📐 Steps for Design of Cantilever Beam (IS 456-2000)

Complete step-by-step procedure for RCC cantilever beam design

Reference diagram for cantilever beam

1. Basic Data

Enter the values of beam width (b), clear span (L), concrete grade (f_ck), steel grade (f_y), clear cover, superimposed load, overall depth (D), diameter of bar (φ). Calculate effective depth provided:

d_prov = D – clear cover – (φ/2)

2. Effective Span

L_eff = min of { L + (b_s/2) and L + (d/2) }

Where b_s is support width, d is effective depth.

3. Factored Shear Force (SF) & Bending Moment (BM)

Self weight of beam = b × D × unit weight of concrete (25 kN/m³ for RCC).

Factored load, w_u = 1.5 × (S.D.L + self weight)

Factored BM, M_u = (w_u × L_eff²) / 2

Factored SF, V_u = w_u × L_eff

4. Design Parameters

Find X_u,max and Q_lim as per IS 456:

X_u,max = 0.87 × f_y / (0.36 × f_ck) × d

Q_lim = 0.36 × X_u,max / d × (1 – 0.42 × X_u,max/d) × f_ck

Find effective depth required for balanced section:

d_bal = √( M_u / (Q_lim × b) )

Also check deflection criteria for cantilever beam as per IS 456 (pg-37):

(L/d)_permissible = 7 × M.F. → d_req = L / (7 × M.F.)

M.F (Modification Factor) is obtained from graph on pg-38 of IS 456 based on tension reinforcement percentage.

Check: Provided depth d_prov should be greater than both d_bal and d_req. If not, increase overall depth.

5. Area of Steel Required (A_st)

Percentage of reinforcement required:

p_t,req = 50 × f_ck / f_y × { 1 – √(1 – (4.6 × M_u) / (f_ck × b × d²)) }

A_st,req = (p_t,req × b × d) / 100

Select number of bars: A_st,provided = N × (π × φ² / 4) ≥ A_st,req

6. Design of Shear Reinforcement

Same as singly reinforced beams. Check nominal shear stress τ_v = V_u / (b×d). Provide minimum shear reinforcement as per IS 456.

τ_v ≤ τ_c,max (from Table 20, IS 456)

If τ_v > τ_c (design shear strength of concrete), provide stirrups.

Spacing = (0.87 × f_y × A_sv) / (b × (τ_v – τ_c))

7. Check for Deflection

As per IS 456-2000, to satisfy deflection criteria:

(L/d)_actual < (L/d)_permissible

(L/d)_permissible = 7 × M.F. (for cantilever beams, pg-37)

M.F is taken from graph on pg-38 of IS 456 based on p_t and f_s.

8. Check for Development Length

Same as singly reinforced beams. Ensure L_d ≤ available length at support.

L_d = (φ × 0.87 × f_y) / (4 × τ_bd)

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