Reinforced concrete beam serviceability to SIA 262

Checks a rectangular or T-shaped reinforced concrete beam under uniform, partial and point loads in service, to SIA 262:2025: the moments of the load combinations, concrete compression and creep, bar stresses and crack control, crack width, long-term deflection with cracking, creep and shrinkage, finishes, comfort and natural frequency. Every step shows its formula and the clause it comes from.

What it checks

• Load combinations: the self-weight g₁ = γ_RC · A_c is added to the loads entered; for each combination, ΣF, R_A, R_B, M_A = −η_A · M_0,max, M_max at x_M and M_B = −η_B · M_0,max, then M_qp, M_fr and M_ra at the critical sections.
• Effective flange width of a T-section: b_eff = b_w + Σ min(0.2 · b_i + 0.1 · l₀ ; 0.2 · l₀ ; b_i), clause 4.1.3.3.2, equations (19) and (20), with l₀ read from the moment diagram (4.1.3.3.3), for the span and for the support.
• Cracking moments M_cr and M′_cr (4.2.1.14), with f_ct,eff = k_t · f_ctm, clause 4.4.1.3, equations (99) and (100).
• Concrete compression, check 1: σ_c,qp ≤ 0.6 · f_cm (3.1.2.6.3). Above 0.4 · f_cm the creep coefficient is raised by β_σc = e^(1.5 · (σ_c/f_cm − 0.4)), equation (14).
• Bar stresses in the span and over the support against σ_s,adm = √(9 · E_s · f_ctm · w_nom / Ø_s) ≤ f_yk, clause 4.4.2.3.4, equation (102), with w_nom from Table 17: at first cracking (minimum reinforcement, 4.4.2.3.3) and under the quasi-permanent load.
• No yielding: σ_s,ra ≤ f_yd − 80 N/mm² under the characteristic combination (Table 17).
• Crack width (optional) to EN 1992-1-1 §7.3.4, equations (7.8) to (7.11), against w_max.
• Deflection: w_c (4.4.3.2.4), the estimates w_cφ = w_c · (1 + φ), equation (103), and w₁₀₄, equation (104), and a detailed calculation of the curvatures along the span to EN 1992-1-1 §7.4.3, equations (7.18) to (7.21).
• Deflection limits (4.4.3.2.1): w_∞ for appearance, Δw = w_∞ − w_g1,0 for finishes and partitions, and the frequent part ψ₁ · q_k for comfort.
• Natural frequency f₁ ≥ f_min (4.4.4.2), from the Rayleigh quotient of the static deflection curve.

What you enter and what you get

You enter the static system (simply supported, fixed at one or both ends, or a span of a continuous member with the support moments η_A and η_B as fractions of M₀, the largest moment of the same loads on a simple span), the span l, the section and its bars, the materials and the creep and shrinkage data. You enter up to five uniform loads, each on the whole span or on a part of it, and up to five point loads at x₁, each with a permanent and a variable part (g_2,1 and q₁, G₁ and Q₁ for the first), then ψ₁ and ψ₂, and whether the beam is cast in one piece or made continuous after its self-weight acts. Then the requirement level, the crack width option and the deflection limits as fractions of the span.

You get φ and ε_cs, the section stiffnesses, the support forces and moments of each load combination, the moments at the critical sections, every check with its utilisation and clause, and both deflection estimates. With the Basic plan, it prints as an A4 calculation note.

Assumptions and limits

• Moments come from an elastic, uncracked analysis; the redistribution caused by cracking is not followed.
• η_A and η_B apply to every load combination: take them from an elastic analysis of the continuous member under a similar layout of the loads.
• The bottom bars are assumed to run to the supports. For the support section, the adjacent span is assumed similar.
• φ follows EN 1992-1-1 Annex B and ε_cs EN 1992-1-1 §3.1.4, or your own values. Shrinkage can be left out.
• The creep model is valid up to 0.6 · f_cm; SIA 262 gives none above.
• Equation (104) is an upper bound (4.4.3.2.6). The detailed calculation is the detailed study of 4.4.3.2.3.
• For finishes, the creep under g₁ before they are placed is counted as occurring after, on the safe side.
• For a beam made continuous after loading, creep builds up part of the support moments, computed with the age-adjusted effective modulus.

Worked example

A T-beam 600 mm deep, b_w = 300 mm, h_f = 240 mm, end span of a continuous member with l = 7 m, 4Ø20 at the bottom, 8Ø20 over the support, f_ck = 30 N/mm², a uniform load on the whole span of g_2,1 = 18 kN/m and q₁ = 10 kN/m, a point load at x₁ = 3.5 m of G₁ = 10 kN and Q₁ = 4 kN, increased requirements and w_max = 0.3 mm. These are the module's own results for its worked example, computed when this page was built.

How this module is verified

Verified clause by clause against SIA 262:2025 and against independent calculations used on real projects, before release.

Questions

Why is the creep coefficient raised in the worked example?

The quasi-permanent compression at the support exceeds 0.4 · f_cm, so creep is no longer linear. φ is multiplied by β_σc = 1.118 for the deflection (3.1.2.6.3).

Which deflection is used in the checks?

You choose. The detailed calculation follows the curvatures along the span. The SIA estimate takes equation (103) when the span stays uncracked, otherwise equation (104). Both are always shown.

Which plan includes this module?

The Basic plan, with its calculation note.

Related

• Concrete section in simple bending
• Concrete slab serviceability
• Concrete beams: all modules
• SIA 262: modules and clauses

Norm: SIA 262:2025 · Page updated: 5 November 2026