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Section Sheet no./rev.

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Etsub M. 7/13/2024 Etsub M.

RC SLAB DESIGN
In accordance with EN1992-1-1:2004 incorporating corrigendum January 2008 and the recommended values

Design summary
Description Unit Provided Required Utilisation Result
Short span
Reinf. at midspan mm2/m 314 220 0.699 PASS
Bar spacing at midspan mm 250 300 0.833 PASS
Reinf. at support mm2/m 314 291 0.925 PASS
Bar spacing at support mm 250 269 0.929 PASS
Shear at cont. supp kN/m 64.2 31.1 0.485 PASS
Shear at discont. supp kN/m 64.6 22.6 0.350 PASS
Deflection ratio 40.00 42.25 0.947 PASS
Long span
Reinf. at midspan mm2/m 251 204 0.813 PASS
Bar spacing at midspan mm 200 297 0.674 PASS
Reinf. at support mm2/m 335 270 0.806 PASS
Bar spacing at support mm 150 299 0.502 PASS
Shear at cont. supp kN/m 60.2 31.1 0.517 PASS
Cover
Min cover top mm 20 20 1.000 PASS
Min cover bottom mm 20 20 1.000 PASS

Slab definition
;
Type of slab; Two way spanning with restrained edges
Overall slab depth; h = 170 mm
Shorter effective span of panel; lx = 5800 mm
Longer effective span of panel; ly = 6000 mm
Support conditions; One long edge discontinuous
Top outer layer of reinforcement; Short span direction
Bottom outer layer of reinforcement; Short span direction
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Loading
Characteristic permanent action; Gk = 5.0 kN/m2
Characteristic variable action; Qk = 2.0 kN/m2
Partial factor for permanent action; γG = 1.35
Partial factor for variable action; γQ = 1.50
Quasi-permanent value of variable action; ψ2 = 0.30
Design ultimate load; q = γG × Gk + γQ × Qk = 9.8 kN/m2
Quasi-permanent load; qSLS = 1.0 × Gk + ψ2 × Qk = 5.6 kN/m2

Concrete properties
Concrete strength class; C20/25
Characteristic cylinder strength; fck = 20 N/mm2
Partial factor (Table 2.1N); γC = 1.50
Compressive strength factor (cl. 3.1.6); αcc = 1.00
Design compressive strength (cl. 3.1.6); fcd = 13.3 N/mm2
Mean axial tensile strength (Table 3.1); fctm = 0.30 N/mm2 × (fck / 1 N/mm2)2/3 = 2.2 N/mm2
Maximum aggregate size; dg = 20 mm
Effective strength factor – exp.3.21; η = 1.00
Effect. compr. zone height factor – exp.3.19; λ = 0.80
Ultimate strain - Table 3.1; εcu2 = 0.0035
Shortening strain - Table 3.1; εcu3 = 0.0035
K1 = 0.44
K2 = 1.25 × (0.6 + 0.0014/εcu2) = 1.25
Design value modulus of elasticity reinf – 3.2.7(4) Es = 200000 N/mm2
Reinforcement properties
Characteristic yield strength; fyk = 400 N/mm2
Partial factor (Table 2.1N); γS = 1.15
Design yield strength (fig. 3.8); fyd = fyk / γS = 347.8 N/mm2

Concrete cover to reinforcement

Nominal cover to outer top reinforcement; cnom_t = 20 mm
Nominal cover to outer bottom reinforcement; cnom_b = 20 mm
Fire resistance period to top of slab; Rtop = 60 min
Fire resistance period to bottom of slab; Rbtm = 60 min
Axia distance to top reinft (Table 5.8); afi_t = 10 mm
Axia distance to bottom reinft (Table 5.8); afi_b = 10 mm
Min. top cover requirement with regard to bond; cmin,b_t = 10 mm
Min. btm cover requirement with regard to bond; cmin,b_b = 10 mm
Reinforcement fabrication; Not subject to QA system
Cover allowance for deviation; ∆cdev = 10 mm
Min. required nominal cover to top reinft; cnom_t_min = 20.0 mm
Min. required nominal cover to bottom reinft; cnom_b_min = 20.0 mm
PASS - There is sufficient cover to the top reinforcement
PASS - There is sufficient cover to the bottom reinforcement
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Etsub M. 7/13/2024 Etsub M.

Reinforcement design at midspan in short span direction (cl.6.1)

Bending moment coefficient; βsx_p = 0.0321
Design bending moment; Mx_p = βsx_p × q × lx2 = 10.5 kNm/m
Reinforcement provided; 10 mm dia. bars at 250 mm centres
Area provided; Asx_p = 314 mm2/m
Effective depth to tension reinforcement; dx_p = h - cnom_b - φx_p / 2 = 145.0 mm
K factor; K = Mx_p / (b × dx_p2 × fck) = 0.025
Redistribution ratio; δ = 1.0
K’ factor; K’ = (2 × η × αcc / γC) × (1 - λ × (δ - K1) / (2 × K2)) × (λ × (δ - K1) / (2 × K2)) =
0.196
K < K' - Compression reinforcement is not required
Lever arm; z = min(0.95 × dx_p, dx_p/2 × [1 + (1 - 2 × K / (η × αcc / γC))0.5]) = 137.8 mm
Area of reinforcement required for bending; Asx_p_m = Mx_p / (fyd × z) = 220 mm2/m
Minimum area of reinforcement required; Asx_p_min = max(0.26 × (fctm/fyk) × b × dx_p, 0.0013×b×dx_p) = 208 mm2/m
Area of reinforcement required; Asx_p_req = max(Asx_p_m, Asx_p_min) = 220 mm2/m
PASS - Area of reinforcement provided exceeds area required
Check reinforcement spacing
Reinforcement service stress; σsx_p = (fyk / γS) × min((Asx_p_m/Asx_p), 1.0) × qSLS / q = 139.6 N/mm2
Maximum allowable spacing (Table 7.3N); smax_x_p = 300 mm
Actual bar spacing; sx_p = 250 mm
PASS - The reinforcement spacing is acceptable
Reinforcement design at midspan in long span direction (cl.6.1)
Bending moment coefficient; βsy_p = 0.0280
Design bending moment; My_p = βsy_p × q × lx2 = 9.2 kNm/m
Reinforcement provided; 8 mm dia. bars at 200 mm centres
Area provided; Asy_p = 251 mm2/m
Effective depth to tension reinforcement; dy_p = h - cnom_b - φx_p - φy_p / 2 = 136.0 mm
K factor; K = My_p / (b × dy_p2 × fck) = 0.025
Redistribution ratio; δ = 1.0
K’ factor; K’ = (2 × η × αcc / γC) × (1 - λ × (δ - K1) / (2 × K2)) × (λ × (δ - K1) / (2 × K2)) =
0.196
K < K' - Compression reinforcement is not required
Lever arm; z = min(0.95 × dy_p, dy_p/2 × [1 + (1 - 2 × K / (η × αcc / γC))0.5]) = 129.2 mm
Area of reinforcement required for bending; Asy_p_m = My_p / (fyd × z) = 204 mm2/m
Minimum area of reinforcement required; Asy_p_min = max(0.26 × (fctm/fyk) × b × dy_p, 0.0013×b×dy_p) = 195 mm2/m
Area of reinforcement required; Asy_p_req = max(Asy_p_m, Asy_p_min) = 204 mm2/m
PASS - Area of reinforcement provided exceeds area required
Check reinforcement spacing
Reinforcement service stress; σsy_p = (fyk / γS) × min((Asy_p_m/Asy_p), 1.0) × qSLS / q = 162.4 N/mm2
Maximum allowable spacing (Table 7.3N); smax_y_p = 297 mm
Actual bar spacing; sy_p = 200 mm
PASS - The reinforcement spacing is acceptable
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Etsub M. 7/13/2024 Etsub M.

Reinforcement design at continuous support in short span direction (cl.6.1)

Bending moment coefficient; βsx_n = 0.0424
Design bending moment; Mx_n = βsx_n × q × lx2 = 13.9 kNm/m
Reinforcement provided; 10 mm dia. bars at 250 mm centres
Area provided; Asx_n = 314 mm2/m
Effective depth to tension reinforcement; dx_n = h - cnom_t - φx_n / 2 = 145.0 mm
K factor; K = Mx_n / (b × dx_n2 × fck) = 0.033
Redistribution ratio; δ = 1.0
K’ factor; K’ = (2 × η × αcc / γC) × (1 - λ × (δ - K1) / (2 × K2)) × (λ × (δ - K1) / (2 × K2)) =
0.196
K < K' - Compression reinforcement is not required
Lever arm; z = min(0.95 × dx_n, dx_n/2 × [1 + (1 - 2 × K / (η × αcc / γC))0.5]) = 137.8 mm
Area of reinforcement required for bending; Asx_n_m = Mx_n / (fyd × z) = 291 mm2/m
Minimum area of reinforcement required; Asx_n_min = max(0.26 × (fctm/fyk) × b × dx_n, 0.0013×b×dx_n) = 208 mm2/m
Area of reinforcement required; Asx_n_req = max(Asx_n_m, Asx_n_min) = 291 mm2/m
PASS - Area of reinforcement provided exceeds area required
Check reinforcement spacing
Reinforcement service stress; σsx_n = (fyk / γS) × min((Asx_n_m/Asx_n), 1.0) × qSLS / q = 184.8 N/mm2
Maximum allowable spacing (Table 7.3N); smax_x_n = 269 mm
Actual bar spacing; sx_n = 250 mm
PASS - The reinforcement spacing is acceptable
Reinforcement design at continuous support in long span direction (cl.6.1)
Bending moment coefficient; βsy_n = 0.0370
Design bending moment; My_n = βsy_n × q × lx2 = 12.1 kNm/m
Reinforcement provided; 8 mm dia. bars at 150 mm centres
Area provided; Asy_n = 335 mm2/m
Effective depth to tension reinforcement; dy_n = h - cnom_t - φx_n - φy_n / 2 = 136.0 mm
K factor; K = My_n / (b × dy_n2 × fck) = 0.033
Redistribution ratio; δ = 1.0
K’ factor; K’ = (2 × η × αcc / γC) × (1 - λ × (δ - K1) / (2 × K2)) × (λ × (δ - K1) / (2 × K2)) =
0.196
K < K' - Compression reinforcement is not required
Lever arm; z = min(0.95 × dy_n, dy_n/2 × [1 + (1 - 2 × K / (η × αcc / γC))0.5]) = 129.2 mm
Area of reinforcement required for bending; Asy_n_m = My_n / (fyd × z) = 270 mm2/m
Minimum area of reinforcement required; Asy_n_min = max(0.26 × (fctm/fyk) × b × dy_n, 0.0013×b×dy_n) = 195 mm2/m
Area of reinforcement required; Asy_n_req = max(Asy_n_m, Asy_n_min) = 270 mm2/m
PASS - Area of reinforcement provided exceeds area required
Check reinforcement spacing
Reinforcement service stress; σsy_n = (fyk / γS) × min((Asy_n_m/Asy_n), 1.0) × qSLS / q = 161.0 N/mm2
Maximum allowable spacing (Table 7.3N); smax_y_n = 299 mm
Actual bar spacing; sy_n = 150 mm
PASS - The reinforcement spacing is acceptable
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Etsub M. 7/13/2024 Etsub M.

Shear capacity check at short span continuous support

Shear force; Vx_n = 1.1 × q × lx / 2 = 31.1 kN/m
Effective depth factor (cl. 6.2.2); k = min(2.0, 1 + (200 mm / dx_n)0.5) = 2.000
Reinforcement ratio; ρl = min(0.02, Asx_n / (b × dx_n)) = 0.0022
Minimum shear resistance (Exp. 6.3N); VRd,c_min = 0.035 N/mm2 × k1.5 × (fck / 1 N/mm2)0.5 × b × dx_n
VRd,c_min = 64.2 kN/m
Shear resistance constant (cl. 6.2.2); CRd,c = 0.18 N/mm2 / γC = 0.12 N/mm2
Shear resistance (Exp. 6.2a);
VRd,c_x_n = max(VRd,c_min, CRd,c × k × (100 × ρl × (fck / 1 N/mm2))0.333 × b × dx_n) = 64.2 kN/m
PASS - Shear capacity is adequate
Shear capacity check at long span continuous support
Shear force; Vy_n = 1.1 × q × lx / 2 = 31.1 kN/m
Effective depth factor (cl. 6.2.2); k = min(2.0, 1 + (200 mm / dy_n)0.5) = 2.000
Reinforcement ratio; ρl = min(0.02, Asy_n / (b × dy_n)) = 0.0025
Minimum shear resistance (Exp. 6.3N); VRd,c_min = 0.035 N/mm2 × k1.5 × (fck / 1 N/mm2)0.5 × b × dy_n
VRd,c_min = 60.2 kN/m
Shear resistance constant (cl. 6.2.2); CRd,c = 0.18 N/mm2 / γC = 0.12 N/mm2
Shear resistance (Exp. 6.2a);
VRd,c_y_n = max(VRd,c_min, CRd,c × k × (100 × ρl × (fck / 1 N/mm2))0.333 × b × dy_n) = 60.2 kN/m
PASS - Shear capacity is adequate
Shear capacity check at short span discontinuous support
Shear force; Vx_d = 0.8 × q × lx / 2 = ;22.6; kN/m;
Reinforcement provided; 8 mm dia. bars at 200 mm centres
Area provided; Asx_d = 251 mm2/m
Effective depth; dx_d = h - cnom_b - φx_d / 2 = ;146.0; mm
Effective depth factor; k = min(2.0, 1 + (200 mm / dx_d)0.5) = 2.000
Reinforcement ratio; ρl = min(0.02, Asx_d / (b × dx_d)) = 0.0017
Minimum shear resistance; VRd,c_min = 0.035 N/mm2 × k1.5 × (fck / 1 N/mm2)0.5× b × dx_d
VRd,c_min = 64.6 kN/m
Shear resistance constant (cl. 6.2.2); CRd,c = 0.18 N/mm2 / γC = 0.12 N/mm2
Shear resistance;
VRd,c_x_d = max(VRd,c_min, CRd,c × k × (100 × ρl × (fck/1 N/mm2))0.333 × b × dx_d) = 64.6 kN/m
PASS - Shear capacity is adequate (0.350)
Basic span-to-depth deflection ratio check (cl. 7.4.2)
Reference reinforcement ratio; ρ0 = (fck / 1 N/mm2)0.5 / 1000 = 0.0045
Required tension reinforcement ratio; ρ = max(0.0035, Asx_p_req / (b × dx_p)) = 0.0035
Required compression reinforcement ratio; ρ’ = Ascx_p_req / (b × dx_p) = 0.0000
Stuctural system factor (Table 7.4N); Kδ = 1.3
Basic limit span-to-depth ratio (Exp. 7.16);
ratiolim_x_bas = Kδ × [11 +1.5×(fck/1 N/mm2)0.5×ρ0/ρ + 3.2×(fck/1 N/mm2)0.5×(ρ0/ρ -1)1.5] = 28.17
Mod span-to-depth ratio limit;
ratiolim_x = min(1.5, (500 N/mm2/ fyk) × (Asx_p / Asx_p_m)) × ratiolim_x_bas = 42.25
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Actual span-to-eff. depth ratio; ratioact_x = lx / dx_p = 40.00

PASS - Actual span-to-effective depth ratio is acceptable

Reinforcement summary
Midspan in short span direction; 10 mm dia. bars at 250 mm centres B1
Midspan in long span direction; 8 mm dia. bars at 200 mm centres B2
Continuous support in short span direction; 10 mm dia. bars at 250 mm centres T1
Continuous support in long span direction; 8 mm dia. bars at 150 mm centres T2
Discontinuous support in short span direction; 8 mm dia. bars at 200 mm centres B1

Reinforcement sketch
The following sketch is indicative only. Note that additional reinforcement may be required in accordance with clauses 9.2.1.2,
9.2.1.4 and 9.2.1.5 of EN 1992-1-1:2004 to meet detailing rules.