CONSULTING Engineering Calculation Sheet. Job Title Member Design - Reinforced Concrete Column BS8110

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E N G I N E E R S Consulting Engineers jxxx 1 Job Title Member Design - Reinforced Concrete Column Effects From Structural Analysis Axial force, N (tension-ve and comp +ve) (ensure >= 0) 8000kN OK

direction), e h = MIN (0.05h, 20mm) 20mm Imperfection eccentricity (in b direction), e b = MIN (0.05b, 20mm) 12mm Major plane eccentric (nominal) moment, M eh = N.

e b 92kNm Major plane max design bending moment, M x = MAX (M xp +M add,x, M eh ) 160kNm Minor plane max design bending moment, M y = MAX (M yp +M add,y, M eb ) 212kNm Material Properties

1 E N G I N E E R S Consulting Engineers jxxx 1 Job Title Member Design - Reinforced Concrete Column Effects From Structural Analysis Axial force, N (tension-ve and comp +ve) (ensure >= 0) 8000kN OK Major plane shear force, V y 400kN Minor plane shear force, V z 400kN Major plane primary bending moment, M xp 0kNm Minor plane primary bending moment, M yp 50kNm Imperfection eccentricity (in h direction), e h = MIN (0.05h, 20mm) 20mm Imperfection eccentricity (in b direction), e b = MIN (0.05b, 20mm) 12mm Major plane eccentric (nominal) moment, M eh = N.e h 160kNm Minor plane eccentric (nominal) moment, M eb = N.e b 92kNm Major plane max design bending moment, M x = MAX (M xp +M add,x, M eh ) 160kNm Minor plane max design bending moment, M y = MAX (M yp +M add,y, M eb ) 212kNm Material Properties Characteristic strength of concrete, f cu ( 105N/mm 2 ; HSC) 35N/mm 2 OK Yield strength of longitudinal steel, f y 460N/mm 2 Yield strength of shear link steel, f yv 460N/mm 2 Bracing or Unbraced Column Braced or unbraced column? (affects slenderness criteria) (Braced columns occurs when lateral loads are resisted by walls or other bracing; unbraced columns occur when lateral loads are resisted by bending in columns) cl Section Dimensions Section type (affects concrete area, slenderness, steel area req) Depth (larger), h (rectangular) or diameter, D (circular) 2250 mm Width (smaller), b (rectangular) or N/A (circular) 230 mm Area of section, A c = b.h (rectangular) or πd 2 /4(circular) mm 2 Major plane clear height, l clear,x 4.000m cl Minor plane clear height, l clear,y 4.000m cl Major plane effective height, l eff,x 4.000m cl Minor plane effective height, l eff,y 4.000m cl Longitudinal steel reinforcement diameter, φ Total longitudinal steel reinforcement number (uniaxial bending), n l mm Total longitudinal steel area provided (uniaxial bending), A sc = n l.π.φ 2 / mm 2 Total longitudinal steel reinforcement number (orthogonal bending), n l+ 0 Total longitudinal steel area provided (orthogonal bending), A sc+ = n l+.π.φ 2 /4 0mm 2 Total longitudinal steel area provided, A sc +A sc mm 2 (Note A sc is the total longitudinal steel area for the relevant uniaxial plane of bending only, whilst A sc+ is the total longitudinal steel area for bending in the orthogonal plane, excluding steel counted within A sc ) Shear link diameter, φ link 16mm Number of links in a cross section, i.e. number of legs, n v 2 Area provided by all links in a cross-section, A sv,prov = n v.π.φ 2 link /4 402mm 2 Pitch of links, S 175mm Cover to all reinforcement, cover (usually 35 (C35) or 30 (C40) internal; 40 e Cover to main reinforcement, cover main = cover + φ link 35mm 51mm

E N G I N E E R S Consulting Engineers jxxx 2 Job Title Member Design - Reinforced Concrete Column Utilisation Summary Braced or unbraced Slenderness (short or slender) Braced [Major] [Minor]

2 E N G I N E E R S Consulting Engineers jxxx 2 Job Title Member Design - Reinforced Concrete Column Utilisation Summary Braced or unbraced Slenderness (short or slender) Braced [Major] [Minor] [Overall] Short Slender Slender Item UT Remark Max (braced) slenderness 43% OK Max (unbraced) slenderness N/A N/A Shear ultimate stress 16% OK Shear (with axial load) design capacity 99% OK Method 1 (nominal moments; slender column Euler buc 42% OK Method 2 (nominal moments; short column crushing) 74% OK Method 3 (small assumed moments; short column crush 84% OK Method 4 (biaxial design moments; short column crush 62% OK Total utilisation 99% OK Detailing requirements OK Convergence Converged Design Column (Iterative) % Vertical reinforcement 2.09 % Estimated steel reinforcement quantity ( kg/m 3 ) 250 kg/m [(A sc +A sc+ ) / A c + A sv,prov.(h+b or 2D)/S) / A c ]; No laps; Estimated steel reinforcement quantity ( kg/m 3 ) 351 kg/m 3 IStructE [(A sc +A sc+ )/ A c + A sv,prov.(h+b or 2D)/S) / A c ]; Laps; [Note that steel quantity in kg/m 3 can be obtained from x % rebar]; Material cost: concrete, c 250 units/m 3 steel, s 3500 units/tonne Reinforced concrete material cost = [c+(est. rebar quant).s].a c 765 units/m Column Effective Height

3 E N G I N E E R S Consulting Engineers jxxx 3 Job Title Member Design - Reinforced Concrete Column Effective Depth and Width Number of layers of steel at each extremity for rect cols, n layers 1layer(s) (Note n layers affects the effective h' or b' depending on equivalent single axis of bending, for rect only) Spacer reinforcement, s r = MAX (φ, 25mm) 25mm Plane of bending b-plane or minor plane Effective depth, h' = h - cover main -[φ+(n layers -1)(φ+s r )]/2 rect 2187mm = D - cover main - φ/2 circular Effective width, b' = b - cover main -[φ+(n layers -1)(φ+s r )]/2 rect 167mm = D - cover main - φ/2 circular (Note multiple steel layer for h'- or b'- plane bending depending on equivalent single axis of bending, for rect o Detailing Instructions h = 2250 mm = D b = 230 mm A sc = 22 T25 Symmetrically Distributed Links = 2 legs of T16@175mm pitch Cover =35 mm Concrete =35 MPa Rebars =460 MPa Links =460 MPa Steel % =2.09 % Bending plane = b-plane n layers =1 (Note rect column shown for bending in h-plane, not b-plane) Bending Moment Sign Convention My h Mx b

4 E N G I N E E R S Consulting Engineers jxxx 4 Job Title Member Design - Reinforced Concrete Column Slenderness of Column (Whether Short or Slender) Major plane slenderness, l eff,x /(h or D) 1.8 Minor plane slenderness, l eff,y /(b or D) 17.4 Short column limiting slenderness (15 braced; 10 unbraced) 15.0 cl Major plane column slenderness (short if < criteria, slender if > criteria) Short Minor plane column slenderness (short if < criteria, slender if > criteria) Slender Overall column slenderness (includes major and minor planes) Slender Major plane max slenderness l clear,x /(h or D) 1.8 cl Minor plane max slenderness l clear,y /(b or D) 17.4 cl Max (braced or unbraced) slenderness utilisation (<= 60) 29% OK Major plane max slenderness l eff,x /(h or D) 1.8 cl Minor plane max slenderness l eff,y /(b or D) 17.4 cl Max (braced) slenderness utilisation (<= 40) 43% OK Major plane max slenderness l clear,x /(b 2 /h or D) cl Minor plane max slenderness l clear,y /(b 2 /h or D) cl Max (unbraced) slenderness utilisation (<= 100) N/A N/A Major plane max slenderness l eff,x /(h or D) 1.8 cl.3.8.5, cl Minor plane max slenderness l eff,y /(b or D) 17.4 cl.3.8.5, cl Max (unbraced) slenderness utilisation (<= 30) N/A N/A Note for RC columns and walls, slenderness limits are as follows:- braced short (stocky) l eff,x/y /(h/b or D) 15 cl braced slender l clear,x/y /(h/b or D) 60 cl braced slender l eff,x/y /(h/b or D) 40 cl unbraced short (stocky) l eff,x/y /(h/b or D) 10 cl unbraced slender l clear,x/y /(b or D) 60 cl unbraced slender l clear,x/y /(b or D) 60, 100b/h cl unbraced slender l eff,x/y /(h/b or D) 30 cl unbraced slender l eff,x/y /(h/b or D) 30 cl Note for plain (unreinforced) walls, slenderness limits are as follows:- braced short (stocky) l eff /THK 15 cl unbraced short (stocky) l eff /THK 10 cl braced or unbraced slender l eff /THK 30 cl

5 E N G I N E E R S Consulting Engineers jxxx 5 Job Title Member Design - Reinforced Concrete Column Member Design - RC Column Moments From Slenderness Effects XX 19/05/2016 Additional moment for slender columns, M add,x 17kNm Additional moment for slender columns, M add,y 162kNm Major plane effective height, l eff,x 4.000m Minor plane effective height, l eff,y 4.000m Deflection in x (h in this equation = h or D) 2mm Deflection in y (h in this equation = b or D) 20mm Coefficient in x (b' in this equation = h or D) Coefficient in y (b' in this equation = b or D) Reduction factor due to axial loads 0.58 Ultimate axial load kn Axial load at balanced failure, N bal = 0.25f cu A c 4528kN Single Axis Moment From Biaxial Moments Major plane max design bending moment, M x 160kNm Minor plane max design bending moment, M y 212kNm Ratio N/(bhf cu ) rectangular or N/(D 2 f cu ) circular 0.44 Enhancement coefficient for biaxial bending, β Effective depth, h' = h or D - cover main - φ/2 2187mm Effective width, b' = b or D - cover main - φ/2 167mm (Note for the purpose of determining equivalent single bending axis, single steel layer assumed) If then increased major plane bending N/A knm If then increased minor plane bending 218 knm Increased single axis bending moment, M Plane of design moment for rectangular columns (h- or b-) 218 knm b-plane

6 E N G I N E E R S Consulting Engineers jxxx 6 Job Title Member Design - Reinforced Concrete Column Member Design - RC Column Shear (With Axial Load) XX 19/05/2016 cl Shear insignificant if M/N < 0.6 (h or b) for rect, 0.6 D for circ mm (Note h or b depending on equivalent single axis of bending, for rect only) Maximum shear force, V d = MAX (V y, V z ) 400kN Ultimate shear stress, v ult = V d / A c (< 0.8f 0.5 cu &{5.0,7.0}N/mm 2 ) 0.77N/mm 2 BC2 Note the ultimate shear stress limit of 5.0 or 7.0N/mm 2 is used for f cu 60 or 105N/mm 2 respecticl Ultimate shear stress utilisation 16% OK Design shear stress, v d = V d / A c 0.77N/mm 2 (Shear capacity enhancement by either calculating v d at d from support and comparing against unenhanced v c as clause or calculating v d at support and comparing against enhanced v c within 2d of the support as clause both not applicable as described in clause ;) Area of tensile steel reinforcement provided (uniaxial bending), A s,prov = A sc / 5400mm 2 ρ w = 100A s,prov /A c 1.04% Effective distance to tension steel, h' or b' 167 mm (Note h' or b' depending on equivalent single axis of bending, for rect only) v c = (0.79/1.25)(ρ w f cu /25) 1/3 (400/(h' or b')) 1/4 ; ρ w <3; f cu <80; (400/(h' or b')) N/mm 2 BC2 cl Including axial force effects 3.82N/mm 2 N/A c 15.5N/mm 2 V d (h or b)/m or V d D/M but < (Note h or b depending on equivalent single axis of bending, for rect only) Minimum shear strength, v r = MAX (0.4, 0.4 (MIN(80, f cu )/40) 2/3 ) 0.40N/mm 2 BC2 cl Check v d < 0.5v c ' for no links (minor structural elements) VALID Concrete shear capacity v c '.(A c ) 1977kN Check 0.0v c ' < v d < v r + v c ' for nominal links VALID Provide nominal links A sv / S > v r.(b or h rect, D circ)/(0.95f yv ) i.e. 2.06mm 2 /mm (Note b or h depending on equivalent single axis of bending, for rect only) Concrete and nominal links shear capacity (v r + v c ').(A c ) 2184kN Check v d > v r + v c ' for design links N/A Provide shear links A sv / S > (b or h rect, D circ)(v d -v c ')/(0.95f yv ) i. 2.06mm 2 /mm (Note b or h depending on equivalent single axis of bending, for rect only) Concrete and design links shear capacity (A sv,prov /S).(0.95f yv ).(h or 2208kN Area provided by all links in a cross-section, A sv,prov 402mm 2 Tried A sv,prov / S value 2.30mm 2 /mm Design shear resistance utilisation 99% OK

7 E N G I N E E R S Consulting Engineers jxxx 7 Job Title Member Design - Reinforced Concrete Column Member Design - RC Column Detailing Requirements XX 19/05/2016 All detailing requirements met? OK By definition, b <= h OK Min dimension (to facilitate concreting >= 200mm) 230 mm OK Min longitudinal steel reinforcement number, n l (>= 4 rectangular; >=6 circu 22 OK Min longitudinal steel reinforcement diameter, φ (>=12mm) 25 mm OK Percentage of reinforcement (A sc +A sc+ )/A c x 100% 2.09% OK Percentage of reinforcement A sc /A c x 100% (>0.40%,[ (f cu -60)]% and <5.00%) TR49 cl Longitudinal steel reinforcement pitch (>75mm+φ, >100mm+φ if T40; <= mm OK Rectangular col bar pitch = [(b or h)-2.cover main -φ]/(n l /(2.n layers )-1 212mm (Note b or h depending on equivalent single axis of bending, for rect only) Circular col bar pitch = π.(d-2.cover main -φ)/n l N/Amm Note an allowance has been made for laps in the min pitch by increasing the criteria by the bar diameter. Min link diameter, φ link (>=0.25φ; >=6mm NSC; >=10mm HSC) 16mm OK Max link pitch, S 175 mm OK Max link pitch, S (<=12 φ NSC, <=10 φ HSC, <=24 φ link HSC, <=300mm, <=(h, b) for rectangular, <=D for ci Require an overall enclosing link. Require additional restraining links for each alternate longitudinal bar in each direction. No unrestrained bar should be further than 150mm clear distance from a restrained bar. Require through slab / beam depth column links in edge and corner columns due to lack of restraint.

8 E N G I N E E R S Consulting Engineers jxxx 8 Job Title Member Design - Reinforced Concrete Column Method 1 (Axial Force; Nominal Moments for Non-Continuous (Precast) Floors; Slender Column Eule Axial buckling capacity (Euler) major plane, N cap,euler = π 2 2.E c,28.i x /l eff,x 2E+06 kn Axial buckling capacity (Euler) minor plane, N cap,euler = π 2 2.E c,28.i y /l eff,y 2E+04 kn Elastic modulus of concrete, 27.0 GPa Cracked second moment of area major plane, 0.5I x = 0.5b.h 3 /12 o 1.1E+11mm 4 Cracked second moment of area minor plane, 0.5I y = 0.5h.b 3 /12 o 1.1E+09mm 4 Axial capacity utilisation = N/N cap,euler 42% OK Method 2 (Axial Force; Nominal Moments for Non-Continuous (Precast) Floors; Short Column Crush Percentage of reinforcement (A sc +A sc+ )/A c x 100% 2.09% Axial capacity, N cap = 0.40f cu.a c + (0.75f y -0.40f cu ).(A sc +A sc+ ) 10820kN cl (Note for perfect axial conditions, N cap = 0.45f cu.a c + (0.95f y -0.45f cu ).(A sc +A sc+ )) Axial capacity utilisation = N/N cap 74% OK ircular)

E N G I N E E R S Consulting Engineers jxxx 9 Job Title Member Design - Reinforced Concrete Column Method 3A (Axial Force; Small Assumed Moments for <15% Adjacent Spans Difference in Continuou

9 E N G I N E E R S Consulting Engineers jxxx 9 Job Title Member Design - Reinforced Concrete Column Method 3A (Axial Force; Small Assumed Moments for <15% Adjacent Spans Difference in Continuou Percentage of reinforcement (A sc +A sc+ )/A c x 100% 2.09% Axial capacity, N cap = 0.35f cu.a c + (0.67f y -0.35f cu ).(A sc +A sc+ ) 9535kN cl Axial capacity utilisation = N/N cap 84% OK Method 3B (Axial Force; Small Assumed Moments; Short Column Crushing; Arup Scheme Design)

10 E N G I N E E R S Consulting Engineers jxxx 10 Job Title Member Design - Reinforced Concrete Column Method 3C (Axial Force; Small Assumed Moments; Short Column Crushing; Economic Concrete Sche

11 E N G I N E E R S Consulting Engineers jxxx 11 Job Title Member Design - Reinforced Concrete Column me Design)

12 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 12 Job Title Member Design - Reinforced Concrete Column

13 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 13 Job Title Member Design - Reinforced Concrete Column Member Design - RC Column Method 4 (Axial Force; Design Biaxial Moments; Short Column Crushing or Slender Column Imperfec (Note where relevant (h and h') or (b and b') depending on equivalent single axis of bending, for rect only) XX 19/05/2016 Depth to compression steel, h c ' = (h or b for rect, D for circ) - (h' or b') 64mm Area of section, A c mm 2 Ratio (h' or b')/(h or b) (rect) or (h'-h c ')/D(circ) 0.72 Strength of concrete, f cu 35N/mm 2 Yield strength of longitudinal steel, f y 460N/mm 2 Rectangular ratio N/bh or circular ratio N/D N/mm 2 Rectangular ratio (M/bh 2 or M/hb 2 ) or circular ratio M/D N/mm 2 Perform iteration Design Column (Iterative) Iterate depth of neutral axis until the two A s expression equal, x 197mm Steel strain, ε s = -ε cu (h' or b' - x)/x Steel strain, ε sc = ε cu (x-h c ')/x BC2 cl cl Steel design yield strength = 460/1.05 (G460) or 250/1.05 (G250) 438N/mm 2 Steel elastic modulus, E s N/mm 2 Steel stress, f s = E s.ε s (< design yield strength) 112N/mm 2 Steel stress, f sc = E s.ε sc (< design yield strength) f cu 422N/mm 2 Rectangular Concrete strain, ε Factor, k 1 ε cu 14.0N/mm ε 2 cu ε Factor, k cu ε cu BC2 cl cl A s = [N-k 1.(b or h).x] /(f sc +f s ) 3331mm 2 OK A s = [M-k 1.(b or h).x.(0.5(h or b)-k 2.x)]/[(f sc -f s ).((h' or b')-0.5(h 3323mm 2 OK A sc,req = MAX (2.average(A s ), 0.40%A c ) if soln; from interaction ch 6654mm 2 100A sc,req /A c 1.29% Circular From interaction charts, A sc,req N/Amm 2 N/A 100A sc,req /A c N/A% Area of longitudinal steel reinforcement required (uniaxial bending), A sc,req 6654mm 2 Area of longitudinal steel reinforcement provided (uniaxial bending), A sc 10799mm 2 Axial capacity utilisation = A sc,req /A sc 62% OK Convergence of interaction equations Converged

14 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 14 Job Title Member Design - Reinforced Concrete Column Member Design - RC Column Scheme Design XX 19/05/2016

Job No. Sheet No. Rev. CONSULTING Engineering Calculation Sheet. Member Design - RC Two Way Spanning Slab XX

Job No. Sheet No. Rev. CONSULTING Engineering Calculation Sheet. Member Design - RC Two Way Spanning Slab XX CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 1 Material Properties Characteristic strength of concrete, f cu ( 60N/mm 2 ; HSC N/A) 35 N/mm 2 OK Yield strength of