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CONCRETE INDUSTRIAL GROUND FLOOR DESIGN TO TR34 THIRD EDITION TEDDS calculation version 1.0.05

Slab detailsSlab description; slabSlab type; Fabric reinforcedSlab thickness; h = 400 mm

Reinforcement detailsCharacteristic strength of steel; fy = 500 N/mm2Fabric reinforcement to bottom of slab; A193Area of reinforcement in each direction; As = 193 mm2/mPercentage of reinforcement provided; As_percent = As / h = 0.048%

Reinforcement is within recommended limitsDiameter of reinforcement; s = 7 mmDepth of nominal cover to reinforcement; cnom = 30 mmAverage effective depth of reinforcement; d = h - cnom - s = 363 mm

Steel fabric reinforcement

dh

Slip membrane

Wearing surface

Reinforced concrete slab

Subgrade

Sub-base

Strength properties for concrete from table 9.1Characteristic compressive strength (cube); fcu = 35 N/mm2Characteristic compressive strength (cylinder); fck = 28 N/mm2Mean compressive strength (cylinder); fcm = fck + 8 N/mm2 = 36 N/mm2Mean axial tensile strength; fctm = 0.3 N/mm2 (fck / 1 N/mm2)2/3 = 2.8 N/mm2Characteristic axial tensile strength (5% fractile); fctk_0.05 = 0.7 fctm = 1.9 N/mm2Secant modulus of elasticity; Ecm = 22000 N/mm2 (fcm / 10 N/mm2)0.3 = 32 kN/mm2Characteristic flexural strength of concrete; fctk_fl = min(2, [1 + (200 mm / h)1/2]) fctk_0.05 = 3.3 N/mm2

k1 = 1 + (200 mm / d)1/2 = 1.7Minimum shear strength of concrete; vRd_ct = 0.035 N/mm2 k13/2 (fck / 1 N/mm2)1/2 = 0.4 N/mm2

Subgrade constructionModulus of subgrade reaction; k = 0.050 N/mm3

Partial safety factorsBar and fabric reinforcement; s = 1.15Reinforced concrete; c = 1.50Permanent actions; G = 1.35Variable actions; Q = 1.50Dynamic actions; D = 1.00

Properties of reinforced slabsAllowance for restraint stresses; frest = 1.5 N/mm2

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Negative moment capacity; Mn = (fctk_fl - frest) h2 / (6 c) = 32.1 kNm/mPositive moment capacity; Mp = min(0.95 As fy d / s, Mn) = 28.9 kNm/mPoissons ratio; = 0.2Radius of relative stiffness; l = [Ecm h3 / (12 (1 2) k)]1/4 = 1.376 mCharacteristic of system; = [3 k / (Ecm h3)]1/4 = 0.519 m-1

Point - Internal point load

Loading detailsNumber of point loads; N = 1Permanent point load; Gk = 0 kNVariable point load; Qk = 500 kNDynamic point load; Dk = 0 kNLength of loaded area; ll = 500 mmWidth of loaded area; lw = 500 mm

a

ll

lw

Calculate contact radius ratioEquivalent contact radius of single load; a = [(ll lw) / pi] = 282 mmRadius ratio; a / l = 0.205Ultimate capacity under single internal concentrated loadFor a / l > 0.2; Pu = 4 pi (Mp + Mn) / [1 - (a / (3 l))] = 823.3 kNCheck ultimate load capacity of slabLoading applied to slab; Fuls = F = N [(Gk G) + (Qk Q) + (Dk D)] = 750.0 kN

PASS - Ultimate capacity of slab is adequate for internal loads

Punching shear at the face of the loaded areaDesign concrete compressive strength (cylinder); fcd = fck / c = 19 N/mm2Shear factor; k2 = 0.6 [1 - (fck / 250 N/mm2)] = 0.53Length of perimeter at face of loaded area; u0 = 2 (ll + lw) = 2000 mmShear stress at face of contact area; vmax_f = 0.5 k2 fcd = 4.973 N/mm2

Maximum load capacity in punching; Pp_max = vmax_f u0 d = 3610.3 kNPASS - Maximum load capacity in punching shear at face of loaded area is adequate for internal loads

Punching shear at the critical perimeterShear factor; k1 = min(1 + (200 mm / d)0.5, 2) = 1.74Ratio of reinforcement by area in x-direction; x = As / d = 0.001Ratio of reinforcement by area in y-direction; y = As / d = 0.001Reinforcement ratio; 1 = ( x y) = 0.001Maximum shear stress at 2d from face of load; vmax_2d = 0.035 k13/2 (fck / 1 N/mm2)1/2 1 N/mm2

vmax_2d = 0.426 N/mm2

Length of perimeter at 2d from face of load; u1 = 2 (ll + lw + 2 d pipipipi) = 6562 mm

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Maximum load capacity in punching at 2d from face; Pp = vmax_2d u1 d = 1014.5 kNPASS - Maximum load capacity in punching shear at 2d from face of loaded area is adequate for internal loads

Deflection of the slabServiceability limit state load; Fsls = N (Gk + Qk + Dk) = 500 kNDeflection coefficient; c = 0.125Deflection of the slab; = c [Fsls / (k l2)] = 0.66 mm