Statics

Statics is the study of bodies at rest under balanced forces — the foundation of every structure. Learn loads on structures (dead, live, wind, snow, seismic), idealisation, free-body diagrams, supports, internal forces and a systematic method for solving statics problems.

Buildings, bridges, towers, retaining walls and dams are designed to stay still. Statics is how civil engineers find the forces acting on a structure, how those forces travel through beams and columns, and what the foundations must resist.

Every structural calculation starts with statics: idealise the structure, estimate the loads, draw the free-body diagram, and apply the equations of equilibrium.

An analogy

A building is a relay race for loads: the slab passes load to beams, beams to columns, columns to foundations, foundations to the soil. Statics tracks the baton at every hand-off.

Loads on structures

Civil structures carry several kinds of load, each estimated from codes.

• Dead (permanent) loads: self-weight of slabs, beams, walls, finishes (concrete 25 kN/m³, steel 78.5 kN/m³, brick ≈ 20 kN/m³).
• Live (imposed) loads: people, furniture, vehicles — e.g. 1.5–2 kN/m² homes, 3–5 kN/m² offices/assembly.
• Environmental loads: wind, snow, temperature, earthquake, water and earth pressure.

Idealisation and free-body diagrams

Real structures are simplified: beams become lines, connections become pins or fixed joints, soil becomes a spring or rigid support. Isolate the body, show every load and reaction, then write equilibrium equations. The quality of the idealisation decides the quality of the answer.

Load paths and tributary areas

A slab spanning between beams sends each beam the load from half the slab on either side (its tributary width). Beams pass reactions to columns; each column collects the load of its tributary floor area on every storey above. Following the load path is how foundations get sized.

Determinacy and stability

A plane structure is statically determinate if the equations of equilibrium alone give all reactions (3 unknowns for a single body). More unknowns → indeterminate (needs deformation analysis); fewer → a mechanism that can move. Structures must be both stable and adequately restrained.

Limit-state design and load combinations

Modern codes (Eurocodes, ASCE 7/ACI/AISC, IS 456/800) check ultimate limit states (collapse) with factored loads such as 1.35G + 1.5Q, and serviceability limit states (deflection, cracking, vibration) with unfactored loads. Combination factors ψ reduce secondary variable loads when several act together.

Formulas

• Equilibrium (2D): ΣF_x = 0, ΣF_y = 0, ΣM = 0
• Self-weight of a member: w = γ · A (e.g. concrete γ ≈ 25 kN/m³)
• Area load to line load: w = q · (tributary width)
• Ultimate load combination (EN 1990): 1.35 G_k + 1.5 Q_k
• Friction limit: F ≤ μ N

Worked example: Floor beam design load

Given: Slab dead load 3 kN/m², imposed 2 kN/m²; Beam spacing (tributary width) 3 m, span 6 m

Find: Ultimate line load, reactions and maximum moment.

• G_k = 3 × 3 = 9 kN/m; Q_k = 2 × 3 = 6 kN/m
• w = 1.35 × 9 + 1.5 × 6 = 21.15 kN/m
• R = wL/2 = 63.5 kN each
• M = wL²/8 = 95.2 kN·m

Answer: w ≈ 21.2 kN/m, R ≈ 63.5 kN, M ≈ 95 kN·m

Worked example: Ladder against a wall

Given: 5 m ladder at 60°, weight 200 N (mid-length); Person 700 N at 4 m up the ladder; Smooth wall

Find: Wall reaction and friction coefficient needed at the floor.

• ΣM_floor: N_w × 5 sin 60° = 200 × 2.5 cos 60° + 700 × 4 cos 60°
• N_w = (250 + 1400)/4.33 = 381 N
• Floor friction = 381 N, normal = 900 N → μ ≥ 0.42

Answer: N_w ≈ 381 N; μ ≥ 0.42

Common mistakes

• Wrong: Forgetting self-weight of the member itself. — Right: Add γ × A of beams, slabs and walls — often the largest load in concrete structures.
• Wrong: Using characteristic loads for strength checks. — Right: Apply the code's partial factors (e.g. 1.35G + 1.5Q) for ultimate limit state.

Applications

• Building design: Load takedowns from roof to foundation for every column and wall.
• Bridges: Dead, traffic and wind loads resolved into girder and bearing reactions.
• Temporary works: Scaffolding, formwork and cranes checked by statics before use.

Key takeaways

• Identify loads, idealise, draw the FBD, apply ΣF = 0, ΣM = 0.
• Follow the load path: slab → beam → column → foundation.
• Use tributary areas for load takedowns.
• Factor loads for strength (ULS), not for deflection (SLS).

Going further

• Pattern loading: Imposed load placed on alternate spans maximises moments in continuous beams — designers check several patterns.
• Accidental & robustness: Codes require structures to survive local damage (tying forces, alternative load paths) to avoid disproportionate collapse.
• Virtual work: An energy approach that elegantly finds reactions and deflections in complex structures.