Table of Contents

Precast concrete columns are reinforced concrete columns that are cast and cured on the ground before being hoisted up and installed in their desired positions. Just like in-situ columns, precast columns are capable of resisting shear, axial force, and bending moment, however, careful attention must be paid to their connection details. The design of precast concrete columns involves the provision of adequate member size, reinforcement, and connection details to satisfy internal stresses due to externally applied loads, second-order effects, and lifting.

Different connection conditions can be adopted by different manufacturers. The foundation connection of a precast column may be achieved by allowing reinforcement bars to project from the column which is then passed through established sleeves before being filled with concrete grout. Alternatively, a base plate can be connected to the column which is then installed in position on a concrete base using bolts and nuts.

Precast columns may have corbels or nibs for supporting the beams. Alternatively, precast beam-column connections can be made using dowels or mechanical couplers.

Precast concrete columns have the following advantages over in-situ concrete construction;

- Increased speed in construction since production of precast elements can commence ahead of time
- Greater flexibility in project management and site planning due to off-site production capacity
- Improved and higher quality of concrete, dimensions, and surface finishes
- Reduction in site labour
- Reduction in formwork requirement
- Less wastage of materials

The design of precast reinforced concrete columns is carried out by a structural engineer and involves the following steps;

- Confirm all dimensions and tolerances of the column and other members.
- Analyse the structure to obtain the design bending moments, axial, and shear force
- Check for column slenderness
- Obtain the final design moments taking into account imperfections and second-order effects (if applicable)
- Provide reinforcements to satisfy bending and axial force
- Check for biaxial bending
- Check for shear
- Check that reinforcement provided satisfies bending and shear due to factory lifting
- Check that reinforcement provided satisfies bending and shear due to site pitching
- Design the connections
- Detail the column as appropriate

**Worked Example on the Design of Precast Columns | EN 1992-1:2004**

Check the capacity of a 4.5m high 450 x 250 mm precast column to resist the action effects given below. The column is reinforced with 6 numbers of H20 mm bars. f_{ck} = 35 N/mm^{2}; f_{yk} = 500 N/mm^{2}; Concrete cover = 35 mm. The design has been executed using Tekla Tedds software.

**Axial load and bending moments from frame analysis**

Design axial load; N_{Ed} = 1350.0 kN

Moment about y-axis at top; M_{top,y} = 55.0 kNm

Moment about y-axis at bottom; M_{btm,y} = 22.0 kNm

Moment about z-axis at top; M_{top,z} = 11.4 kNm

Moment about z-axis at bottom; M_{btm,z} = 5.5 kNm

**Column geometry**

Overall depth (perpendicular to y-axis); h = **450** mm

Overall breadth (perpendicular to z-axis); b = **250**; mm

Stability in the z-direction; **Braced**

Stability in the y-direction; **Braced**

**Concrete details**

Concrete strength class; C30/37

Partial safety factor for concrete (2.4.2.4(1)); γ_{C} = **1.50**

Coefficient α_{cc} (3.1.6(1)); α_{cc} = **0.85**

Maximum aggregate size; d_{g} = **20** mm

**Reinforcement details**

Nominal cover to links; c_{nom} = **35** mm

Longitudinal bar diameter; ϕ = **20** mm

Link diameter; ϕ_{v} = **8** mm

Total number of longitudinal bars; N = **6**

No. of bars per face parallel to y-axis; N_{y} = **2**

No. of bars per face parallel to z axis; N_{z} = ;**3**

Area of longitudinal reinforcement; A_{s} = N × π × ϕ^{2} / 4 = **1885** mm^{2}

Characteristic yield strength; f_{yk} = **500** N/mm^{2}

Partial safety factor for reinft (2.4.2.4(1)); γ_{S} = **1.15**

E_{s} = 200000 MPa

**Column effective lengths**

Effective length for buckling about y-axis; l_{0y} = 3500 mm

Effective length for buckling about z-axis; l_{0z} =** **3900 mm

**Effective depths of bars for bending about y-axis**

Area per bar; A_{bar} = π × ϕ^{2}/4 = **314** mm^{2}

Spacing of bars in faces parallel to z-axis (centre to centre);

s_{z} = h – 2 × (c_{nom} + ϕ_{v}) – ϕ)/ (N_{z} – 1) = **172** mm

Layer 1 (in tension face); d_{y1} = h – c_{nom} – ϕ_{v} – ϕ/2 = **397** mm

Layer 2; d_{y2} = d_{y1} – s_{z} = **225** mm

Layer 3; d_{y3} = d_{y2} – s_{z} = **53** mm

2nd moment of area of reinforcement about y axis;

I_{sy} = 2 × A_{bar} × [N_{y} × (d_{y1} – h/2)^{2}] = **3718** cm^{4}

Radius of gyration of reinforcement about y-axis; i_{sy} = √(I_{sy}/A_{s}) = **140** mm

Effective depth about y axis (5.8.8.3(2)); d_{y} = h/2 + i_{sy} = **365** mm

**Effective depths of bars for bending about z-axis**

Area of per bar; A_{bar} = π × ϕ^{2} / 4 = **314** mm^{2}

Spacing of bars in faces parallel to y axis (c/c); s_{y} = (b – 2 × (c_{nom} + ϕ_{v}) – ϕ) / (N_{y} – 1) = **144** mm

Layer 1 (in tension face); d_{z1} = b – c_{nom} – ϕ_{v} – ϕ/2 = **197** mm

Layer 2; d_{z2} = d_{z1} – s_{y} = **53** mm

Effective depth about z axis; d_{z} = d_{z1} = **197** mm

**Column slenderness about y-axis**

Radius of gyration; i_{y} = h/√(12) = **13.0** cm

Slenderness ratio (5.8.3.2(1)); l_{y} = l_{0y} / i_{y} = **26.9**

**Column slenderness about z-axis**

Radius of gyration; i_{z} = b/√(12) = **7.2** cm

Slenderness ratio (5.8.3.2(1));l_{z} = l_{0z} / i_{z} = **54.0**

**Design bending moments**

**Frame analysis moments about y axis combined with moments due to imperfections (cl. 5.2 & 6.1(4))**

Eccentricity due to geometric imperfections (y axis); e_{iy} = l_{0y} /400 = **8.8** mm

Min end moment about y-axis; M_{01y} = min(|M_{topy}|, |M_{btmy}|) + e_{iy}N_{Ed} = **33.8** kNm

Max end moment about y-axis; M_{02y} = max(|M_{topy}|, |M_{btmy}|) + e_{iy}N_{Ed} = **66.8** kNm

**Slenderness limit for buckling about y axis (cl. 5.8.3.1)**

A = **0.7**

Mechanical reinforcement ratio; ω = A_{s} × f_{yd} / (A_{c} × f_{cd}) = **0.429**

Factor B; B = √(1 + 2ω) = **1.363**

Moment ratio; r_{my} = M_{01y} / M_{02y} = **0.506**

Factor C; C_{y} = 1.7 – r_{my} = **1.194**

Relative normal force; n = N_{Ed} / (A_{c} × f_{cd}) = **0.706**

Slenderness limit; l_{limy} = 20 × A × B × C_{y} / √(n) = **27.1**

l_{y} < l_{limy} – Second order effects may be ignored

**Frame analysis moments about z-axis combined with moments due to imperfections (cl. 5.2 & 6.1(4))**

Ecc. due to geometric imperfections (z axis); e_{iz} = l_{0z} /400 = **9.8** mm

Min end moment about z axis; M_{01,z} = min(|M_{topz}|, |M_{btmz}|) + e_{iz}N_{Ed} = **18.7** kNm

Max end moment about z axis; M_{02,z} = max(|M_{topz}|, |M_{btmz}|) + e_{iz}N_{Ed} = **24.5** kNm

**Slenderness limit for buckling about y-axis (cl. 5.8.3.1)**

A = 0.7

Mechanical reinforcement ratio; w = A_{s} × f_{yd} / (A_{c} × f_{cd}) = **0.429**

Factor B; B = √(1 + 2ω) = **1.363**

Moment ratio; r_{mz} = **1.000**

Factor C; C_{z} = 1.7 – r_{mz} = **0.700**

Relative normal force; n = N_{Ed} / (A_{c} × f_{cd}) = **0.706**

Slenderness limit; l_{limz} = 20 × A × B × C_{z} / √(n) = **15.9**

l_{z} > l_{limz} – Second order effects must be considered

**Design bending moments (cl. 6.1(4))**

Design moment about y axis; M_{Edy} = max(M_{02y}, N_{Ed} × max(h/30, 20 mm)) = **66.8** kNm

**Local second order bending moment about z-axis (cl. 5.8.8.2 & 5.8.8.3)**

Relative humidity of ambient environment; RH = **50** %

Column perimeter in contact with atmosphere; u = **1400** mm

Age of concrete at loading; t_{0} = **28** day

Parameter n_{u}; n_{u} = 1 + w = **1.429**

n_{bal} = 0.4

Approx value of n at max moment of resistance; n_{bal} = **0.4**

Axial load correction factor; K_{r} = min(1.0 , (n_{u} – n) / (n_{u} – n_{bal})) = **0.703**

Reinforcement design strain; ε_{yd} = f_{yd}/E_{s} = **0.00217**

Basic curvature; curve_{basic_z} = ε_{yd} / (0.45 × d_{z}) = **0.0000245** mm^{-1}

Notional size of column; h_{0} = 2 × A_{c} / u = **161** mm

Factor a_{1} (Annex B.1(1)); a_{1} = (35 MPa / f_{cm})^{0.7} = **0.944**

Factor a_{2} (Annex B.1(1)); a_{2} = (35 MPa / f_{cm})^{0.2} = **0.984**

Relative humidity factor (Annex B.1(1));

ϕ_{RH} = [1 + ((1 – RH/100%) / (0.1 mm^{-1/3} × (h_{0})^{1/3})) × a_{1}] × a_{2} = **1.838**

Concrete strength factor (Annex B.1(1));

β_{fcm} = 16.8 × (1 MPa)^{1/2} / √(f_{cm}) = **2.725**

Concrete age factor (Annex B.1(1));

β_{t0} = 1 / (0.1 + (t_{0} / 1 day)^{0.2}) = **0.488**

Notional creep coefficient (Annex B.1(1));

ϕ_{0} = ϕ_{RH} × β_{fcm} × β_{t0} = **2.446**

Final creep development factor; (at t = ∞); β_{c∞} = 1.0

Final creep coefficient (Annex B.1(1));ϕ_{∞} = ϕ_{0} × β_{c∞} = **2.446**

Ratio of SLS to ULS moments r_{Mz} (say) = **0.80**

Effective creep ratio (5.8.4(2)); f_{efz} = f_{∞} × r_{Mz} = **1.957**

Factor β; β_{z} = 0.35 + f_{ck} / 200 MPa – l_{z} / 150 = **0.140**

Creep factor; K_{ϕz} = max(1.0, 1 + β_{z} × ϕ_{efz}) = **1.273**

Modified curvature; curve_{mod_z} = K_{r} × K_{ϕz} × curve_{basic_z} = **0.0000219** mm^{-1}

Curvature distribution factor; c = **10**

Deflection; e_{2z} = curve_{mod_z} × l_{0z}^{2}/c = **33.4** mm

Nominal 2^{nd} order moment;

M_{2z} = N_{Ed} × e_{2z} = **45.1** kNm

**Design bending moment about z-axis (cl. 5.8.8.2 & 6.1(4))**

Equivalent moment from frame analysis;

M_{0ez} = max(0.6 × M_{02z} + 0.4 × M_{01z}, 0.4 × M_{02z}) = **22.2** kNm

**Design moment;**

M_{Edz} = max(M_{02z}, M_{0ez} + M_{2z}, M_{01z} + 0.5 × M_{2z}, N_{Ed }× max(b/30, 20 mm))

M_{Edz} = **67.2** kNm

**Moment capacity about y-axis with axial load (1350.0 kN)**

Moment of resistance of concrete

By iteration:

Position of neutral axis; y = **317.8** mm

Concrete compression force (3.1.7(3));

F_{yc} = h × f_{cd} × min(l_{sb} × y, h) × b = **1080.6** kN

Moment of resistance;

M_{Rdyc} = F_{yc} × [h / 2 – (min(l_{sb} × y, h)) / 2] = **105.8** kNm

**Moment of resistance of reinforcement**

Strain in layer 1; ε_{y1} = ε_{cu3} × (1 – d_{y1}/y) = **-0.00087**

Stress in layer 1; σ_{y1} = max(-1 × f_{yd}, E_{s} × ε_{y1}) = **-174.4** N/mm^{2}

Force in layer 1; F_{y1} = N_{y} × A_{bar} × σ_{y1} = **-109.6** kN

Moment of resistance of layer 1; M_{Rdy1} = F_{y1} × (h/2 – d_{y1}) = **18.8** kNm

Strain in layer 2; ε_{y2} = ε_{cu3} × (1 – d_{y2} / y) = **0.00102**

Stress in layer 2; σ_{y2} = min(f_{yd}, E_{s} × ε_{y2}) – h × f_{cd} = **187.4** N/mm^{2}

Force in layer 2; F_{y2} = 2 × A_{bar} × σ_{y2} = **117.8** kN

Moment of resistance of layer 2; M_{Rdy2} = F_{y2} × (h/2 – d_{y2}) = **0.0** kNm

Strain in layer 3; ε_{y3} = ε_{cu3} × (1 – d_{y3}/y) = **0.00292**

Stress in layer 3; σ_{y3} = min(f_{yd}, E_{s} × ε_{y3}) – h × f_{cd} = **417.8** N/mm^{2}

Force in layer 3; F_{y3} = N_{y} × A_{bar} × σ_{y3} = **262.5** kN

Moment of resistance of layer 3; M_{Rdy3} = F_{y3} × (h/2 – d_{y3}) = **45.2** kNm

Resultant concrete/steel force; F_{y} = **1351.2** kN

PASS – This is within half of one percent of the applied axial load

Combined moment of resistance

Moment of resistance about y axis; M_{Rdy} = **169.8** kNm

PASS – The moment capacity about the y axis exceeds the design bending moment

**Moment capacity about z-axis with axial load (1350.0 kN)**

**Moment of resistance of concrete**

By iteration, position of neutral axis; z = **171.9** mm

Concrete compression force (3.1.7(3)); F_{zc} = h × f_{cd} × min(l_{sb} × z, b) × h = **1051.9** kN

Moment of resistance; M_{Rdzc} = F_{zc} × [b / 2 – (min(l_{sb} × z, b)) / 2] = **59.2** kNm

**Moment of resistance of reinforcement**

Strain in layer 1; ε_{z1} = ε_{cu3} × (1 – d_{z1} / z) = **-0.00051**

Stress in layer 1; σ_{z1} = max(-1 × f_{yd}, E_{s} × ε_{z1}) = **-102.3** N/mm^{2}

Force in layer 1; F_{z1} = N_{z} × A_{bar} × σ_{z1} = **-96.4** kN

Moment of resistance of layer 1; M_{Rdz1} = F_{z1} × (b / 2 – d_{z1}) = **6.9** kNm

Strain in layer 2; ε_{z2} = ε_{cu3} × (1 – d_{z2}/z) = **0.00242**

Stress in layer 2; σ_{z2} = min(f_{yd}, E_{s} × ε_{z2}) – h × f_{cd} = **417.8** N/mm^{2}

Force in layer 2; F_{z2} = N_{z} × A_{bar} × σ_{z2} = **393.8** kN

Moment of resistance of layer 2; M_{Rdz2} = F_{z2} × (b/2 – d_{z2}) = **28.4** kNm

Resultant concrete/steel force; F_{z} = **1349.2** kN** PASS** – This is within half of one percent of the applied axial load

Combined moment of resistance

Moment of resistance about z-axis; M_{Rdz} = **94.5** kNm** PASS** – The moment capacity about the z-axis exceeds the design bending moment

**Biaxial bending**

Determine if a biaxial bending check is required (5.8.9(3))

Ratio of column slenderness ratios; ratio_{l} = max(l_{y}, l_{z}) / min(l_{y}, l_{z}) = **2.01**

Eccentricity in direction of y axis; e_{y} = M_{Edz}/N_{Ed} = **49.8** mm

Eccentricity in direction of z axis; e_{z} = M_{Edy}/N_{Ed} = **49.5** mm

Equivalent depth; h_{eq} = i_{y} × √(12) = **450** mm

Equivalent width; b_{eq} = i_{z} × √(12) = **250** mm

Relative eccentricity in direction of y-axis; e_{rel_y} = e_{y}/b_{eq} = **0.199**

Relative eccentricity in direction of z-axis; e_{rel_z} = e_{z}/h_{eq} = **0.110**

Ratio of relative eccentricities;

ratio_{e} = min(e_{rel_y}, e_{rel_z})/max(e_{rel_y}, e_{rel_z}) = **0.552**

ratio_{l} > 2 and ratio_{e} > 0.2

Therefore, biaxial bending check is required.

**Biaxial bending (5.8.9(4))**

Design axial resistance of section; N_{Rd} = (A_{c} × f_{cd}) + (A_{s} × f_{yd}) = **2732.0** kN

Ratio of applied to resistance axial loads; ratio_{N} = N_{Ed} / N_{Rd} = **0.494**

Exponent a; a = **1.33**

Biaxial bending utilisation; UF = (M_{Edy}/M_{Rdy})^{a} + (M_{Edz}/M_{Rdz})^{a} = **0.926** (Okay)

**Shear **

Design shear force; V_{Ed} = V_{Ed,y} = **25.8** kN

C_{Rd,c} = 0.18/γ_{C} = **0.12**

Tension reinforcement; A_{sl} = N_{z} × π × ϕ^{2}/4 = **942** mm^{2}

Depth of tension reinforcement; d_{v} = d_{z1} = **197** mm

k_{shear} = min(1 + (200 mm / d_{v})^{0.5}, 2) = **2.000**

Width of the cross section in tensile area; b_{w} = h = **450** mm

Longitudinal reinforcement ratio; r_{l} = min(A_{sl}/(b_{w} × d_{v}), 0.02) = **0.01063**

Axial pressure in cross-section; σ_{cp} = min(N_{Ed}/A_{c}, 0.2 × f_{cd}) = **3.40** N/mm^{2}

v_{min} = 0.035 N^{0.5}/mm × k_{shear}^{3/2} × f_{ck}^{1/2} = **0.54** N/mm^{2}

k_{1,shear} = **0.15**

Design shear resistance – exp. 6.2 a & b;

V_{Rd,c} = max(C_{Rd,c} × k_{shear} × (100 N^{2}/mm^{4} × r_{l} × f_{ck})^{1/3}, v_{min}) × b_{w} × d_{v} + k_{1,shear} × σ_{cp} × b_{w} × d_{v} = **112.7** kN

V_{Ed} / V_{Rd,c} = **0.23**

PASS – Design shear resistance exceeds design shear force

**Factory Lifting Check**

**Precast element details**

Total length of column; L_{element} = **4500** mm

Distance between lifting points; L_{lift} = **2500** mm

Lifting load coefficient; f_{lifting} = **1.50**

Permanent load factor; γ_{G} = **1.35**

Formwork adhesion force; q_{formwork} = **2.0** kN/m^{2}

Self weight of precast element; w_{self_precast} = b × h × ρ_{conc} × g_{acc} + q_{formwork} × b = **3.3** kN/m

**Lifting check (positive moment)**

Design bending moment; M = γ_{G} × f_{lifting} × (w_{self_precast} × L_{lift}^{2} /8 – w_{self_precast} × ((L_{element} – L_{lift}) / 2)^{2}/2) = **1.9** kNm

Effective depth of tension reinforcement; d = **397** mm

Redistribution ratio; d = **1.000**

K = M / (b × d^{2} × f_{ck}) = **0.002**

No compression reinforcement is required

Lever arm; z = min(0.5 × d × (1 + (1 – 2 × K / (h × a_{cc} / γ_{C}))^{0.5}), 0.95 × d) = **377** mm

Depth of neutral axis; x = 2 × (d – z)/l_{sb} = **50** mm

Area of tension reinforcement required; A_{s,pos} = M / (f_{yd} × z) = **11** mm^{2}

Tension reinforcement provided; 2H20 mm (A_{s,prov} = **628** mm^{2})

Minimum area of reinforcement – exp.9.1N; A_{s,min} = max(0.26 × f_{ctm}/f_{yk}, 0.0013) × b × d = **149** mm^{2}

Maximum area of reinforcement – cl.9.2.1(3); A_{s,max} = 0.04 × b × h = **4500** mm^{2}

Required area of reinforcement; A_{s,req} = **149** mm^{2}

A_{s,req} / A_{s,prov} = **0.24** (okay)

**Lifting check (negative moment)**

Design bending moment; M = γ_{G} × f_{lifting} × w_{self_precast} × ((L_{element} – L_{lift}) / 2)^{2} / 2 = **3.3** kNm

Effective depth of tension reinforcement; d = **397** mm

Redistribution ratio; d = **1.000**

K = M / (b × d^{2} × f_{ck}) = **0.003**

Area of tension reinforcement required; A_{s,neg} = M / (f_{yd} × z) = **20** mm^{2}

Tension reinforcement provided; 2H20 mm (A_{s,prov} = **628** mm^{2})

Minimum area of reinforcement – exp.9.1N; A_{s,min} = max(0.26 × f_{ctm}/f_{yk}, 0.0013) × b × d = **149** mm^{2}

Maximum area of reinforcement – cl.9.2.1(3); A_{s,max} = 0.04 × b × h = **4500** mm^{2}

Required area of reinforcement; A_{s,req} = **149** mm^{2}

A_{s,req} / A_{s,prov} = **0.24** (Okay)

**Lifting check (Shear)**

Design shear force at critical shear plane;

V_{Ed} = γ_{G} × f_{lifting} × w_{self_precast} × max(L_{lift} / 2, (L_{element} – L_{lift}) / 2) = **8.2** kN

C_{Rd,c} = 0.18/γ_{C} = **0.12**

Tension reinforcement; A_{sl} = N_{y} × π × ϕ^{2} / 4 = **628** mm^{2}

Depth of tension reinforcement; d_{v} = d_{y1} = **397** mm

k_{shear} = min(1 + (200 mm / d_{v})^{0.5}, 2) = **1.710**

Width of the cross section in tensile area; b_{w} = b = **250** mm

Longitudinal reinforcement ratio; ρ_{l} = min(A_{sl} / (b_{w} × d_{v}), 0.02) = **0.00633**

v_{min} = 0.035 N^{0.5}/mm × k_{shear}^{3/2} × f_{ck}^{1/2} = **0.43** N/mm^{2}

Design shear resistance – exp. 6.2 a & b;

V_{Rd,c} = max(C_{Rd,c} × k_{shear} × (100 N^{2}/mm^{4} × ρ_{l} × f_{ck})^{1/3}, v_{min}) × b_{w} × d_{v}

V_{Rd,c} = **54.3** kN

V_{Ed} / V_{Rd,c} = **0.15** (This is okay)

**On-site Pitching Check**

**Precast element details**

Total length of column; L_{element} = **4500** mm

Distance to the pitching point; L_{pitch} = **1800** mm

Distance from pitching point to end of column;L_{end} = **2700** mm

Lifting load coefficient; f_{pitching} = **1.25**

Permanent load factor; g_{G} = **1.35**

Self weight of precast element; w_{self_precast} = b × h × ρ_{conc} × g_{acc} = **2.8** kN/m

**Lifting check (positive moment)**

Design bending moment (at 3750 mm);

M = g_{G} × f_{pitching} × w_{self_precast} × L_{element}^{2} / (2 × L_{end}) × (0.25 × L_{element}^{2}/L_{end} – L_{pitch}) = **1.3** kNm

Effective depth of tension reinforcement; d = **397** mm

Redistribution ratio; d = **1.000**

K = M / (b × d^{2} × f_{ck}) = **0.001**

Area of tension reinforcement required; A_{s,pos} = M / (f_{yd} × z) = **8** mm^{2}

Tension reinforcement provided; 2H20 mm (A_{s,prov} = **628** mm^{2})

Minimum area of reinforcement – exp.9.1N; A_{s,min} = max(0.26 × f_{ctm}/f_{yk}, 0.0013) × b × d = **149** mm^{2}

Maximum area of reinforcement – cl.9.2.1(3); A_{s,max} = 0.04 × b × h = **4500** mm^{2}

Required area of reinforcement; A_{s,req} = **149** mm^{2}

A_{s,req} / A_{s,prov} = **0.24** (Okay)

**Lifting check (negative moment)**

Design bending moment; M = g_{G} × f_{pitching} × w_{self_precast} × L_{pitch} ^{2} / 2 = **7.5** kNm

Effective depth of tension reinforcement; d = **397** mm

Redistribution ratio; d = **1.000**

K = M / (b × d^{2} × f_{ck}) = **0.006**

Area of tension reinforcement required; A_{s,neg} = M / (f_{yd} × z) = **46** mm^{2}

Tension reinforcement provided; 2H20 mm (A_{s,prov} = **628** mm^{2})

Minimum area of reinforcement – exp.9.1N; A_{s,min} = max(0.26 × f_{ctm}/f_{yk}, 0.0013) × b × d = **149** mm^{2}

Maximum area of reinforcement – cl.9.2.1(3); A_{s,max} = 0.04 × b × h = **4500** mm^{2}

Required area of reinforcement; A_{s,req} = **149** mm^{2}

A_{s,req} / A_{s,prov} = **0.24** (Okay)

**Lifting check (Shear)**

Design shear force at critical shear plane;

V_{Ed} = g_{G} × f_{pitching} × w_{self_precast} × max(L_{pitch}, abs(L_{element} – 0.5 × L_{element}^{2} / L_{end}), abs(L_{end} – (L_{element} – 0.5 × L_{element}^{2} / L_{end}))) = **9.1** kN

C_{Rd,c} = 0.18/γ_{C} = **0.12**

Tension reinforcement; A_{sl} = N_{y} × π × ϕ^{2} / 4 = **628** mm^{2}

Depth of tension reinforcement; d_{v} = d_{y1} = **397** mm

k_{shear} = min(1 + (200 mm / d_{v})^{0.5}, 2) = **1.710**

Width of the cross section in tensile area; b_{w} = b = **250** mm

Longitudinal reinforcement ratio; ρ_{l} = min(A_{sl} / (b_{w} × d_{v}), 0.02) = **0.00633**

v_{min} = 0.035 N^{0.5}/mm × k_{shear}^{3/2} × f_{ck}^{1/2} = **0.43** N/mm^{2}

Design shear resistance – exp. 6.2 a & b;

V_{Rd,c} = max(C_{Rd,c} × k_{shear} × (100 N^{2}/mm^{4} × ρ_{l} × f_{ck})^{1/3}, v_{min}) × b_{w} × d_{v}

V_{Rd,c} = **54.3** kN

V_{Ed} / V_{Rd,c} = **0.17** (Okay)

**Connection**

The connection of the column can be designed and checked depending on the method adopted.