the section by strain compatibility, so a bar near the compression face gives a small, brittle capacity. The reliability target (EN 1990 reliability class RC2: β = 3.8 for 50 years, failure probability about 7×10⁻⁵) was confirmed from a web search of EN 1990 summaries. Ronan Point facts (16 May 1968, about 5:45 am, 18th floor, 22-storey, Canning Town, 4 dead and 17 injured, Griffiths inquiry, 1970 Fifth Amendment on disproportionate collapse, missing bolts found in later investigation) come from the Wikipedia article on Ronan Point. The code names in the table, the partial factors 1.5 and 1.15, the response modification factor range 1.5 to 8, tensile strength about a tenth of compressive strength, and Freyssinet as pioneer of prestressing are standard engineering knowledge not re-checked against a primary source in this session; the code table lists best-known names only and codes are revised often. The ASCE 7 target reliability was not verified.
Go deeper. Wight & MacGregor, Darwin–Dolan–Nilson, McCormac & Csernak, Salmon & Johnson, Salvadori and Petroski are standard titles; check the current edition. The MIT OpenCourseWare page was confirmed.