Structures for architects

In short

Structures for architects is the study of how a building carries loads safely to the ground — what forces act, how they travel through slabs, beams, columns, walls and foundations, and what size and material each member must be. An architect is not expected to produce a structural consultant's calculations, but must choose a sound structural system, fix grids and depths at concept stage, read a structural drawing, and know the Indian codes that govern them. It is examined in B.Arch Building Technology/Structures papers (statics, SFD-BMD, stress, columns, trusses, limit state basics), in the Council of Architecture's syllabus, and in GATE-AR Part B. On the job it decides column grids in housing and IT parks, spans in auditoria and stadia, and the coordination between architect and structural engineer at every firm from a small practice to Larsen & Toubro, Tata Projects, Arup, AECOM or STUP.

Explained

Loads, load path and structural actions

• Dead load (DL): self-weight of the structure and all permanent construction — RCC 25 kN/m³, brick masonry 19–20 kN/m³, plain concrete 24 kN/m³, steel 78.5 kN/m³, as listed in IS 875 (Part 1).
• Imposed (live) load (LL): people, furniture, movable partitions — IS 875 (Part 2): typically 2 kN/m² in residential rooms, 2.5–4 kN/m² in offices, 3–4 kN/m² in corridors and stairs, 5 kN/m² and above in assembly halls and shops. Check the current edition for the exact occupancy row.
• Wind load: IS 875 (Part 3):2015. Snow: Part 4. Special loads and load combinations: Part 5. Earthquake: IS 1893 (Part 1):2016. Others: earth pressure, water pressure, temperature, shrinkage, creep, settlement, impact and vibration.
• Load path: load → slab → beam → column → footing → soil. Every load must have a continuous, stiff path to the ground; a column that stops at a floor needs a transfer beam or girder, which is costly and congested.
• Tributary (influence) area: the floor area a beam or column carries. For a regular grid, an internal column takes the full bay area; an edge column about half, a corner column about a quarter.
• Structural actions in a member: axial tension, axial compression, bending (flexure), shear, torsion, bearing. Members are named by the dominant action — tie (tension), strut/column (compression), beam (bending), shear wall (in-plane shear).
• One-way versus two-way slabs: if the long side ÷ short side of a panel is greater than 2, the slab bends essentially one way (spans the short direction); if 2 or less, it acts two-way and load goes to all four beams.

Statics, equilibrium and analysis of determinate structures

• Equilibrium: for a plane structure, ΣFx = 0, ΣFy = 0, ΣM = 0. These three equations solve any statically determinate structure.
• Supports: roller (1 reaction), hinge/pin (2 reactions), fixed (3 reactions — including a moment), guided roller. Count reactions first.
• Determinacy of a plane pin-jointed truss: m + r = 2j → determinate; m + r > 2j → indeterminate; m + r < 2j → unstable mechanism (m = members, r = reactions, j = joints).
• Steps to analyse a beam: (1) draw the free-body diagram, (2) find reactions from ΣM and ΣFy, (3) write shear and moment at sections, (4) plot the SFD and BMD, (5) locate maximum moment where shear crosses zero.
• Shapes to remember: UDL gives a linear SFD and a parabolic BMD; a point load gives a constant-step SFD and a triangular BMD; moment is maximum where the SFD crosses zero; a point of zero moment is a point of contraflexure.
• Truss analysis: method of joints (two unknowns per joint, good for finding all forces) and method of sections (cut and use ΣM, best for one specific member). Assumption: pin joints, loads at joints only, so members carry pure axial force.
• Indeterminate structures (continuous beams, rigid frames) are solved by moment distribution, slope-deflection or stiffness (matrix) methods — in practice by software such as STAAD.Pro or ETABS. They are safer (alternate load paths) but develop stresses from settlement and temperature.
• Three-hinged arch is determinate; a two-hinged or fixed arch is indeterminate. An arch converts load into mainly compression plus a horizontal thrust at the springings, which must be taken by abutments or a tie.
• Cables carry pure tension and take a funicular shape — parabolic under uniform load along the span, catenary under uniform load along the cable.

Stress, strain and section properties

• Stress σ = P/A (N/mm² = MPa); strain ε = ΔL/L; Hooke's law σ = Eε within the elastic limit. E ≈ 2×10⁵ N/mm² for steel; for concrete IS 456 gives Ec = 5000√fck.
• Stress-strain curve of mild steel: proportional limit → elastic limit → upper and lower yield → strain hardening → ultimate stress → necking → fracture. Cold-worked bars (Fe500) have no sharp yield; 0.2% proof stress is used.
• Characteristic strengths: concrete M20, M25, M30… (fck = 28-day cube strength, N/mm²); steel Fe415, Fe500, Fe550 (fy = yield/proof stress). Minimum grade for RCC in moderate exposure is M25 as per IS 456 durability clauses.
• Moment of inertia (second moment of area) governs bending stiffness; section modulus Z = I/ymax governs bending stress. Depth matters far more than width — doubling depth multiplies I by 8.
• Efficient shapes: I-sections and box sections put material far from the neutral axis for bending; hollow circular sections are efficient in torsion; solid square sections are the least efficient for bending per kilogram.
• Bending (flexure) formula: σ = My/I; the neutral axis passes through the centroid in elastic homogeneous bending, with compression one side and tension the other.
• Poisson's ratio ≈ 0.3 for steel, 0.15–0.2 for concrete; factor of safety in working stress design versus partial safety factors in limit state design.

Beams, slabs and columns

• Limit state design (IS 456:2000): design for collapse (flexure, shear, torsion, bond) and check serviceability (deflection, cracking, vibration). Partial safety factors: loads 1.5 for DL+LL; materials γc = 1.5 (so 0.67fck/1.5 = 0.446fck) and γs = 1.15 (so 0.87fy).
• RCC beam in flexure: concrete takes compression, steel takes tension. Under-reinforced section (xu < xu,max) fails by steel yielding first — ductile, with warning, and is what codes require. Over-reinforced fails by sudden concrete crushing and is not permitted. Balanced is the boundary; xu,max/d = 0.48 for Fe415 and 0.46 for Fe500.
• Shear: diagonal tension cracks near supports are resisted by stirrups (vertical shear reinforcement) and bent-up bars; nominal shear stress τv = Vu/(bd) is compared with τc from IS 456 Table 19, and must never exceed τc,max.
• Reinforcement rules (IS 456): minimum tension steel in beams As/bd = 0.85/fy; maximum 4% of bd; minimum steel in slabs 0.12% of gross area for HYSD bars; columns 0.8% to 6% (practically 4%); nominal cover from Table 16 — 20 mm beams (mild exposure), 50 mm footings (cl 26.4.2.2), 45 mm for severe exposure (check the table for the exposure class).
• Deflection control by span/effective-depth ratio (IS 456 cl 23.2): 7 for cantilevers, 20 for simply supported, 26 for continuous (for spans up to 10 m), modified for tension and compression steel. Deflection limits: total L/250, and after partitions L/350 or 20 mm, whichever is less.
• Columns: short if the effective length ÷ least lateral dimension is less than 12, otherwise slender and the load capacity is reduced. Minimum eccentricity must be allowed for. Lateral ties prevent buckling of longitudinal bars; spiral columns have about 5% higher capacity.
• Euler buckling: Pcr = π²EI/le², so slender compression members fail by buckling well below their crushing strength. Effective length le depends on end conditions: both ends pinned L, both fixed 0.5L (0.65L in code practice), one fixed one free 2L, fixed-pinned 0.7L.
• Beam-column joints, continuity and cantilevers: continuous beams have hogging (negative) moment over supports, so top steel runs over columns; a cantilever has tension at the top throughout — reversing this bar is a classic error.
• Steel design (IS 800:2007, limit state): γm0 = 1.10 for yielding, γm1 = 1.25 for ultimate/bolt rupture. Section classification plastic / compact / semi-compact / slender decides whether the plastic modulus Zp or elastic modulus Ze is used. Connections are bolted (bearing or HSFG friction) or welded (fillet, butt).
• Masonry (IS 1905) and timber (IS 883): unreinforced masonry walls are designed for compression with a slenderness-and-eccentricity stress reduction factor; timber uses permissible stresses by species and grade.

Structural systems for buildings

• Load-bearing masonry: walls carry load; cheap and simple up to about 3–4 storeys; rigid planning, thick walls at lower levels, poor in seismic zones unless confined/reinforced with bands.
• RCC framed structure (beam-column-slab): the Indian default — free planning, infill walls non-load-bearing; moment-resisting frames for lateral load.
• Flat slab / flat plate: slab directly on columns, with drops and column capitals in flat slabs; saves floor-to-floor height and formwork, used in basements and malls; punching shear at columns is the critical check and it is weak as a lateral system, so shear walls are added.
• Waffle, ribbed, grid (coffered) slabs: reduce self-weight for long spans (10–15 m).
• Shear wall and core systems, tube and outrigger systems: required for tall buildings; the lift and stair core is usually the shear core.
• Long-span roofs: steel trusses (plane, north-light, bowstring), space frames, portal frames, arches, folded plates, shells (cylindrical, hyperbolic paraboloid, domes), cable-stayed and tensile membrane roofs, pneumatic structures. Shells and membranes work by shape (form-resistant), carrying load with minimal thickness.
• Pre-engineered buildings (PEB) for factories and warehouses, precast and prestressed concrete for repetitive spans (hollow-core slabs, double-tees, bridge girders).
• Expansion, contraction and seismic separation joints: IS 456 suggests an expansion joint when a structure exceeds about 45 m in length; seismic separation between blocks must allow the sum of the two deflections.

Foundations and soil

• Safe bearing capacity (SBC) of soil (kN/m²) comes from a geotechnical investigation; typical indicative values — soft clay 50–100, medium sand 150–250, dense gravel 300–450, hard rock far higher. Always design to the soil report, never to a remembered value.
• Shallow foundations: isolated (pad) footing, combined footing, strap footing, strip/wall footing, raft/mat (when SBC is low or loads are heavy and close). Raft spreads load over the whole plan area.
• Deep foundations: bored cast-in-situ or driven piles (IS 2911), under-reamed piles in expansive black cotton soil, pile caps, well foundations for bridges. Piles carry load by end bearing plus skin friction.
• Codes: IS 1904 (general requirements of foundations), IS 1080 (shallow), IS 2911 (piles), IS 6403 (bearing capacity), IS 1888/IS 1904 family for testing — quote the subject if unsure of the number.
• Checks on a footing: bearing pressure ≤ SBC under service load, one-way shear, two-way (punching) shear, bending, and settlement — differential settlement is usually more damaging than total settlement.
• Footings are sized on service (unfactored) loads against SBC, but their reinforcement is designed for factored loads — mixing these up is a standard exam error.

Lateral loads: wind and earthquake

• Wind (IS 875 Part 3:2015): design wind speed Vz = Vb·k1·k2·k3·k4 (risk, terrain/height, topography, importance for cyclonic regions); design wind pressure pz = 0.6Vz² in N/m² with Vz in m/s. Basic wind speeds Vb range about 33–55 m/s across India (50 m/s on much of the east coast; 33 m/s over large inland areas). Force = (Cpe − Cpi)·A·pd, plus along-wind dynamic effects for slender buildings.
• Earthquake (IS 1893 Part 1:2016): four zones II, III, IV, V with zone factors Z = 0.10, 0.16, 0.24, 0.36 (Zone I was merged into II). Design horizontal seismic coefficient Ah = (Z/2)(Sa/g)/(R/I); base shear VB = Ah·W, distributed over the height in proportion to Wi·hi².
• R = response reduction factor (e.g. 3 for an ordinary RC moment frame, 5 for a special moment-resisting frame detailed to IS 13920:2016); I = importance factor (1.0 ordinary, 1.2–1.5 for hospitals, schools and other important buildings). Higher R is allowed only because ductile detailing lets the frame deform without collapsing.
• Architectural causes of seismic damage: soft/weak storey (open ground-storey stilt parking), short-column effect, floating columns, re-entrant corners in L, T and U plans, mass and stiffness irregularity, plan and vertical torsion from eccentric cores, heavy overhangs and unanchored parapets. IS 1893 lists these as plan and vertical irregularities.
• Ductile detailing essentials (IS 13920): closely spaced closed stirrups with 135° hooks in beam and column ends, strong-column-weak-beam, confinement at joints, no lap splices in plastic hinge zones.
• National Building Code of India 2016, Part 6 (Structural Design) is the umbrella document; it adopts the IS codes section by section and is referred by municipal bye-laws. Part 4 covers fire and life safety, which interacts with structure through fire resistance and cover.

Key points

• Load path - every load must reach the soil through a continuous, stiffer-downward sequence of members.
• IS 875 - Part 1 dead, Part 2 imposed, Part 3 wind, Part 4 snow, Part 5 special loads and combinations.
• Determinacy - three equations of equilibrium solve a determinate plane structure; m + r = 2j for a plane truss.
• Maximum bending moment occurs where shear force is zero; point of contraflexure is where moment is zero.
• wL²/8 - maximum moment of a simply supported beam under UDL; wL²/2 for a cantilever.
• Depth governs stiffness - bending stiffness varies with d³ (I = bd³/12), so deepening a beam beats widening it.
• Section modulus Z = I/ymax - bending stress σ = M/Z; capacity of a section in bending.
• Under-reinforced section - steel yields first, failure is ductile and warned; required by IS 456.
• xu,max/d - 0.48 for Fe415 and 0.46 for Fe500; beyond this the section is over-reinforced.
• Span/depth ratio - 7 cantilever, 20 simply supported, 26 continuous (IS 456) for quick concept sizing.
• Short column - effective length ÷ least lateral dimension < 12; otherwise slender, with reduced capacity.
• Euler buckling - Pcr = π²EI/le²; end restraint changes le from 0.5L (fixed-fixed) to 2L (cantilever).
• Arch and cable - shape-dependent systems; arches push outward (thrust), cables pull inward on supports.
• Two-way slab - panel aspect ratio ≤ 2; beyond 2 it spans one way only.
• Flat slab - punching shear at columns is the governing check; needs shear walls for lateral load.
• Seismic zones II-V with Z = 0.10/0.16/0.24/0.36; VB = Ah·W from IS 1893 (Part 1):2016.
• Soft storey - the single most common architect-created seismic weakness in Indian buildings.
• Footing sizing uses service loads against SBC; reinforcement uses factored loads.

Formulas and examples

Example 1 - beam moment, stress and deflection. A simply supported RCC beam 300 × 600 mm spans 6 m and carries a total load of 20 kN/m (including self-weight). M25 concrete, Ec = 25,000 N/mm².

• Reactions: R = wL/2 = 20 × 6/2 = 60 kN each; maximum shear = 60 kN.
• Mmax = wL²/8 = 20 × 6²/8 = 90 kN·m.
• I = bd³/12 = 300 × 600³/12 = 5.4 × 10⁹ mm⁴; Z = bd²/6 = 300 × 600²/6 = 1.8 × 10⁷ mm³.
• Elastic bending stress σ = M/Z = 90 × 10⁶/1.8 × 10⁷ = 5.0 N/mm² (gross-section check only).
• δ = 5wL⁴/(384EI) with w = 20 N/mm, L = 6000 mm: numerator = 5 × 20 × 1.296 × 10¹⁵ = 1.296 × 10¹⁷; denominator = 384 × 25,000 × 5.4 × 10⁹ = 5.184 × 10¹⁶ → δ = 2.5 mm, i.e. L/2400, well within L/250 = 24 mm.

Example 2 - flexural steel for the same beam. Fe500, b = 300 mm, effective depth d = 550 mm.

• Factored moment Mu = 1.5 × 90 = 135 kN·m.
• xu = 0.87 × 500 × Ast/(0.36 × 25 × 300) = 0.1611Ast; Mu = 435Ast(550 − 0.42 × 0.1611Ast) = 239,250Ast − 29.44Ast².
• Solving 29.44Ast² − 239,250Ast + 135 × 10⁶ = 0 gives Ast = 610 mm² → provide 2 nos 20 mm (628 mm²).
• Check: xu = 0.1611 × 628 = 101 mm < xu,max = 0.46 × 550 = 253 mm → under-reinforced, ductile. Minimum steel = 0.85/500 × 300 × 550 = 281 mm² < 610 mm². Satisfactory.
• Quick-check rule for design offices: Ast ≈ Mu/(0.87fy × 0.9d) = 135 × 10⁶/(435 × 495) = 627 mm², close to the exact value.

Example 3 - column load take-down and size. A 4-storey office building, internal column on a 5 m × 6 m grid; slab 150 mm thick, floor finish 1.0 kN/m², imposed load 3.0 kN/m².

• Tributary area = 30 m²; slab self-weight = 0.15 × 25 = 3.75 kN/m²; total = 3.75 + 1.0 + 3.0 = 7.75 kN/m².
• Per floor = 7.75 × 30 = 232.5 kN; four floors = 930 kN; add beams, walls and column self-weight, say 70 kN → service load ≈ 1,000 kN.
• Factored Pu = 1.5 × 1000 = 1,500 kN. Try 300 × 450 mm (Ag = 135,000 mm²) with 1% steel: Asc = 1,350 mm², Ac = 133,650 mm².
• Pu,capacity = 0.4 × 25 × 133,650 + 0.67 × 500 × 1,350 = 1,336,500 + 452,250 = 1,788,750 N = 1,789 kN > 1,500 kN — safe.
• Storey height 3.0 m: le/least dimension = 3000/300 = 10 < 12 → short column, no slenderness reduction.
• Footing: SBC = 150 kN/m² → area = 1000/150 = 6.67 m², add 10% for footing weight → about 2.7 m × 2.7 m isolated footing.

Example 4 - truss by method of joints. A triangular roof truss spans 8 m with a rise of 2 m and a 20 kN point load at the apex.

• Reactions = 10 kN each (symmetry). Top chord slope: tanθ = 2/4 = 0.5 → θ = 26.57°, sinθ = 0.447, cosθ = 0.894.
• At the left support joint, ΣFy = 0: F_rafter × 0.447 = 10 → F_rafter = 22.4 kN compression.
• ΣFx = 0: F_tie = 22.4 × 0.894 = 20.0 kN tension in the bottom chord.
• Check determinacy for a 3-member, 3-joint truss on a pin and roller: m + r = 3 + 3 = 6 = 2j = 6 → determinate.

Example 5 - buckling and effective length. A 3.5 m tall steel strut, ISA/tube with I = 2.0 × 10⁶ mm⁴, A = 1,800 mm², E = 2 × 10⁵ N/mm².

• Both ends pinned: le = 3,500 mm; Pcr = π² × 2 × 10⁵ × 2.0 × 10⁶/3,500² = 3.9478 × 10¹²/1.225 × 10⁷ = 322,272 N ≈ 322 kN.
• Both ends fixed: le = 0.5 × 3,500 = 1,750 mm → Pcr becomes four times = 1,289 kN. End restraint is worth more than extra material.
• Radius of gyration r = √(I/A) = √(2 × 10⁶/1800) = 33.3 mm → λ = 3500/33.3 = 105, a slender member.

Where it is used

• Architectural practice: fixing column grids, beam depths and floor-to-floor heights at concept stage; coordinating drawings with structural and MEP consultants; reading reinforcement and steel fabrication drawings.
• Real estate and housing: RCC framed apartment towers with shear-wall cores; aluminium-formwork and precast systems in large projects by Godrej Properties, Prestige, L&T and the PMAY light-house projects.
• Industrial and warehousing: pre-engineered steel buildings and portal frames for factories and logistics parks; crane gantries and mezzanines.
• Long-span public buildings: space frames and tensile roofs at airport terminals, metro stations, stadia and convention centres (DMRC, AAI, state PWDs, CPWD).
• Job roles: architect/project architect, design coordinator, site/execution engineer, structural draughtsman, quantity surveyor estimating concrete and steel, building-plan approval and municipal scrutiny roles.
• Retrofitting and safety audits: structural audits of ageing buildings, seismic retrofitting of schools and hospitals, and heritage conservation work where structural intervention must be minimal.

Interview questions

• Q: What do you check first when you see a floating column on a plan? A: Whether the load has a continuous path down — a column landing on a beam needs a transfer girder, increases the member sizes and creates a seismic irregularity flagged by IS 1893, so it should be avoided or justified by the structural engineer.
• Q: Why is a soft storey dangerous in an earthquake? A: The open ground storey (typically stilt parking) is far less stiff than the infilled floors above, so almost all lateral drift concentrates there and the ground-storey columns fail; IS 1893 treats it as a vertical irregularity requiring special analysis and stiffening.
• Q: Where does maximum bending moment occur in a beam? A: At the section where shear force is zero — at mid-span for a symmetric simply supported beam, and at the fixed end for a cantilever.
• Q: Why do we deepen a beam rather than widen it? A: Moment of inertia varies with depth cubed (bd³/12) and section modulus with d², so depth is far more effective per unit of material for both strength and stiffness.
• Q: What is an under-reinforced section and why is it preferred? A: A section where steel yields before concrete crushes (xu < xu,max); failure is gradual with visible cracking and deflection, giving warning, which is why IS 456 limits xu/d.
• Q: Give a quick rule for beam and slab depth at concept stage. A: Beam depth roughly span/12 to span/15; one-way slab roughly span/25 to span/30, which follows from the IS 456 span/effective-depth limits of 20 for simply supported and 26 for continuous members.
• Q: How does a slab decide whether it is one-way or two-way? A: By the panel aspect ratio — long span ÷ short span greater than 2 makes it one-way; up to 2 it bends in both directions and loads all four beams.
• Q: What is the difference between a short and a slender column? A: A short column has effective length ÷ least lateral dimension less than 12 and fails by crushing; a slender column buckles and its design capacity is reduced accordingly.
• Q: What forces does an arch transmit to its supports and how are they resisted? A: Mainly inclined compression, which has a horizontal thrust component, resisted by heavy abutments, buttresses, tie rods or opposing arches.
• Q: Which Indian codes would you cite for loads, concrete, steel and earthquake design? A: IS 875 Parts 1–5 for loads, IS 456:2000 for RCC, IS 800:2007 for steel, IS 1893 (Part 1):2016 for seismic with IS 13920:2016 for ductile detailing, all under NBC 2016 Part 6.
• Q: Why does IS 1893 allow a higher response reduction factor R for a special moment-resisting frame? A: Because ductile detailing per IS 13920 lets the frame absorb energy through plastic hinging without collapse, so a lower elastic design force is acceptable.
• Q: Should a footing be designed for factored or service loads? A: Its plan area is fixed by service loads against the safe bearing capacity, while its thickness and reinforcement are designed for factored loads.
• Q: What governs the design of a flat slab? A: Punching (two-way) shear around the columns, which is why drop panels, column capitals or shear studs are used; lateral stability needs separate shear walls or a core.

Common mistakes

• Using factored loads against the soil's safe bearing capacity, or service loads for reinforcement design.
• Mixing units — kN with N, m with mm, kN/m² with kN/m — so answers come out 1,000 or 10⁶ times wrong; convert everything to N and mm before substituting.
• Putting cantilever tension steel at the bottom; the hogging moment puts tension at the top throughout a cantilever and over the supports of a continuous beam.
• Forgetting the beam's own self-weight, finishes and partitions in the load take-down, then being surprised by the consultant's larger sections.
• Confusing moment of inertia (mm⁴) with section modulus (mm³), or using the full depth instead of the effective depth in RCC calculations.
• Treating an indeterminate frame as determinate and "solving" it with three equations.
• Designing an attractive plan with re-entrant corners, eccentric cores, floating columns or stilt parking and leaving the seismic consequences to the structural engineer.
• Quoting remembered SBC or basic wind speed values instead of the soil report and the IS 875 (Part 3) map for the actual site.

Related topics

Building construction · Building materials: cement, aggregates and bricks · Building services: plumbing, electrical and HVAC · Architectural design and space planning · Construction management and estimation · Building bye-laws and the National Building Code