CONSULTING Engineering Calculation Sheet. Structure, Member Design - Geotechnics Pile Cap XX

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1 E N G I N E E R S Consulting Engineers jxxx Material Properties Characteristic strength of concrete, f cu ( 60N/mm ; HSC N/A) 40N/mm Yield strength of longitudinal steel, f y 460N/mm Yield strength of shear link steel, f yv 460N/mm Type of concrete and density, ρ c 4kN/m 3 Factor of Safety Loading factor, K (between.40 and.60 depending on DL to LL ratio).40 BS80 Note loading factor K multiplies SLS loads for ULS loads for section (reinforcement) design; cl Pile Cap Dimension Definitions b h 4 b h 3 3 b h x y

2 E N G I N E E R S Consulting Engineers jxxx First Shear Perimeter Second Shear Perimeter 8 5 Shear Links Zone Shear Links Zone

3 E N G I N E E R S Consulting Engineers jxxx 3 Pile Cap Dimensions Pile group arrangement Number of piles in pile group, Σn 5 Number of piles in pile group, Σn (generic only) N/A N/A Pile shaft diameter (circular) or width (square), D 600 mm in x in y Pile group pile spacing, S mm Note that spacing, S refers to distance from c/l to c/l between piles; S >= perimeter π.d (or simply 3.0D) for circular friction piles and 4.0D for square friction piles; S >=.0D b for end bearing piles; in x in y Projection of pile cap beyond face of pile, c proj (usually 50) mm Width of pile cap in x, 6.00m P: = D +.c proj N/Am P: = D +.c proj N/Am 3P: =.0S + D +.c proj N/Am 4P: =.0S + D +.c proj N/Am 5P: =.45S + D +.c proj N/Am 6P: =.0S + D +.c proj N/Am 7P: =.734S + D +.c proj N/Am 8P: =.0S + D +.c proj N/Am 9P: =.0S + D +.c proj N/Am 0P: =.0S + D +.c proj N/Am P: =.0S + D +.c proj N/Am P: =.0S + D +.c proj N/Am 3P: =.0S + D +.c proj N/Am 4P: =.0S + D +.c proj N/Am 5P: =.0S + D +.c proj 6.00m Generic: = user-defined N/Am Length of pile cap in y, 8.00m P: = D +.c proj N/Am P: =.0S + D +.c proj N/Am 3P: =.0S + D +.c proj N/Am 4P: =.0S + D +.c proj N/Am 5P: =.45S + D +.c proj N/Am 6P: =.0S + D +.c proj N/Am 7P: =.0S + D +.c proj N/Am 8P: =.0S + D +.c proj N/Am 9P: =.0S + D +.c proj N/Am 0P: = 3.0S + D +.c proj N/Am P: = 3.0S + D +.c proj N/Am P: = 3.0S + D +.c proj N/Am 3P: = 4.0S + D +.c proj N/Am 4P: = 5.0S + D +.c proj N/Am 5P: = 4.0S + D +.c proj 8.00m Generic: = user-defined N/Am Banding ratio (affects truss base force and enhanced shear capacity) Banding ratio in plane of width, b r,x = / (3.0D) cl Banding ratio in plane of width, b r,x (generic only) N/A BS80 Banding ratio in plane of length, b r,y = / (3.0D).0.48 cl Banding ratio in plane of length, b r,y (generic only) N/A BS80 Note only steel reinforcement within.5d from pile centre considered effective;

4 E N G I N E E R S Consulting Engineers jxxx 4 Stress concentration (affects bending moment and shear force) Stress concentration in plane of width, s c,x Stress concentration in plane of length, s c,y Basis: BS80 cl (3D Effect) Factor, s c,x = /3 /(h or D + 3d x ) cl applicable if / > 3/4(h or D)+9/4d x 4.00 <= 8.0 m BS80 Factor, s c,y = /3 / (b or D + 3d y ) cl applicable if / > 3/4(b or D)+9/4d y 3.00 <= 8.04 m BS80 Basis: BS80 cl (D Effect) Factor, s c,x = /(h or D + /5) 3.06 cl Factor, s c,y = / (b or D + /5).83 BS80 Thickness of pile cap, T cap 3.500m Note usually T cap (MIN(L db,x,l db,y )/)/ tan45 + cover + φ link,/3 + ( m to T cap (MIN(L db,x,l db,y )/)/ tan30 + cover + φ link,/3 + ( m for single layer base steel and angle 45 to 30 from vertical to line of compression; Note sufficient pile cap rebar anchorage, T cap t anchor,pilecap -D/-c proj +cover +cover +cover 3 + φ link,/3 +(0.5 to.5). φ b 0.90 m for single layer base steel; Note also that the minimum (large) bending radius needs to be evaluated; Note sufficient pile rebar anchorage, T cap t anchor,pile +cover +cover 3.00 m Pile longitudinal steel reinforcement diameter, φ p 5 mm Note tension anchorage, t anchor = (/.05).f y. φ/4/f bu.a s /A s,prov,b, f bu =(0.50 G460, 0.8 G50). f cu, A s /A s,p Column base section type (for punching shear only) Column base depth, h (rectangular)( b) or diameter, D (circular) 400 mm 6.9 Column base width, b ( h) (rectangular) or N/A (circular) 00 mm Note where applicable, it is assumed that h is in same plane as and that the column base N/mm is always interior and located in the centre of the pile cap and ; Generally h b (not mandatory); Centroid of pile group in x, x c = Σx n /Σn.800m Centroid of pile group in y, y c = Σy n /Σn 3.600m Second moment of distance of pile group in x, I = Σx n-c 3m Second moment of distance of pile group in y, I = Σy n-c 97m Second moment of distance of pile group in xy, I = Σx n-c.y n-c 0m

5 E N G I N E E R S Consulting Engineers jxxx 5 Coordinates and Geometrical Properties Pile n Coordinates (m) eneric Coordinates (m Offset (m) Geometrical Properties (m ) x n y n x n y n x n-c y n-c x n-c y n-c x n-c.y n-c N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A Σ

6 E N G I N E E R S Consulting Engineers jxxx 6 Pile Cap Reinforcement Cover to all (bottom) reinforcement, cover (usually 00) Cover to all (side) reinforcement, cover (usually 75) Cover to all (top) reinforcement, cover 3 (usually 45 integrated base slab and 75mm 75mm 75mm Base steel reinforcement diameter in direction of width x, φ b,x 0mm Base steel reinforcement pitch for resistance in direction of width x, p b,x 05mm Note for accuracy, goal seek pitch, p b,x to achieve a whole no. for the actual no. of rebars below; Number of layers of base steel for resistance in direction of width x, n layers,base 4layer(s) Base steel area provided per metre in direction of width x, A s,prov,b,x = (π.φ b,x / 67mm /m Spacer for base steel, s r,base,x ( MAX (φ b,x, 5mm)) 00mm Base steel area provided in direction of width x, A s,prov,b,x = A s,prov,b,x. 504mm No. of rebars, n x = A s,prov,b,x /(π.φ b,x /4) 59.9 ~ 60.0 numbers Actual bar pitch, p b,x = (n x.p b,x.cover 3.φ b,x )/ n x 04mm Base steel reinforcement diameter in direction of length y, φ b,y 3mm Base steel reinforcement pitch for resistance in direction of length y, p b,y 8mm Note for accuracy, goal seek pitch, p b,y to achieve a whole no. for the actual no. of rebars below; Number of layers of base steel for resistance in direction of length y, n layers,bas 4layer(s) Base steel area provided per metre in direction of length y, A s,prov,b,y = (π.φ b,y 763mm /m Spacer for base steel, s r,base,y = ( MAX (φ b,y, 5mm)) 00mm Base steel area provided in direction of length y, A s,prov,b,y = A s,prov,b,y. 0938mm No. of rebars, n y = A s,prov,b,y /(π.φ b,y /4) 35.9 ~ 36.0 numbers Actual bar pitch, p b,y = (n y.p b,y.cover 3.φ b,y )/ n y 8mm Goal Seek Goal Seek Shear link diameter for first and second shear perimeter, φ link,/3 5mm Number of links for first shear perimeter, n l, 5 Number of perimeters within first shear perimeter, n p, (>= ) 4 Area provided by all links for first shear perimeter, A sv,prov, = n l,.π 6359mm Distance between perimeters within first shear perimeter, S = S l, 300mm Number of links for second shear perimeter, n l,3 30 Number of perimeters within second shear perimeter, n p,3 (>= ) 7 Area provided by all links for second shear perimeter, A sv,prov,3 = n 4844mm Distance between perimeters within second shear perimeter, S 3 = 300mm Shear link diameter, φ link = φ link,/3 5mm Number of link legs per metre, n link = /S l,/ 3.3/m Area provided by all links per metre, A sv,prov = n link.π.φ link /4 636mm /m Pitch of links in zone and zone, S l,/ Zone 300 Zone 300mm First Shear Perimeter Second Shear Perimeter Side steel reinforcement diameter, φ s Side steel reinforcement pitch, p s 6mm 5mm Detailing code of practice Internal radius of bend for resistance in x and y, r x/y 00 50mm Effective depth to base steel in direction of width x, d x P to P: d x = T cap - cover - φ link,/3 -[ φ b,x +(n layers,base,x -)( φ 3P to 5P: d x = T cap - cover - φ link,/3 -[ φ b,x +(n layers,base,x -)( φ Effective depth to base steel in direction of length y, d y P to P: d y = T cap - cover - φ link,/3 -[ φ b,y +(n layers,base,y -)( φ 3P to 5P: d y = T cap - cover - φ link,/3 -[ φ b,y +(n layers,base,y -)( φ 378mm N/Amm 378mm 366mm N/Amm 366mm Estimated steel reinforcement quantity 58kg/m 3 55 Base steel with full anchorage, shear links with 8 x φ link,/3 anchorage, binder 08kg/m {T0EW@p b, T0@S l, in x and T0@S l, / in y, none} with 700mm anchor 50kg/m 3 75

7 E N G I N E E R S Consulting Engineers jxxx 7 Structure, Member Design - Geotechnics Pile Cap XX 6--5 Pile Cap SLS Loading SLS vertical (downward) load from column and base slab, F col,v 459kN Note that F col,v is positive (downward) and includes SLS loads from suspended or integrated base slab; Coordinate of F col,v loading in x, x Fcol,v, centroid at.800 m.800m Coordinate of F col,v loading in y, y Fcol,v, centroid at m 3.600m Eccentricity of F col,v from centroid in x, e = x Fcol,v - x c 0.000m Eccentricity of F col,v from centroid in y, e = y Fcol,v - y c 0.000m SLS horizontal load from column in x, F col,h SLS horizontal load from column in y, F col,h SLS moment from column in plane of x, M (defined to add to positive e ecce SLS moment from column in plane of y, M (defined to add to positive e ecce 0kN 0kN 0kNm 0kNm Note M is defined to add to the corresponding positive eccentricity, hence enter a positive or negative value to match the sign of the corresponding eccentricity; Pile cap weight, F cap..t cap.ρ c 47kN Total pile cap SLS vertical (downward) load, F pilecap,v = F col,v + F cap 49500kN Note that water uplift force at pile and pile cap base have been ignored in the calculation of F pilecap,v ; Goal Seek Note compression is positive, tension negative; Equation set to employ, symmetrical or unsymmetrical? For pile groups symmetrical about at least one (of the two) axis:- Note A = (F col,v.e )/( Σx n-c ); Note D = (M )/( Σy n-c ); Note B = (F col,v.e )/( Σy n-c ); Note E = (F col,h.t cap )/( Σx n-c ); Note C = (M )/( Σx n-c ); Note F = (F col,h.t cap )/( Σy n-c ); For pile groups unsymmetrical about both axes:- Note A = (F col,v.e. Σy n-c F col,v.e. Σx n-c.y n-c )/( Σx n-c. Σy n-c (Σx n-c.y n-c ) ); Note B = (F col,v.e. Σx n-c F col,v.e. Σx n-c.y n-c )/( Σx n-c. Σy n-c (Σx n-c.y n-c ) ); Note C = (M. Σy n-c M. Σx n-c.y n-c )/( Σx n-c. Σy n-c (Σx n-c.y n-c ) ); Note D = (M. Σx n-c M. Σx n-c.y n-c )/( Σx n-c. Σy n-c (Σx n-c.y n-c ) ); Note E = (F col,h.t cap. Σy n-c F col,h.t cap. Σx n-c.y n-c )/( Σx n-c. Σy n-c (Σx n-c.y n-c ) ); Note F = (F col,h.t cap. Σx n-c F col,h.t cap. Σx n-c.y n-c )/( Σx n-c. Σy n-c (Σx n-c.y n-c ) ); Note F pile,v,n = F pilecap,v / Σn + A.x n-c + B.y n-c + C.x n-c + D.y n-c + E.x n-c + F.y n-c ; Pile Cap ULS Loading ULS vertical (downward) load from column and base slab, F col,v,uls = K.F col,v Note that F col,v,uls is positive (downward); 633kN kg/m kg/m kg/m [Base steel + top steel] [Binders + shear links]

8 E N G I N E E R S Consulting Engineers jxxx 8 Axial Force (kn) Due To Pile n Σn F col,v.e and F col,v.e M and M col,h.t cap and F col,h.t c F pile,v,n F pilecap,v /Σn A.x n-c B.y n-c C.x n-c D.y n-c E.x n-c F.y n-c N/A N/A N/A N/A N/A N/A N/A N/A 7 N/A N/A N/A N/A N/A N/A N/A N/A 8 N/A N/A N/A N/A N/A N/A N/A N/A 9 N/A N/A N/A N/A N/A N/A N/A N/A 0 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A 3 N/A N/A N/A N/A N/A N/A N/A N/A 4 N/A N/A N/A N/A N/A N/A N/A N/A 5 N/A N/A N/A N/A N/A N/A N/A N/A 6 N/A N/A N/A N/A N/A N/A N/A N/A 7 N/A N/A N/A N/A N/A N/A N/A N/A 8 N/A N/A N/A N/A N/A N/A N/A N/A 9 N/A N/A N/A N/A N/A N/A N/A N/A 30 N/A N/A N/A N/A N/A N/A N/A N/A 3 N/A N/A N/A N/A N/A N/A N/A N/A 3 N/A N/A N/A N/A N/A N/A N/A N/A 33 N/A N/A N/A N/A N/A N/A N/A N/A 34 N/A N/A N/A N/A N/A N/A N/A N/A 35 N/A N/A N/A N/A N/A N/A N/A N/A 36 N/A N/A N/A N/A N/A N/A N/A N/A 37 N/A N/A N/A N/A N/A N/A N/A N/A 38 N/A N/A N/A N/A N/A N/A N/A N/A 39 N/A N/A N/A N/A N/A N/A N/A N/A 40 N/A N/A N/A N/A N/A N/A N/A N/A 4 N/A N/A N/A N/A N/A N/A N/A N/A 4 N/A N/A N/A N/A N/A N/A N/A N/A 43 N/A N/A N/A N/A N/A N/A N/A N/A 44 N/A N/A N/A N/A N/A N/A N/A N/A 45 N/A N/A N/A N/A N/A N/A N/A N/A 46 N/A N/A N/A N/A N/A N/A N/A N/A 47 N/A N/A N/A N/A N/A N/A N/A N/A 48 N/A N/A N/A N/A N/A N/A N/A N/A 49 N/A N/A N/A N/A N/A N/A N/A N/A 50 N/A N/A N/A N/A N/A N/A N/A N/A

9 E N G I N E E R S Consulting Engineers jxxx 9 Pile Cap Spanning Theory Continuous Spans (Rigid Piles, Flexible Pile Cap) Theory Span / depth ratio in width x (continuous spans), S / d x 0.57 Span / depth ratio in length y (continuous spans), S / d y 0.57 Note based on continuous spans, S / d usually.0 to.0; Pile cap spanning theory in width x Truss / Deep Beam Theory Too Deep Pile cap spanning theory in length y Truss / Deep Beam Theory Too Deep Note shallow beam theory is applicable for continuous span / depth >.0 (Mosley 5th 0.7); Note truss / deep beam theories are applicable for.0 continuous span / depth.0 (CIRIA Guide cl..3) Inverted Cantilever Spans (Rigid Pile Cap, Flexible Piles) Theory Span / depth ratio in width x (inverted cantilever spans), MAX (x n-c ) / d x 0.57 Span / depth ratio in width x (inverted cantilever spans), MIN (x n-c ) / d x 0.57 Span / depth ratio in length y (inverted cantilever spans), MAX (y n-c ) / d y.4 Span / depth ratio in length y (inverted cantilever spans), MIN (y n-c ) / d y 0.57 Note based on inverted cantilever spans, MAX or MIN (x n-c / y n-c ) / d usually 0.5 to.0; Note MAX would be critical for longitudinal shear, MIN would be critical for deep beam bending and shear; Pile cap spanning theory in width x Pile cap spanning theory in length y Truss / Deep Beam Theory Shallow Beam Theory Note shallow beam theory is applicable for cantilever span / depth >.0; Note truss / deep beam theories are applicable for 0.5 cantilever span / depth.0; Adopted Pile Cap Spanning Theory Span / depth ratio definition adopted Note that for pile caps with 5 or more piles, only the Inverted Cantilever Span theory is valid for bending theory to be applicable, i.e. for there to be only sagging steel (base steel) and such that the distribution of loads into the multiple piles is fairly uniform, say to 95% uniformity. For the verification of the validity of the Inverted Cantilever Span theory, a soil-structure interaction needs to be carried out to ensure that the pile cap thickness is sufficiently stiff with respect to the vertical pile stiffness; Pile cap spanning theory in width x Truss / Deep Beam Theory Pile cap spanning theory in length y Shallow Beam Theory Pile Group Layout COORDINATE, X (M) Pile Group Layout COORDINATE, Y (M) n x... y x.. n y Note that the coordinate datum is chosen as centre of pile ; Note enter piles from up to Σn; Note x n-c = x n x c and y n-c = y n y c ; NTS

10 E N G I N E E R S Consulting Engineers jxxx 0 Structure, Member Design - Geotechnics Pile Cap XX 6--5 Pile Cap Design Theory Compression in diagonal Tension in base ); Pile cap design theory (truss theory) Pile cap design theory (shallow beam bending theory) Pile cap design theory (deep beam bending and shear theory) Note although truss / deep beam theory may not apply for the extreme piles in certain pile caps due to their large width and / or length, it may be prudent to include them in circumstances where there exist a significant number of piles which are also very close to the column; Effect of b, h dimensions on truss base force Base bending moment calculation method Note herewith that both shallow beam and deep beam bending moments are affected; Method Cantilever Span Moment (Modified) Average Effect of b, h dimensions on base bending moment User-defined factor for M x to correlate with F.E. analysis, f mx.00 User-defined factor for M y to correlate with F.E. analysis, f my.00 Note in Method, it may be unconservative to calculate bending moments to the face of the column (as opposed to the centroid of the column) unless the dimension of the column in the direction orthogonal to the plane under consideration is significant with respect to the pile cap dimension also in the direction orthogonal to the plane under consideration; Method Timoshenko Simply-Supported Coefficients (Modified) Aspect ratio, actual and adopted.0 Note Method only applicable for centrally loaded pile caps without column moments as shown Peak in Timoshenko Theory of Plates and Shells pp.39. The theory which assumes a continuous simply-supported rectangular plate is then factored by the ratio of moment coefficients between a corner-supported and simply-supported (but uniformly loaded) rectangular plate; Method 3 GPSS GSA Corner-Supported Coefficients Aspect ratio, actual and adopted.0 Average Effect of b, h dimensions on shear span Note that it may be unconservative to calculate the shear span, a v to the face of the column (as opposed to the centroid of the column) unless the dimension of the column in the direction orthogonal to the plane under consideration is significant with respect to the pile cap dimension also in the direction orthogonal to the plane under consideration. This option affects the shallow beam enhanced shear capacity in x and y but not the enhanced punching shear capacity, whereby the b and h dimensions are always included in the calculation of the shear enhancement. This option also affects the shear span in the deep beam shear capacity in x and y calculations; Inclusion of punching shear at first shear perimeter check Note that the punching shear at the first shear perimeter check may not be appropriate in the case where the column dimensions extend significantly beyond the perimeter in question; Inclusion of punching shear at first and second shear perimeter check Note that the punching shear at the first and second shear perimeter check may be excluded if it is deemed that the distance between the extreme piles is less than 3D (cl BS80) and that deep beam theory is applicable for the MAX (x n-c ) / d x and MAX (x n-c ) / d y cases; Ultimate shear force theory (deep beam theory) Check longitudinal shear within section Criteria Not Met

11 E N G I N E E R S Consulting Engineers jxxx Executive Summary Pile Cap Pile Cap Pile Pile Safe Concrete Size Size Depth R x R y Shape ReferenceDiameter Capacity Grade S x S y D (B) (B) (mm) (kn) (mm) (mm) (mm) PC5P PC5P C x40T0 4x34T3 T x T y Min Col Min Col Binder Binder Shear Shear Overall Overall (T) (T) Size, C x Size, C y Number Hooks Hooks Tonnage Tonnage (mm) (mm) (Zone ) (Zone ) kg/m 3 kg/m 40T0 34T T6-5 6 T5-300EWT5-300EW Perform optimisation Optimise! Tidy Up! Optimisation algorithm Thickness of pile cap, T cap to 3.000m Base steel pitch x, p b,x 50 to 300mm Base steel pitch y, p b,y 50 to 300mm Pitch of links in zone, S l, 300 to 450mm Pitch of links in zone, S l, 0 to 0mm Pile cap spanning theory in width x Pile cap spanning theory in length y Truss / Deep Beam Theory Shallow Beam Theory Base tension capacity (truss theory) Applicable 54% Diagonal compression capacity (truss theory) 0% NOT Sagging bending moment (shallow beam theory) 63% Sagging bending moment (deep beam theory) 90% % Min base reinforcement 74% Punching shear at column base face 77% Punching shear at first shear perimeter Nom.Links 69% Punching shear at second shear perimeter Nom.Links 85% Ultimate shear stress 8% Design shear resistance (shallow beam theonom.links Des.Links 53% Ultimate shear force (deep beam theory) 99% Design shear resistance (deep beam theory)nom.linksnom.links 63% Longitudinal shear within section (EC) 5% Longitudinal shear within section (BS80) 89% Longitudinal shear within section (BS5400-4) 74% Adequacy of shear links when design links not required Detailing requirements Input parameters checks Minimum recommended depth of pile cap Spanning and design theory checks Deep beam depth zone Min breadth for deep beam bending Overall utilisation summary 0% % Base reinforcement % Estimated pile cap steel reinforcement quantity (0 50kg/m 3 ) 58 kg/m 3 [Note that steel quantity in kg/m 3 can be obtained from 78.5 x % rebar]; Material cost: concrete, c 305 units/m 3 steel, s 4600 units/tonne Reinforced concrete material cost = c+(est. rebar quant).s 03 units/m 3

12 E N G I N E E R S Consulting Engineers jxxx Pile Cap Base Reinforcement Design (Truss Theory) ULS vertical (downward) load from column and base slab, F col,v,uls Note that F col,v,uls is positive (downward); 633kN ULS base force in plane of width, F base,uls,x ULS base force in plane of length, F base,uls,y 955kN 000kN F base,uls,x F base,uls,y P: N/A N/A N/A N/A kn P: N/A N/A F col,v,uls.s/(4d y ) N/A kn Mosley 3P: F col,v,uls.s/(4.5d x ) N/A F col,v,uls.s/(4.5d y ) N/A kn Mosley 4P: F col,v,uls.s/(4d x ) N/A F col,v,uls.s/(4d y ) N/A kn Mosley 5P: F col,v,uls.s/(5d x ) N/A F col,v,uls.s/(5d y ) N/A kn Masterseries 6P: F col,v,uls.s/(4d x ) N/A F col,v,uls.s/(3d y ) N/A kn Masterseries 7P: F col,v,uls.s/(4d x ) N/A F col,v,uls.s/(3.5d y ) N/A kn Masterseries 8P: F col,v,uls.s/(3d x ) N/A F col,v,uls.s/(3d y ) N/A kn Masterseries 9P: F col,v,uls.s/(3d x ) N/A F col,v,uls.s/(3d y ) N/A kn Masterseries 0P: F col,v,uls.s/(3d x ) N/A F col,v,uls.s/(3d y ) N/A kn Extrapolation P: F col,v,uls.s/(3d x ) N/A F col,v,uls.s/(3d y ) N/A kn Extrapolation P: F col,v,uls.s/(3d x ) N/A F col,v,uls.s/(3d y ) N/A kn Extrapolation 3P: F col,v,uls.s/(3d x ) N/A F col,v,uls.s/(3d y ) N/A kn Extrapolation 4P: F col,v,uls.s/(3d x ) N/A F col,v,uls.s/(3d y ) N/A kn Extrapolation 5P: F col,v,uls.s/(3d x ) 955 F col,v,uls.s/(3d y ) 000 kn Extrapolation Generic: user-defined N/A user-defined N/A kn Note that F base,uls is positive (tensile); ULS base force in plane of width per metre, F base,uls,x / 458kN/m ULS base force in plane of length per metre, F base,uls,y / 936kN/m ULS base force in plane of width per metre, b r,x.f base,uls,x / 458kN/m cl ULS base force in plane of length per metre, b r,y.f base,uls,y / kn/m BS80 Area of steel required in x per metre, A s,t,x = (b r,x.f base,uls,x / ) / (0.95f y ) 3336mm /m Area of steel required in y per metre, A s,t,y = (b r,y.f base,uls,y / ) / (0.95f y ) 5085mm /m Note that F col,v,uls does not account for primary moments nor secondary moments due to eccentricity of vertical loading and horizontal loading, thus not accounted for within the base area steel; Area of tensile steel reinforcement provided in x per metre, A s,prov,b,x 67mm /m Base tension capacity in x utilisation = A s,t,x / A s,prov,b,x 54% Area of tensile steel reinforcement provided in y per metre, A s,prov,b,y 763mm /m Base tension capacity in y utilisation = A s,t,y / A s,prov,b,y 9% Pile Cap Diagonal Compression Capacity Design (Truss Theory) ULS diagonal force, F diagonal,uls = K. MAX (F pile,v,i ). (d +L d ) 0.5 / d 7464kN L d L d L d P/6P/P: N/A N/A.8S N/A.803S N/A mm P/7P/P: 0.5S N/A.0S N/A.803S N/A mm 3P/8P/3P: 0.6S N/A.44S N/A.0S N/A mm 4P/9P/4P: 0.707S N/A.44S N/A.5S N/A mm 5P/0P/5P:.0S N/A.5S N/A.36S 405 mm Generic: user-defined N/A mm Note that L d is the distance of the furthest pile from the centroid of the column load; Diagonal compression capacity, N cap = 0.60f cu.(π.d /4) 6786kN Diagonal compression capacity utilisation = F diagonal,uls / N cap 0% NOT

13 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 3 Pile Cap Base Reinforcement Design (Shallow and Deep Beam Theory) ULS moment at column base in plane of width, M x ULS moment at column base in plane of length, M y 4580kNm 74844kNm P: N/A N/A N/A N/A knm P: N/A N/A M y ={M only} N/A knm 3P: M x ={M, M, M3} N/A M y ={M, M, M3} N/A knm 4P: M x ={M, M, M3} N/A M y ={M, M, M3} N/A knm 5P: M x ={M, M, M3} N/A M y ={M, M, M3} N/A knm 6P: M x ={M, M, M3} N/A M y ={M, M, M3} N/A knm 7P: M x ={M, M, M3} N/A M y ={M, M, M3} N/A knm s 8P: M x ={M, M, M3} N/A M y ={M, M, M3} N/A knm s 9P: M x ={M, M, M3} N/A M y ={M, M, M3} N/A knm s 0P: M x ={M, M, M3} N/A M y ={M, M, M3} N/A knm s P: M x ={M, M, M3} N/A M y ={M, M, M3} N/A knm s P: M x ={M, M, M3} N/A M y ={M, M, M3} N/A knm n 3P: M x ={M, M, M3} N/A M y ={M, M, M3} N/A knm n 4P: M x ={M, M, M3} N/A M y ={M, M, M3} N/A knm n 5P: M x ={M, M, M3} 4580 M y ={M, M, M3} knm n Generic: user-defined N/A user-defined N/A knm Note moment calculations based on either: - Method Cantilever Span Moment (Modified) M x = f mx.k. ΣF pile,v,i.(x i-c -b/) M y = f my.k. ΣF pile,v,i.(y i-c -h/) Method Timoshenko S/S Coefficients (Modified) M x = K.F pilecap,v. β. M y = K.F pilecap,v. β. Method 3 GPSS GSA C/S Coefficients M x = K.F pilecap,v. β. M y = K.F pilecap,v. β. M x M y ULS moment at column base in plane of width per metre, M x / ULS moment at column base in plane of length per metre, M y / ULS moment at column base in plane of width per metre, s c,x.m x / ULS moment at column base in plane of length per metre, s c,y.m y / 507kNm/m 07kNm/m 507kNm/m 07kNm/m Concrete moment capacity in x per metre, M u,x = 0.56f cu.000.d x 630 knm/m Concrete moment capacity in y per metre, M u,y = 0.56f cu.000.d y 6547 knm/m Bending stress in x, [M/bd ] x = (s c,x.m x / )/[(000).d x ] 0.50N/mm Bending stress in y, [M/bd ] y = (s c,y.m y / )/[(000).d y ].0N/mm Bending stress ratio in x, K x = [M/bd ] x / f cu <= Bending stress ratio in y, K y = [M/bd ] y / f cu <= Lever arm in x, z x = d x.[0.5 + (0.5-K x /0.9) 0.5 ] <= 0.95d x 309mm Lever arm in y, z y = d y.[0.5 + (0.5-K y /0.9) 0.5 ] <= 0.95d y 3008mm Area of steel required in x per metre, A s,m,x = (s c,x.m x / )/[(0.95f y ).z x ] 3843mm /m Area of steel required in y per metre, A s,m,y = (s c,y.m y / )/[(0.95f y ).z y ] 984mm /m

14 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 4 Area of steel required in x per metre (deep beam), A s,m,x,db =.75(s c,x.m x / 55mm /m Reynolds Area of steel required in y per metre (deep beam), A s,m,y,db =.75(s c,y.m y / 3mm /m T.48 Note A s,m,x,db to be distributed over depth of (5T cap L db,x )/0 from soffit 695 mm cl..4. Depth of zone used by A s,m,x,db ( 0.75(5T cap L db,x )/0) 80% 555 mm Note A s,m,y,db to be distributed over depth of (5T cap L db,y )/0 from soffit 55 mm cl..4. Depth of zone used by A s,m,y,db ( 0.75(5T cap L db,y )/0) 7% 603 mm L db,x L db,y P: N/A N/A N/A N/A mm P: N/A N/A.0S N/A mm 3P:.0S N/A.0S N/A mm 4P:.0S N/A.0S N/A mm 5P:.45S N/A.45S N/A mm 6P:.0S N/A.0S N/A mm 7P:.734S N/A.0S N/A mm 8P:.0S N/A.0S N/A mm 9P:.0S N/A.0S N/A mm 0P:.0S N/A 3.0S N/A mm P:.0S N/A 3.0S N/A mm P:.0S N/A 3.0S N/A mm 3P:.0S N/A 4.0S N/A mm 4P:.0S N/A 5.0S N/A mm 5P:.0S S 700 mm Generic: user-defined N/A user-defined N/A mm Area of tensile steel reinforcement provided in x per metre, A s,prov,b,x 67mm /m Sagging bending moment (shallow beam theory) in x utilisation = A s,m,x / A s,p 63% Sagging bending moment (deep beam theory) in x utilisation = A s,m,x,db / A s,p 90% Area of tensile steel reinforcement provided in y per metre, A s,prov,b,y 763mm /m Sagging bending moment (shallow beam theory) in y utilisation = A s,m,y / A s,p 5% Sagging bending moment (deep beam theory) in y utilisation = A s,m,y,db / A s,p 74% Base Reinforcement Percentage % Min base reinforcement in x (>= T cap G50; >= % % Min base reinforcement in x utilisation 74% % Min base reinforcement in y (>= T cap G50; >= % % Min base reinforcement in y utilisation 6%

15 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 5 Structure, Member Design - Geotechnics Pile Cap XX 6--5 Pile Cap Punching Shear Reinforcement Design ULS vertical (downward) load from column and base slab, F col,v,uls Note that F col,v,uls is positive (downward); 633kN Area of column base section, A c = b.h (rectangular) or πd /4(circular) mm Effective depth to base steel, d = (d x + d y )/ 37mm Area of tensile steel reinforcement provided per metre, (A s,prov,b,x. + A s,prov 080mm /m ρ w = 00A s,prov,b /(000.d) 0.35% cl BS80 First shear perimeter, ν c = (0.79/.5)(ρ w f cu /5) /3 (400/d) /4 ; ρ w < N/mm T.3.8 Second shear perimeter, ν c = (0.79/.5)(ρ w f cu /5) /3 (400/d) /4 ; ρ N/mm BS80 Column Base Face Perimeter Shear force at column base face, V = ABS(F col,v,uls ) 633kN Effective shear force, V eff, =.00. V (moment effects ignored) 633kN Column base face perimeter, u 500mm Rectangular Circular Internal column:.(b+h) 500 π.d N/A mm Shear stress at column base face perimeter, ν = V eff, / u d (< 0.8f 0.5 cu & 5N/ 3.84N/mm Ultimate shear stress utilisation 77% First Shear Perimeter Shear force 0% D inside face of pile from column base face, V = F col,v,uls - F 5870kN P/6P/P: N/A N/A 0.M(F P ) N/A.M(F P ) N/A kn P/7P/P: N/A N/A.M(F P ) N/A 0.M(F P ) N/A kn 3P/8P/3P: 0.M(F P ) N/A 0.M(F P ) N/A.M(F P ) N/A kn 4P/9P/4P: 0.M(F P ) N/A.M(F P ) N/A 0.M(F P ) N/A kn 5P/0P/5P:.M(F P ) N/A 0.M(F P ) N/A.M(F P ) 460 kn Generic: user-defined N/A kn Note M(F P ) above refers to K. MIN (F pile,v,i ); Effective shear force, V eff, =.00. V (moment effects ignored) Column base first shear perimeter, u Internal column: F N/A 5870kN 960mm P: N/A N/A mm P: N/A N/A mm 3P:.0S-D+.(0.D)] +.[( ) 0.5 S-D+.(0.D)] N/A mm 4P: 4.[.0S-D+.(0.D)] N/A mm 5P: 4.[.45S-D+.(0.D)] N/A mm 6P:.[.0S-D+.(0.D)] +.[.0S-D+.(0.D)] N/A mm 7P: 6.[.0S-D+.(0.D)] N/A mm 8P: 4.[.0S-D+.(0.D)] N/A mm 9P: 4.[.0S-D+.(0.D)] N/A mm 0P: 4.[( ) 0.5 S-D+.(0.D)] N/A mm P:( ) 0.5 S-D+.(0.D)] +.[.0S-D+.(0.D)] N/A mm P:.[.0S-D+.(0.D)] +.[.0S-D+.(0.D)] N/A mm 3P:( ) 0.5 S-D+.(0.D)] +.[.0S-D+.(0.D)] N/A mm 4P:.[.0S-D+.(0.D)] +.[.0S-D+.(0.D)] N/A mm 5P: 4.[.0S-D+.(0.D)] 960 mm Generic: user-defined N/A mm Note first shear perimeter refers to first perimeter 0% D inside face of pile; Shear stress at column base first shear perimeter, ν = V eff, / u d.43n/mm (Shear capacity enhancement by calculating v d at "support" and comparing against enhanced v c within F N/A.5d of the "support" as clause BS80 employed, that of clause BS80 not applicable;) F N/A Rectangular or Circular

16 E N G I N E E R S Consulting Engineers jxxx 6 Distance 0% D inside face of pile from column base face, a v ( 0.375d) 90mm cl.6..3(8) P: N/A N/A mm EC P: N/A N/A mm 3P: MAX [(.0S-D-b)/+0.D, (4/3S-D-h)/+0.D] N/A mm 4P: MAX [(.0S-D-b)/+0.D, (.0S-D-h)/+0.D] N/A mm 5P: MAX [(.45S-D-b)/+0.D, (.45S-D-h)/+0.D] N/A mm 6P: MAX [(.0S-D-b)/+0.D, (.0S-D-h)/+0.D] N/A mm 7P: MAX [(.734S-D-b)/+0.D, (.0S-D-h)/+0.D] N/A mm 8P: MAX [(.0S-D-b)/+0.D, (.0S-D-h)/+0.D] N/A mm 9P: MAX [(.0S-D-b)/+0.D, (.0S-D-h)/+0.D] N/A mm 0P: MAX [(.0S-D-b)/+0.D, (.0S-D-h)/+0.D] N/A mm P: MAX [(.0S-D-b)/+0.D, (.0S-D-h)/+0.D] N/A mm P: MAX [(.0S-D-b)/+0.D, (.0S-D-h)/+0.D] N/A mm 3P: MAX [(.0S-D-b)/+0.D, (.0S-D-h)/+0.D] N/A mm 4P: MAX [(.0S-D-b)/+0.D, (.0S-D-h)/+0.D] N/A mm 5P: MAX [(.0S-D-b)/+0.D, (.0S-D-h)/+0.D] 00 mm Generic: user-defined N/A mm Note b and h above are replaced by D for circular columns, here D referring to the column dimension; Note conservatively, the furthest pile in the relevant perimeter is taken for the calculation of a v ; (Note that a v is limited to.5d, beyond which no shear capacity enhancement is exhibited, i.e..5d/a v =;) Shear enhancement, a v = 90 mm <=.5d = 4758 mm Adopted Enhanced shear capacity,.5dν c /a v x N/mm Enhanced shear capacity,.5dν c /a v (< 0.8f cu 0.5 & 5N/mm ) x N/mm Note that the enhanced shear capacity is limited to 0.8f cu 0.5 & 5N/mm ; Case ν <.5dν c /a v VALID No nominal / design links require 4609 >= 3768 mm Case.5dν c /a v < ν <.6(.5dν c /a v ) N/A N/A >= N/A mm Note > Note that v c above refers to.5dv c /a v ; Case.6(.5dν c /a v ) < ν <.0(.5dν c /a v ) N/A N/A >= N/A mm Note > Note that v c above refers to.5dv c /a v ; Case ν >.0(.5dν c /a v ) N/A Shear link diameter for first shear perimeter, φ link,/3 5mm No. of links for first shear perimeter, n l, 5 No. of perimeters within first shear perimeter, n p, (>= ) 4 No. of links, n l,,0/-5/-0/-5/-0 = (u No. of links, n l,,-/-6/-/-6/- = (u No. of links, n l,,-/-7/-/-7/- = (u No. of links, n l,,-3/-8/-3/-8/-3 = (u No. of links, n l,,-4/-9/-4/-9/-4 = (u Note links are to be distributed over perimeters (spaced at 0.75d) within the first shear perimeter (of zone.5d) with a pitch of links of.5d. Links should be anchored round at least layer of tension rebars, i.e. bottom rebars; Effective area provided by all links for first shear perimeter, 0.75A sv,prov, 4609mm Note only links within the central 0.75a v effectively cross the inclined shear cracks (EC cl.6..3(8), BS80 cl First shear perimeter shear utilisation 69%

17 E N G I N E E R S Consulting Engineers jxxx 7 Structure, Member Design - Geotechnics Pile Cap XX 6--5 Second Shear Perimeter Shear force 0% D inside face of pile from column base face, V 3 = F col,v,uls 4946kN P/6P/P: N/A N/A N/A N/A.M(F P ) N/A kn P/7P/P: N/A N/A N/A N/A.M(F P ) N/A kn 3P/8P/3P: N/A N/A N/A N/A 3.M(F P ) N/A kn 4P/9P/4P: N/A N/A N/A N/A.M(F P ) N/A kn 5P/0P/5P: N/A N/A.M(F P ) N/A 3.M(F P ) 3860 kn Generic: user-defined N/A kn Note M(F P ) above refers to K. MIN (F pile,v,i ); Effective shear force, V eff,3 =.00. V 3 (moment effects ignored) Column base second shear perimeter, u 3 Internal column: F N/A F N/A F N/A Rectangular or Circular 4946kN 060mm P: N/A N/A mm P: N/A N/A mm 3P: N/A N/A mm 4P: N/A N/A mm 5P: N/A N/A mm 6P: N/A N/A mm 7P: N/A N/A mm 8P: N/A N/A mm 9P: N/A N/A mm 0P:( ) 0.5 S-D+.(0.D)] +.[.0S-D+.(0.D)] N/A P:( ) 0.5 S-D+.(0.D)] +.[3.0S-D+.(0.D)] N/A mm mm P:.[.0S-D+.(0.D)] +.[3.0S-D+.(0.D)] N/A mm 3P:( ) 0.5 S-D+.(0.D)] +.[3.0S-D+.(0.D)] N/A mm 4P:.[.0S-D+.(0.D)] +.[3.0S-D+.(0.D)] N/A mm 5P:.[.0S-D+.(0.D)] +.[4.0S-D+.(0.D)] 060 mm Generic: user-defined N/A mm Note second shear perimeter refers to second perimeter 0% D inside face of pile; Shear stress at column base second shear perimeter, ν 3 = V eff,3 / u 3 d 0.77N/mm (Shear capacity enhancement by calculating v d at "support" and comparing against enhanced v c within.5d of the "support" as clause BS80 employed, that of clause BS80 not applicable;) l );

18 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 8 Distance 0% D inside face of pile from column base face, a v ( 0.375d) 70mm cl.6..3(8) P: N/A N/A mm EC P: N/A N/A mm 3P: N/A N/A mm 4P: N/A N/A mm 5P: N/A N/A mm 6P: N/A N/A mm 7P: N/A N/A mm 8P: N/A N/A mm 9P: N/A N/A mm 0P: MAX [(.0S-D-b)/+0.D, (3.0S-D-h)/+0.D] N/A mm P: MAX [(.0S-D-b)/+0.D, (3.0S-D-h)/+0.D] N/A mm P: MAX [(.0S-D-b)/+0.D, (3.0S-D-h)/+0.D] N/A mm 3P: MAX [(.0S-D-b)/+0.D, (4.0S-D-h)/+0.D] N/A mm 4P: MAX [(.0S-D-b)/+0.D, (3.0S-D-h)/+0.D] N/A mm 5P: MAX [(.0S-D-b)/+0.D, (4.0S-D-h)/+0.D] 70 mm Generic: user-defined N/A mm Note b and h above are replaced by D for circular columns, here D referring to the column dimension; Note conservatively, the furthest pile in the relevant perimeter is taken for the calculation of a v ; (Note that a v is limited to.5d, beyond which no shear capacity enhancement is exhibited, i.e..5d/a v =;) Shear enhancement, a v = 70 mm <=.5d = 4758 mm Adopted Enhanced shear capacity,.5dν c /a v x N/mm Enhanced shear capacity,.5dν c /a v (< 0.8f cu 0.5 & 5N/mm ) x N/mm Note that the enhanced shear capacity is limited to 0.8f cu 0.5 & 5N/mm ; Case ν 3 <.5dν c /a v VALID No nominal / design links require 83 >= mm Case.5dν c /a v < ν 3 <.6(.5dν c /a v ) N/A N/A >= N/A mm Note > Note that v c above refers to.5dv c /a v ; Case.6(.5dν c /a v ) < ν 3 <.0(.5dν c /a v ) N/A N/A >= N/A mm Note > Note that v c above refers to.5dv c /a v ; Case ν 3 >.0(.5dν c /a v ) N/A Shear link diameter for second shear perimeter, φ link,/3 5mm No. of links for second shear perimeter, n l,3 30 No. of perimeters within second shear perimeter, n p,3 (>= ) 7 No. of links, n l,3,0/-5/-0/-5/-0 = (u No. of links, n l,3,-/-6/-/-6/- = (u No. of links, n l,3,-/-7/-/-7/- = (u No. of links, n l,3,-3/-8/-3/-8/-3 = (u No. of links, n l,3,-4/-9/-4/-9/-4 = (u Note links are to be distributed over perimeters (spaced at 0.75d) within the second shear perimeter (of zone.5d) with a pitch of links of.5d. Links should be anchored round at least layer of tension rebars, i.e. bottom rebars; Effective area provided by all links for second shear perimeter, 0.75A sv,prov,3 83mm Note only links within the central 0.75a v effectively cross the inclined shear cracks (EC cl.6..3(8), BS80 cl Second shear perimeter shear utilisation 85%

19 E N G I N E E R S Consulting Engineers jxxx 9 Pile Cap Shear Reinforcement Design (Shallow Beam Theory) ULS shear force for bending in plane of width, V x ULS shear force for bending in plane of length, V y 300kN 770kN cl BS80 V x V y P: N/A N/A N/A N/A kn P: N/A N/A K. ΣF pile,v,i N/A kn 3P: K. ΣF pile,v,i N/A K. ΣF pile,v,i N/A kn 4P: K. ΣF pile,v,i N/A K. ΣF pile,v,i N/A kn 5P: K. ΣF pile,v,i N/A K. ΣF pile,v,i N/A kn 6P: K. ΣF pile,v,i N/A K. ΣF pile,v,i N/A kn 7P: K. ΣF pile,v,i N/A K. ΣF pile,v,i N/A kn 8P: K. ΣF pile,v,i N/A K. ΣF pile,v,i N/A kn 9P: K. ΣF pile,v,i N/A K. ΣF pile,v,i N/A kn 0P: K. ΣF pile,v,i N/A K. ΣF pile,v,i N/A kn P: K. ΣF pile,v,i N/A K. ΣF pile,v,i N/A kn P: K. ΣF pile,v,i N/A K. ΣF pile,v,i N/A kn 3P: K. ΣF pile,v,i N/A K. ΣF pile,v,i N/A kn 4P: K. ΣF pile,v,i N/A K. ΣF pile,v,i N/A kn 5P: K. ΣF pile,v,i 300 K. ΣF pile,v,i 770 kn Generic: user-defined N/A user-defined N/A kn ULS shear force in plane of width per metre, V x / ULS shear force in plane of length per metre, V y / ULS shear force in plane of width per metre, s c,x.v x / ULS shear force in plane of length per metre, s c,y.v y / 87kN/m 447kN/m 87kN/m 447kN/m Ultimate shear stress in x, v ult,x =(s c,x.v x / )/(000.d x )(< 0.8f 0.5 cu & 5N/mm 0.89N/mm Ultimate shear stress in x utilisation 8% Ultimate shear stress in y, v ult,y =(s c,y.v y / )/(000.d y )(< 0.8f 0.5 cu & 5N/mm.4N/mm Ultimate shear stress in y utilisation 8% Design shear stress in x, v d,x =(s c,x.v x / )/(000.d x ) 0.89N/mm Design shear stress in y, v d,y =(s c,y.v y / )/(000.d y ).4N/mm (Shear capacity enhancement by calculating v d at "support" and comparing against enhanced v c within d of the "support" as clause BS80 employed, that of clause BS80 not applicable;) Area of tensile steel reinforcement provided in x per metre, A s,prov,b,x 67mm /m ρ w,x = 00A s,prov,b,x /(000.d x ) 0.9% Coefficient, (400/d x ) /4 >0.67 no links, (400/d x ) /4 >.00 with links.00 T.3.8 v c,x = (0.79/.5)(ρ w,x f cu /5) /3 (400/d x ) /4 ; ρ w,x <3; f cu <40; (400/d x ) /4 >( N/mm Area of tensile steel reinforcement provided in y per metre, A s,prov,b,y 763mm /m ρ w,y = 00A s,prov,b,y /(000.d y ) 0.56% BS80 Coefficient, (400/d y ) /4 >0.67 no links, (400/d y ) /4 >.00 with links.00 T.3.8 v c,y = (0.79/.5)(ρ w,y f cu /5) /3 (400/d y ) /4 ; ρ w,y <3; f cu <40; (400/d y ) /4 >( N/mm BS80 l );

20 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 0 Structure, Member Design - Geotechnics Pile Cap XX 6--5 Distance 0% D inside face of pile from column base face, a v,x ( 0.5d x ) 60mm cl.6..3(8) Distance 0% D inside face of pile from column base face, a v,y ( 0.5d y ) 340mm EC a v,x P: N/A N/A N/A N/A mm P: N/A N/A (.0S-D-h)/+0.D N/A mm 3P: (.0S-D-b)/+0.D N/A (4/3S-D-h)/+0.D N/A mm 4P: (.0S-D-b)/+0.D N/A (.0S-D-h)/+0.D N/A mm 5P:(.45S-D-b)/+0.D N/A (.45S-D-h)/+0.D N/A mm 6P: (.0S-D-b)/+0.D N/A (.0S-D-h)/+0.D N/A mm 7P:(.734S-D-b)/+0.D N/A (.0S-D-h)/+0.D N/A mm 8P: (.0S-D-b)/+0.D N/A (.0S-D-h)/+0.D N/A mm 9P: (.0S-D-b)/+0.D N/A (.0S-D-h)/+0.D N/A mm 0P: (.0S-D-b)/+0.D N/A (3.0S-D-h)/+0.D N/A mm P: (.0S-D-b)/+0.D N/A (3.0S-D-h)/+0.D N/A mm P: (.0S-D-b)/+0.D N/A (3.0S-D-h)/+0.D N/A mm 3P: (.0S-D-b)/+0.D N/A (4.0S-D-h)/+0.D N/A mm 4P: (.0S-D-b)/+0.D N/A (5.0S-D-h)/+0.D N/A mm 5P: (.0S-D-b)/+0.D 60 (4.0S-D-h)/+0.D 340 mm Generic: user-defined N/A user-defined N/A mm Note b and h above are replaced by D for circular columns, here D referring to the column dimension; Note conservatively, the furthest pile in the relevant direction is taken for the calculation of a v ; (Note that a v is limited to d, beyond which no shear capacity enhancement is exhibited, i.e. d/a v =;) Shear enhancement, a v,x = 60 mm <= d x = 6356 mm Adopted Shear enhancement, a v,y = 340 mm <= d y = 633 mm Adopted Enhanced shear capacity in x, d x v c,x /a v,x x N/mm Enhanced shear capacity in y, d y v c,y /a v,y x.85.3n/mm Enhanced shear capacity in x, [(d x v c,x /a v,x ).(3.0D) +v c,x.( - x N/mm cl Enhanced shear capacity in y, [(d y v c,y /a v,y ).(3.0D) +v c,y.( -B ca x.74.06n/mm BS80 Note that enhanced shear capacity is reduced to account for effective breadth and limited to 0.8f cu 0.5 & 5N/mm a v,y Shear Resistance for Bending in Plane of Width Check v d,x < d x v c,x /a v,x for no nominal / design links Concrete shear capacity d x v c,x /a v,x.(000.d x ) VALID 534kN/m Check v d,x >= d x v c,x /a v,x for design links N/A Provide shear links A sv / S l > 000.(v d,x -d x v c,x /a v,x )/(0. 0.9mm /mm/m Concrete and design links shear capacity (0.75A sv,prov /S 005kN/m Shear Resistance for Bending in Plane of Length Check v d,y < d y v c,y /a v,y for no nominal / design links Concrete shear capacity d y v c,y /a v,y.(000.d y ) N/A 3353kN/m Check v d,y >= d y v c,y /a v,y for design links VALID Provide shear links A sv / S l > 000.(v d,y -d y v c,y /a v,y )/(0. 0.9mm /mm/m Concrete and design links shear capacity (0.75A sv,prov /S 903kN/m Effective area provided by all links per metre, 0.75A sv,prov 7mm /m Tried effective 0.75A sv,prov / S l,/ value 4.09mm /mm/m Design shear resistance (shallow beam theory) in x utilisation 53% Design shear resistance (shallow beam theory) in y utilisation 50% Design shear resistance (shallow beam theory) in x and y combined utilisatio 53%

21 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx Pile Cap Shear Reinforcement Design (Deep Beam Theory) ULS shear force for bending in plane of width, V x ULS shear force for bending in plane of length, V y 300kN 770kN Reynolds T.48 ULS shear force in plane of width per metre, s c,x.v x / 87kN/m Ultimate shear force limit, 000.T cap.f c '/0γ m 7389kN/m cl..4. Note f c ' is the cylinder compressive strength and γ m =.5; Reynolds Ultimate shear force limit, min{000.t cap.ν u,.000.t cap ν c,x k s,x /a x } 6975kN/m cl..4. Note ν u ultimate concrete shear strength from CP 0 T.6 and T.6 replaced by min{0.8f cu 0.5, CIRIA 5.0}N/mm }, ν c,x design concrete shear strength from CP 0 T.5 and T.5 replaced by v c,x Guide and factor, k s,x =.0 for T cap / < 4, else 0.6; Ultimate shear force (deep beam theory) in x utilisation 40% ULS shear force in plane of length per metre, s c,y.v y / 447kN/m Ultimate shear force limit, 000.T cap.f c '/0γ m 7389kN/m cl..4. Note f c ' is the cylinder compressive strength and γ m =.5; Reynolds Ultimate shear force limit, min{000.t cap.ν u,.000.t cap ν c,y k s,y /a y } 455kN/m cl..4. Note ν u ultimate concrete shear strength from CP 0 T.6 and T.6 replaced by min{0.8f cu 0.5, CIRIA 5.0}N/mm }, ν c,y design concrete shear strength from CP 0 T.5 and T.5 replaced by v c,y Guide and factor, k s,y =.0 for T cap / < 4, else 0.6; Ultimate shear force (deep beam theory) in y utilisation 99% Area of tensile steel reinforcement provided in x per metre, A s,prov,b,x 67mm /m Area of tensile steel reinforcement provided in y per metre, A s,prov,b,y 763mm /m Distance to face of pile from column base face, a x = MAX (0, a v,x - 0.D) Distance to face of pile from column base face, a y = MAX (0, a v,y - 0.D) Angle between horizontal bar and critical diagonal crack, θ x = tan - (T cap /a x ) 500mm 3300mm 66.8degrees Angle between horizontal bar and critical diagonal crack, θ y = tan - (T cap /a y ) 46.7degrees Empirical coefficient, k = {0.70 NWC, 0.50 LWC} 0.70 Empirical coefficient, k = {00 plain round bars, 5 deformed bars} 5N/mm Cylinder splitting tensile strength, f t = 0.5(f cu ) N/mm Min breadth for deep beam bending in x, b L MAX {0, 0.65V x /[k.(t cap -0.35a 80mm Min breadth for deep beam bending in y, b B MAX {0, 0.65V y /[k.(t cap -0.35a 347mm Shear Resistance for Bending in Plane of Width No design links Concrete shear capacity, V,x 7643kN/m Note V,x = MAX[0,k.(T cap -0.35a x ).f t.000]+k.a s,prov,b,x.d x.sin θ/t cap ; Design links Note design links are not calculated as they require horizontal links; Shear Resistance for Bending in Plane of Length No design links Concrete shear capacity, V,y 709kN/m Note V,y = MAX[0,k.(T cap -0.35a y ).f t.000]+k.a s,prov,b,y.d y.sin θ/t cap ; Design links Note design links are not calculated as they require horizontal links; Design shear resistance (deep beam theory) in x utilisation 37% Design shear resistance (deep beam theory) in y utilisation 63%

22 Longitudinal shear stress limit, v Rdi.84.84N/mm cl.6..5 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx Pile Cap Longitudinal Shear Within Section (EC) EC V x V y Longitudinal shear stress, N/mm cl.6..5 Ratio, β = cl.6..5 Transverse shear force, V Ed = {s c,x.v x /, s c,y.v y / } kN/m cl.6..5 Lever arm, z = {z x, z y } m cl.6..5 Width of the interface, b i = 000mm mm cl.6..5 Note c.f ctd = 0.00 if σ n is negative (tension); cl.6..5 Roughness coefficient, c cl.6..5 Roughness coefficient, µ 0.9 cl.6..5 Design tensile strength, f ctd.40n/mm with α ct =.0, γ C =.5.0N/mm 3.00N/mm 40N/mm cl.3..6 T.3. T.3. T.3. Characteristic cylinder strength of concrete, f ck 3N/mm T.3. Characteristic cube strength of concrete, f cu 40N/mm T.3. Normal stress across longitudinal shear interface, σ n N/mm Note σ n = Σ[factor. 0.75F pile,v,n /(. )]; Reinforcement ratio, ρ = A s / A i cl.6..5 Area of reinforcement, A s = A sv,prov / S l,/ mm /m/m Note that the area of reinforcement crossing the shear interface may include ordinary shear reinforcement with adequate anchorage at both cl.6..5 sides of the interface; Area of the joint, A i = 000.b i mm /m/m Design yield strength of reinforcement, f yd = f yv / γ S, γ S =.5 400N/mm cl Angle of reinforcement, α = 90.0 Design compressive strength, f cd N/mm with α cc =.0, γ C =.5 Strength reduction factor for concrete cracked in shear, ν degrees cl.6..5 cl.3..6 cl.6.. Longitudinal shear stress limit utilisation, v Edi /v Rdi 33% 5%

23 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 3 Pile Cap Longitudinal Shear Within Section (BS80) BS80 Longitudinal shear stress, ν h = K S. F c / (b w. x).87.3n/mm cl Change of total compression force over x, F c kN/m cl Note F c = {(s c,x.m x / 0)/z x, (s c,y.m y / 0)/z y }; Lever arm, z = {z x, z y } m Length under consideration, x = {L db,x /, L db,y /} mm Note x is the beam length between the point of maximum design moment and the point of zero moment; Shear stress distribution factor, K S = The average design shear stress should then be distributed in proportion to the vertical design shear force diagram to give the horizontal shear stress at any point along the length of the member. For UDLs, K S maybe taken as.00 for simply supported beams,.33 for continuous beams and.00 for cantilever beams; Width, b w = 000mm mm M x M y cl cl Longitudinal shear stress limit for no nominal / design vertical reinforcement,.50n/mm Surface type T.5.5 Longitudinal shear stress limit for no nominal / design vertical rein 75% 89% Required nominal vertical reinforcement per unit length, 0.5%b w mm /m/m cl Provided vertical reinforcement per unit length, A e mm /m/m Note A e = A sv,prov / S l,/ ; Required nominal vertical reinforcement per unit length utilisation 8% 8% Note UT set to 0% if longitudinal shear stress limit for no nominal vertical reinforcement UT <= 00%; Required design vertical reinforcement per unit length, A h mm /m/m cl Required design vertical reinforcement per unit length utilisation, 0% 0% Note UT set to 0% if longitudinal shear stress limit for no design vertical reinforcement UT <= 00%;