IS 456:2000 Beam Design Worked Example — Real Software Output, Not Illustrative Numbers

Most “worked examples” published by structural-software vendors are illustrative: rounded numbers, a tidy $M_u \approx M_{u,\text{provided}}$, no messy edge cases. This one isn’t. Every number below — the required steel area, the stirrup spacing, the development length, the bar bending schedule weights — is the literal output of a real Civora runCoordinatedBeamDesign execution against a real IS 456:2000 beam project. You can reproduce this exact run yourself: open it live in Civora →.

1. Problem Statement

A rectangular RC beam spans 5.0 m between two simply supported bearings (pinned / roller idealization, 230mm bearing width each), carrying a uniformly distributed service dead load of 15.0 kN/m and a service live load of 10.0 kN/m.

This is the exact input set behind the ?example=beam-is456-annexg deep link — you’re reading the same beam Civora’s own onboarding flow builds.

2. Load Takedown (Clause 18.2.3.1 / Clause 36.4.1)

IS 456’s Limit State of Collapse combines dead and live load with a single partial safety factor:

$w_u = 1.5\,(w_{DL} + w_{LL}) = 1.5 \times (15.0 + 10.0) = 37.5\text{ kN/m}$

(IS 456:2000 Table 18 / Clause 36.4.1 — Load Combination 1.5(DL+LL); this factored line load is exactly the value the beam’s setup was built with — self-weight was folded into the given dead load rather than iterated separately for this example.)

Design actions on a simply supported span under uniform load:

$M_u = \frac{w_u L^2}{8} = \frac{37.5 \times 5.0^2}{8} = 117.1875\text{ kN}\cdot\text{m}$ $V_u = \frac{w_u L}{2} = \frac{37.5 \times 5.0}{2} = 93.75\text{ kN}$

Both figures are read directly off Civora’s structural analysis envelope for this beam — $M_u$ at midspan, $V_u$ at the support face.

3. Step-by-Step Flexural Design (IS 456:2000 Annex G.1.1)

3.1 Effective depth (reconciled, not assumed)

Civora doesn’t take the nominal cover/stirrup/bar hints at face value — it reconciles the effective depth against whatever stirrup and bar sizes the shear and longitudinal-selection stages actually adopt. For this run:

$d = D - c_{nom} - \phi_{stirrup} - \frac{\phi_{bar}}{2} = 450 - 30 - 10 - \frac{25}{2} = 397.5\text{ mm}$

3.2 Limiting neutral axis depth ratio

$\frac{x_{u,max}}{d} = \frac{700}{1100 + 0.87 f_y} = \frac{700}{1100 + 0.87(415)} = 0.4791 \qquad \textit{(IS 456:2000 Annex G.1.1)}$

$x_{u,max} = 0.4791 \times 397.5 = 190.4\text{ mm}$

3.3 Limiting moment of resistance

$M_{u,lim} = 0.36\,f_{ck}\,b\,x_{u,max}\,(d - 0.42\,x_{u,max}) = 125.17\text{ kN}\cdot\text{m} \qquad \textit{(Annex G.1.1)}$

Since $M_u = 117.19\text{ kN·m} < M_{u,lim} = 125.17\text{ kN·m}$, a singly-reinforced section is valid — no compression steel required.

3.4 Required tension steel

$A_{st} = \frac{0.5\,f_{ck}}{f_y}\left[1 - \sqrt{1 - \frac{4.6\,M_u}{f_{ck}\,b\,d^2}}\right] b\,d = 997.7\text{ mm}^2 \qquad \textit{(Annex G.1.1)}$

3.5 Minimum steel check (Clause 26.5.1.1)

$A_{st,min} = \frac{0.85\,b\,d}{f_y} = \frac{0.85 \times 230 \times 397.5}{415} = 187.3\text{ mm}^2 < 997.7\text{ mm}^2$

Flexural demand governs, not the code minimum.

3.6 Neutral axis check (Clause 38.1)

$x_u = \frac{0.87\,f_y\,A_{st}}{0.36\,f_{ck}\,b} = 174.01\text{ mm}$

$\frac{x_u}{x_{u,max}} = \frac{174.01}{190.4} = 0.914 < 1.0$

(Under-reinforced, ductile — Pass ✓)

Back-substituting confirms internal consistency: $M_u(A_{st}=997.7\text{mm}^2) = 116.86\text{ kN·m}$, matching the $117.19\text{ kN·m}$ demand to within $0.3\%$ (the residual is the numerical gap between the closed-form quadratic in §3.4 and the direct $x_u$ recomputation in §3.6 — not a design shortfall).

4. Detailing

4.1 Bar selection — bottom (flexural) steel

$A_{st,req} = 997.7\text{ mm}^2$ doesn’t divide evenly into standard metric bar sizes at 3 bars across a 230mm web. Civora’s longitudinal-selection engine picked 3 × T25 ($A_{st,prov} = 1{,}472.6\text{ mm}^2$) over 3×T20 (942.5mm² — short of the requirement) as the smallest constructible arrangement, at 37.5mm clear spacing and a reinforcement centroid 52.5mm from the bottom fibre (which is exactly what reconciles $d = 450 - 52.5 = 397.5\text{ mm}$ above).

This is worth sitting with. $1{,}472.6\text{ mm}^2$ provided is $48\%$ over the $997.7\text{ mm}^2$ required — because the balanced steel area at $x_{u,max}$ is only:

$A_{st,bal} = \frac{0.36\,f_{ck}\,b\,x_{u,max}}{0.87\,f_y} = 1{,}091.6\text{ mm}^2$

Provided steel ($1{,}472.6\text{mm}^2$) exceeds this limit, not just the required minimum — meaning the section’s real flexural capacity is capped at $M_{u,lim} = 125.17\text{ kN·m}$ (§3.3), not something that scales further with the extra bar area. Demand-vs-capacity for this beam is therefore $M_u / M_{u,lim} = 117.19 / 125.17 = 0.936$, not the naive (and invalid) figure you’d get by plugging $1{,}472.6\text{mm}^2$ back into the Clause 38.1 linear formula. See §9 for why this happens and how to catch it.

4.2 Top steel

2 × T12 nominal/hanger bars, centroid 46mm from the top fibre — construction steel to hold the stirrups, not flexure-designed (no top-face moment demand on a simply supported span under gravity load only).

4.3 Shear design (Clause 40, Table 19/20)

$\tau_v = \frac{V_u}{b\,d} = \frac{93{,}750}{230 \times 397.5} = 1.026\text{ N/mm}^2 \ll \tau_{c,max}\,(\text{Table 20}) \quad \Rightarrow \quad \text{section size adequate}$

Civora’s shear optimizer evaluated T10/T12/T16 two-legged candidates across the full span and recommended:

T10, 2-legged, @300mm centres, uniform along the span — providedAv/s = 0.5236mm²/mm against a required 0.2548mm²/mm, demand/capacity = $93.75 / 137.0 = \mathbf{0.684}$.

Torsion (Clause 41) is not triggered — $T_u = 0$ for this beam, so the interaction check is trivially satisfied.

4.4 Development length (Clause 26.2.1)

$\tau_{bd} = 1.6 \times 1.4 = 2.24\text{ N/mm}^2 \quad \textit{(M25, deformed HYSD bars, Cl 26.2.1.1)}$ $L_d = \frac{0.87\,f_y\,\phi}{4\,\tau_{bd}} = \frac{0.87 \times 415 \times 25}{4 \times 2.24} = 1{,}007.4\text{ mm}$

The bottom bars run uncurtailed the full span, giving 2,500mm of available embedment past the critical section on each side — more than double what’s required. Verified, not marginal.

4.5 Side-face reinforcement (Clause 26.5.1.3)

$D = 450\text{ mm} \le 750\text{ mm} \quad \Rightarrow \quad \textbf{not required}$

Civora’s own engine trace confirms this explicitly rather than silently skipping the check: “IS 456:2000 Cl 26.5.1.3 (not triggered: D ≤ 750mm)”.

5. Bar Bending Schedule

Stirrup mark ST1’s 1,080mm centreline length comes straight from the section geometry: four legs of 160mm/380mm/160mm/380mm around the 230×450mm perimeter, less cover, with four 90° bends — this is the actual rectangular stirrup shape Civora’s fabrication engine computed, not a rule-of-thumb “perimeter minus cover” estimate.

6. Section Drawing

(Cover, bar sizes, and centroid depths are drawn to the real reconciled values from §4 — 30mm clear cover, 397.5mm effective depth, 52.5mm and 46mm bar-centroid offsets.)

7. Demand vs. Capacity Summary

Deflection is deliberately not included in this table — see §10.

8. Cross-Code Comparison: IS 456 vs. ACI 318-19 vs. Eurocode 2

Same beam. Same 230×450mm section, M25/25MPa concrete, Fe415/415MPa steel, 15kN/m dead + 10kN/m live service load. The only thing that changes below is which code’s own load-factor combination and design mechanics are applied:

Why they differ: the load-factor philosophy alone spans a $10.5\%$ range in factored moment (106.25 → 117.19 kN·m) from identical service loads, before any difference in flexural stress-block mechanics enters the picture. That demand spread cascades downstream — IS 456’s higher $M_u$ is what pushes bar selection from 3-T20 up to 3-T25. And EC2’s own governing shear check for this identical section lands at $\text{D/C} = 0.993$ — the tightest of the three — because EC2’s variable-strut-inclination method (§6.2.3) doesn’t credit shear reinforcement below the concrete-alone threshold $V_{Rd,c}$ the way ACI’s and IS 456’s continuous $V_c + V_s$ formulas do; near mid-span, where demand drops under $V_{Rd,c}$, EC2 reports capacity as concrete-alone, which is the binding case for this beam’s uniform-spacing zone.

9. Common Mistakes

Checking $A_{st,req}$ against the code minimum but not against the balanced limit. As §4.1 showed, rounding a required steel area up to standard bar sizes can silently push the provided area past $A_{st,bal}$ (the area at $x_{u,max}$) even while comfortably satisfying $A_{st,min}$. When that happens, capacity caps at $M_{u,lim}$ — extra bar area beyond the balanced point doesn’t buy extra moment capacity. Always re-check $x_u$ against $x_{u,max}$ using the as-provided steel, not just the theoretical required area.

Checking development length against half the bar length instead of the actual embedment. For an uncurtailed bar running the full span, available anchorage past any interior section is the distance to the nearer bar end — not some fraction of span assumed by habit.

Applying side-face reinforcement out of habit. Clause 26.5.1.3 only triggers above $D = 750\text{mm}$. This 450mm beam doesn’t need it — adding it anyway wastes steel and clutters the bar schedule.

Reusing a detailing “starter” stirrup diameter as the final design value. An 8mm nominal hint is common in setup forms, but constructible candidate generation here excluded anything under 10mm — check what the optimizer actually recommends, not what you typed in as a starting guess.

10. Known Coverage Gaps (Disclosed, Not Hidden)

Three checks in this pipeline are not yet code-branched the way flexure, shear, development length, and side-face reinforcement are above:

1. Hooked-bar development length and curtailment/cutoff extensions remain ACI 318-19-only regardless of the selected design code — the generated PDF report’s own disclosure banner states this plainly rather than silently applying ACI mechanics under an IS 456 label.
2. EC2 skin/side-face reinforcement (the Eurocode equivalent of IS 456 Cl 26.5.1.3 / ACI §9.7.2.3) is not yet evaluated.
3. Deflection is currently computed via an ACI 318-19-specific formula (§24.2.2 / §24.2.3.5 / §24.2.4.1.1) regardless of design code. For this exact beam at its real 450mm trial depth, that ACI-based check fails ($25.6\text{mm}$ computed against a $10.4\text{mm}$ allowable) — but since the formula hasn’t been branched to IS 456 Clause 23.2, that result isn’t a validated IS 456 deflection outcome, and it’s intentionally left out of §7’s demand/capacity table rather than presented as one.

11. Regional Practice Notes

India: IS 456’s Limit State Method is the baseline most municipal building byelaws point to (via the National Building Code), and Fe415/Fe500 HYSD bars are near-universal on new RC construction. Table 16’s 30mm clear cover for moderate exposure — used throughout this example — is standard for enclosed, non-coastal urban framing; severe/marine exposure classes require more.

Gulf / South Asia cross-border projects: several regional authorities accept IS 456-designed structural packages for India-affiliated consultants while requiring ACI 318 stamps for others on the same project — which is exactly the scenario §8’s cross-code table is built for: the same beam, three governing codes, one comparison.

12. Downloads

Download the real engineering PDF for this beam (report + drawing + BBS sheets) — generated by the same CompleteBeamPdfReport.build pipeline the app’s own Export button calls, from this exact run. It contains the executive design-basis pages, a landscape reinforcement elevation with envelope BMD/SFD panels, and the bar bending schedule sheet behind §5 above. Beam doesn’t yet have a separate DXF export path (unlike Pile, Pile Cap, and Foundation, which do) — rather than fake one, the drawing and BBS live inside this one PDF.

Open this exact project in Civora → — the deep link hydrates the identical beam used throughout this post, so you can change any input and watch every number above recompute live.