Reinforced Concrete Wall Adequacy Check

1.0 INPUT DATA

1.1 Material Properties

f_cu = MPa Characteristic concrete cube strength

f_y = MPa Characteristic steel yield strength

E_s = MPa Steel modulus of elasticity

γ_c = Partial safety factor for concrete (Cl 6.1.2.4)

γ_s = Partial safety factor for steel (Cl 6.1.2.4)

1.2 Wall Geometry

c_c = mm Concrete cover

L_w = mm Wall length

t_w = mm Wall thickness

H_u = mm Unsupported height

Frame Type:

Top Condition:

Bottom Condition:

Figure 1: Wall Section

1.3 Reinforcement Details

φ_v = mm Vertical bar diameter

s_v = mm Vertical bar spacing

Layers = Number of reinforcement layers

Horizontal Reinforcement

φ_h = mm Horizontal bar diameter

s_h = mm Horizontal bar spacing

1.4 Applied Loads (ULS)

N_Ed = kN Design axial force

M_u2x = kNm In-plane moment (larger end moment)

M_u1y = kNm Out-of-plane moment (smaller end moment)

M_u2y = kNm Out-of-plane moment (larger end moment)

2.0 CALCULATIONS

2.1 Geometry Check

Effective length factor (Table 6.13)

k = 0.80 (Based on end conditions)

H_e = k × H_u

H_e = 0.80×5825 = 4660.00 mm

Wall classification

L_w/t_w = 1200/250 = 4.80

Is Wall: YES (L_w/t_w > 4 per Cl 1.4.4)

2.2 Slenderness Check (Cl 6.2.2)

Slenderness ratio

λ = H_e/t_w

λ = 4660/250 = 18.64

λ_limit = 45 (Table 6.15)

Check λ: PASS (λ = 18.64 ≤ 45)

Short vs Slender Check (Cl 6.2.2.3)

Wall Type: SLENDER (λ = 18.64 > 15)

2.3 Minimum Reinforcement (Cl 9.6)

Concrete area

A_c = L_w × t_w

A_c = 1200×250 = 300000 mm²

Provided reinforcement

A_{s,per m} = (Layers×π×φ_v²/4)×(1000/s_v)

A_{s,per m} = 2×π×20²/4×(1000/125) = 502.65 mm²/m

A_s,total = A_{s,per m} × (L_w/1000)

A_s,total = 502.65×1.2 = 603.19 mm²

Reinforcement ratio

ρ = A_s,total × 100/(L_w × t_w)

ρ = 603.19×100/(1200×250) = 0.201 %

Min Reinforcement Check: PASS (ρ = 0.201% > 0.40% and ≤ 4.0%)

2.4 Second-Order and Minimum Moments

Additional moment factor (Cl 6.2.1.4)

β_a = (1/2000) × λ²

β_a = (1/2000)×18.64² = 0.174

Curvature correction factor K (Cl 6.2.1.4.2)

K = min(1.0; (1.2 − N_Ed×1000/(A_c×f_cu))/0.7)

K = min(1.0; 1.2-1742×1000/(300000×45)/0.7) = 1.00

Additional moment

M_a = (N_Ed × t_w × β_a × K)/1000

M_a = 1742×250×0.174×1.00/1000 = 75.83 kNm

Minimum eccentricity (Cl 6.2.1.2)

e_min,y = max(0.05×t_w; 20)

e_min,y = max(0.05×250; 20) = 20.00 mm

e_min,x = max(0.05×L_w; 20)

e_min,x = max(0.05×1200; 20) = 60.00 mm

M_y,min = N_Ed × e_min,y/1000

M_y,min = 1742×20/1000 = 34.84 kNm

M_x,min = N_Ed × e_min,x/1000

M_x,min = 1742×60/1000 = 104.52 kNm

Combined out-of-plane moment

M_iy = max(0.4×M_u2y; 0.4×M_u1y + 0.6×M_u2y)

M_iy = max(0.4×0.50; 0.4×0.35+0.6×0.50) = 0.44 kNm

Total design moments

M_total,y = max(M_u2y; M_iy+M_a; M_u1y+M_a/2; M_y,min)

M_total,y = 76.27 kNm

M_total,x = max(M_u2x; M_x,min)

M_total,x = 448.00 kNm

2.5 Capacity Analysis - Biaxial Interaction

Idealization of Wall into 4-Bar Column for Design

Steel geometry

d₂ = c_c + φ_h + φ_v/2

d₂ = 35+10+20/2 = 55.00 mm

d = t_w − d₂

d = 250-55 = 195.00 mm

ε_cu = 0.0035

Design stresses

f_y,d = f_y/γ_s

f_y,d = 500/1.15 = 434.78 MPa

f_cu,d = 0.67×f_cu/γ_c

f_cu,d = 0.67×45/1.5 = 20.10 MPa

2.6 Out-of-Plane Capacity (M_Rd,y)

Neutral axis position (solved from equilibrium)

x_y = 87.50 mm (Limited per Cl 6.1.2.4)

Force components

F_cy = f_cu,d×L_w×min(0.9×x_y; t_w)/1000

F_cy = 1974.38 kN

F_s1y = (A_s,total/2 × min(max(ε_cu × (x_y - d₂) / x_y × E_s; -f_y,d); f_y,d)) / 1000

F_s1y = 920.24 kN

F_s2y = (A_s,total/2 × min(max(ε_cu × (x_y - d) / x_y × E_s; -f_y,d); f_y,d)) / 1000

F_s2y = -1311.27 kN

Out-of-plane moment capacity

M_Rd,y = (F_cy×(t_w/2 − 0.45×x_y) + F_s1y×(t_w/2 − d₂) + F_s2y×(t_w/2 − d))/1000

M_Rd,y = 76.27 kNm

2.7 In-Plane Capacity (M_Rd,x)

Neutral axis position (solved from equilibrium)

x_x = 343.75 mm (Limited per Cl 6.1.2.4)

Force components

F_cx = f_cu,d×t_w×min(0.9×x_x; L_w)/1000

F_cx = 1742.70 kN

F_s1x = (A_s,total/2 × min(max(ε_cu × (x_x - d₂) / x_x × E_s; -f_y,d); f_y,d)) / 1000

F_s1x = 1311.27 kN

F_s2x = (A_s,total/2 × min(max(ε_cu × (x_x - (L_w - d₂)) / x_x × E_s; -f_y,d); f_y,d)) / 1000

F_s2x = -1311.27 kN

In-plane moment capacity

M_Rd,x = (F_cx×(L_w/2 − 0.45×x_x) + F_s1x×(L_w/2 − d₂) + F_s2x×(L_w/2 − (L_w − d₂)))/1000

M_Rd,x = 448.00 kNm

2.8 Biaxial Interaction Check

Balance point capacity

N_uz = (0.35×f_cu×(A_c − A_s,total) + 0.67×f_y×A_s,total)/1000

N_uz = 0.35×45×(300000-603.19)+0.67×500×603.19/1000 = 6308.91 kN

Exponent α_n

α_n = min(2.0; max(1.0; 1.0 + (N_Ed/N_uz − 0.2)/0.6))

α_n = min(2.0; max(1.0; 1.0+(1742/6308.91-0.2)/0.6)) = 1.00

Quick biaxial interaction check

(M_total,x/M_Rd,x)^α_n + (M_total,y/M_Rd,y)^α_n

= (448.00/2172.54)^1.10 + (66.94/327.91)^1.10 = 0.35

Biaxial Check: FAIL (2.00 ≥ 1)

2.9 Biaxial Design per Clause 6.1.2.4

Interpolation factor β (Table 6.14)

N_ratio = N_Ed×1000/(A_c×f_cu)

N_ratio = 1742×1000/(300000×45) = 0.129

β = max(min(−1.16×N_ratio + 1; 1); 0.3)

β = max(min(-1.16×0.129+1; 1); 0.3) = 0.85

Effective dimensions

h' = min(0.75×L_w; L_w − d₂)

h' = min(0.75×1200; 1200-55) = 900.00 mm

b' = t_w − d₂

b' = 250-55 = 195.00 mm

Effective moment ratio check

M_total,x/h' = 448/900 = 0.498

M_total,y/b' = 76.27/195 = 0.391

Effective moment

M_eff,x = M_total,x + β×(h'/b') (X-axis dominates)

M_eff,x = 448 + 0.85×(900/195) = 722.00 kNm

Utilization ratio

Utilization = M_eff,x/M_Rd,x

Utilization = 722/448 = 1.61

Slender Wall Check: FAIL (Utilization = 1.61 ≥ 1)

Figure 2: Idealization of Wall into 4-Bar Column

2.10 Axial Capacity Check (Cl 6.5.2)

Axial capacity

N_Rd = (0.35×f_cu×(A_c − A_s,total) + 0.67×f_y×A_s,total)/1000

N_Rd = 0.35×45×(300000-603.19)+0.67×500×603.19/1000 = 6308.91 kN

Axial utilization

N_Ed/N_Rd = 1742/6308.91 = 0.276

Axial Capacity Check: PASS (N_Ed = 1742.00 kN ≤ N_Rd = 6308.91 kN)

2.11 Horizontal Reinforcement Check (Cl 9.6.3)

Required horizontal reinforcement

A_sh,min1 = 0.001×A_c

A_sh,min1 = 0.001×300000 = 300.00 mm²

A_sh,min2 = 0.25×A_s,total

A_sh,min2 = 0.25×603.19 = 150.80 mm²

A_sh,min = max(A_sh,min1; A_sh,min2)

A_sh,min = max(300; 150.80) = 300.00 mm²

Provided horizontal reinforcement

A_sh,prov = (Layers×π×φ_h²/4)×(H_e/s_h)

A_sh,prov = 2×π×10²/4×(4660/200) = 366.44 mm²

Horizontal Reinforcement: PASS (A_sh,prov = 366.44 mm² ≥ A_sh,min = 300.00 mm²)

* OUTPUT SUMMARY *

Design Summary

Wall Classification: WALL

Slenderness Ratio, λ = 18.64 ≤ 45

Wall Type: SLENDER

Effective Height, H_e = 4660.00 mm

Total Reinforcement, A_s,total = 603.19 mm²

Reinforcement Ratio, ρ = 0.201 %

Min Reinforcement Check: PASS

Additional Moment, M_a = 75.83 kNm

In-Plane Capacity, M_Rd,x = 448.00 kNm

Out-of-Plane Capacity, M_Rd,y = 76.27 kNm

Biaxial Check: FAIL

Slender Wall Utilization: 1.61

Axial Capacity: PASS

Horizontal Reinforcement: PASS

RESULTS

DESIGN CHECK - INCREASE WALL CAPACITY OR REDUCE LOADS

NOTE: ALWAYS VERIFY BI-AXIAL RESULTS USING MORE ACCURATE TOOLS LIKE Oasys AdSec or spColumn

REINFORCED CONCRETE WALL ADEQUACY CHECK

1.0 INPUT DATA

1.1 Material Properties

1.2 Wall Geometry

1.3 Reinforcement Details

1.4 Applied Loads (ULS)

2.0 CALCULATIONS

2.1 Geometry Check

2.2 Slenderness Check (Cl 6.2.2)

2.3 Minimum Reinforcement (Cl 9.6)

2.4 Second-Order and Minimum Moments

2.5 Capacity Analysis - Biaxial Interaction

2.6 Out-of-Plane Capacity (M_Rd,y)

2.7 In-Plane Capacity (M_Rd,x)

2.8 Biaxial Interaction Check

2.9 Biaxial Design per Clause 6.1.2.4

2.10 Axial Capacity Check (Cl 6.5.2)

2.11 Horizontal Reinforcement Check (Cl 9.6.3)

* OUTPUT SUMMARY *

Design Summary

RESULTS

Other Tools

1.0 INPUT DATA

1.1 Material Properties

1.2 Wall Geometry

1.3 Reinforcement Details

1.4 Applied Loads (ULS)

2.0 CALCULATIONS

2.1 Geometry Check

2.2 Slenderness Check (Cl 6.2.2)

2.3 Minimum Reinforcement (Cl 9.6)

2.4 Second-Order and Minimum Moments

2.5 Capacity Analysis - Biaxial Interaction

2.6 Out-of-Plane Capacity (MRd,y)

2.7 In-Plane Capacity (MRd,x)

2.8 Biaxial Interaction Check

2.9 Biaxial Design per Clause 6.1.2.4

2.10 Axial Capacity Check (Cl 6.5.2)

2.11 Horizontal Reinforcement Check (Cl 9.6.3)

*** OUTPUT SUMMARY ***

Design Summary

RESULTS

Other Tools

2.6 Out-of-Plane Capacity (M_Rd,y)

2.7 In-Plane Capacity (M_Rd,x)

* OUTPUT SUMMARY *