Footing Design Calculation

FOOTING DESIGN

FOR HEALTH CLUB

STRUCTURAL DESIGN CALCULATION

Submitted Date April 26, 2012

Table of Contents Page No.

1. Design of Footing F1 3




5. Design of Grade Beam GB1 39

SheetJob Number

Job Title

Client

Calcs by Checked by Date

Software Consultants (Pty) LtdInternet: http://www.prokon.comE-Mail : [email protected]

Column Base Design : CORNER COLUMN C15

Input Data

Base length A (m)Base width B (m)Column(s)

C (m)D (m)E (m)F (m)Stub column height X (m)Base depth Y (m)Soil cover Z (m)Concrete density (kN/m3)Soil density (kN/m3)Soil friction angle (°)Base friction constantRebar depth top X (mm)Rebar depth top Y (mm)Rebar depth bottom X (mm)Rebar depth bottom Y (mm)ULS ovt. LF: Self weight

ULS LF: Self weightMax. SLS bearing pr. (kN/m²)S.F. Overturning (ULS)S.F. Slip (ULS)

fcu base (MPa)fcu columns (MPa)fy (MPa)

4.53.5

Col 1 Col 2

.7

.5

1.5.81.3525

18220.575

7575750.9

1.425011

3030460

Unfactored Loads

Load Case

Colno.

LFULSovt

LFULS

P(kN)

Hx(kN)

Hy(kN)

Mx(kNm)

My(kNm)

1 1 1.5 1.4 225 171 1 1.5 1.4 114 156 1 1.5 1.6 272 374

2 1 1.5 1.4 225 171 1 1.5 1.4 114 156 1 1.5 1.4 -219 -244

3 1 1.5 1.4 225 171 1 1.5 1.4 114 156 1 1.5 1.4 -196 -234

4 1 1.5 1.4 225 171 1 1.5 1.4 114 156 1 1.5 1.4 -253 -302

5 1 1.5 1.2 225 171 1 1.5 1.2 114 156 1 1.5 1.2 272 374

1 1.5 1.2 -219 -244 6 1 1.5 1.2 225 171 1 1.5 1.2 114 156 1 1.5 1.2 272 374 1 1.5 1.2 -196 -234 7 1 1.5 1.2 225 171

1 1.5 1.2 114 156 1 1.5 1.2 272 374 1 1.5 1.2 -253 -302

3 of 45

SheetJob Number

Job Title

Client



A

X

Y

Y

BC1

D1

PMx

Z

Hx

Y

X

BS8110 - 1997

Sketch of Base

Output for Load Case 1

Output for Load Case 1Soil pressure (ULS) (kN/m²) 372.98Soil pressure (SLS) (kN/m²) 244.69

SF overturning (SLS) 1.83SF overturning (ULS) 1.44Safety Factor slip (ULS) 1.08Safety Factor uplift (ULS) >100

Bottom Design moment X (kNm/m) 414.11Reinforcement X (mm²/m) 1372Design moment Y (kNm/m) 65.41

Reinforcement Y (mm²/m) 217Top

Design moment X (kNm/m) -111.35Reinforcement X (mm²/m) 369

Design moment Y (kNm/m) 0.00Reinforcement Y (mm²/m) 0Linear Shear X (MPa) 0.380vc (MPa) 0.386

Linear Shear Y (MPa) 0.062vc (MPa) 0.357Linear Shear Other (MPa) 0.000Punching Shear (MPa) 0.289vc (MPa) 0.376Cost 6652.42

4 of 45

SheetJob Number

Job Title

Client



4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

244.69 kN/m²

4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

372.98 kN/m²

Soil Pressures at ULSSoil Pressures at SLS

LegendMax M (+)Max M (-)Max Shear

Load Case:1

BS8110 - 1997








Linear Shear Y (MPa) 0.012vc (MPa) 0.357Linear Shear Other (MPa) 0.000Punching Shear (MPa) 0.033

vc (MPa) 0.357Cost 5796.56

5 of 45

SheetJob Number

Job Title

Client



4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

68.37 kN/m²

4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

95.72 kN/m²



Load Case:2

BS8110 - 1997









vc (MPa) 0.357Cost 5816.07

6 of 45

SheetJob Number

Job Title

Client



4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

71.78 kN/m²

4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

100.49 kN/m²



Load Case:3

BS8110 - 1997






Design moment X (kNm/m) 0.00Reinforcement X (mm²/m) 0



vc (MPa) 0.357Cost 5736.44

7 of 45

SheetJob Number

Job Title

Client



4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

54.92 kN/m²

4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

76.89 kN/m²



Load Case:4

BS8110 - 1997









vc (MPa) 0.357Cost 6137.89

8 of 45

SheetJob Number

Job Title

Client



4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

161.65 kN/m²

4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

200.31 kN/m²



Load Case:5

BS8110 - 1997









vc (MPa) 0.357Cost 6154.78

9 of 45

SheetJob Number

Job Title

Client



4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

165.15 kN/m²

4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

204.48 kN/m²



Load Case:6

BS8110 - 1997









vc (MPa) 0.357Cost 6083.92

10 of 45

SheetJob Number

Job Title

Client



4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

145.88 kN/m²

4.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.3

5

Hx

0.80

1.50

183.00 kN/m²



Load Case:7

BS8110 - 1997

11 of 45

SheetJob Number

Job Title

Client



Schematic reinforcement of Base

23Y25-B-200 (B2)

18Y25-A-200 (B1)

23Y20-D-200 ABR (T2)

18Y20-C-200 ABR (T1)

col1

PLAN

SECTION

B B B B B B B B B B B B B B B B B B B B B B B

3R10-H

R10-H

6Y32-G6Y32-F +4Y32-E +

E

E

E

E

F FF FF F

G

G

G

G

G

G

SECTION: col1

12 of 45

SheetJob Number

Job Title

Client



Column Base Design : CORNER COLUMN-F2 C15

Input Data





3.63

Col 1 Col 2

.7

.5

1.2.71.0525

18220.575

7575750.9

1.425011

3030460

Unfactored Loads

Load Case

Colno.

LFULSovt

LFULS

P(kN)

Hx(kN)

Hy(kN)

Mx(kNm)

My(kNm)

1 1 1.5 1.4 200 116 1 1.5 1.4 95 102 1 1.5 1.6 228 243

2 1 1.5 1.4 200 116 1 1.5 1.4 95 102 1 1.5 1.4 -246 -244

3 1 1.5 1.4 200 116 1 1.5 1.4 95 102 1 1.5 1.4 -109 -127

4 1 1.5 1.2 200 116 1 1.5 1.2 95 102 1 1.5 1.2 228 243

1 1.5 1.2 -246 -244 5 1 1.5 1.2 200 116 1 1.5 1.2 95 102

1 1.5 1.2 228 243 1 1.5 1.2 -109 -127

A

X

Y

Y

B

C1

D1

PMx

Z

Hx

Y

X

BS8110 - 1997

Sketch of Base

13 of 45

SheetJob Number

Job Title

Client








Design moment X (kNm/m) -52.99Reinforcement X (mm²/m) 204Design moment Y (kNm/m) 0.00Reinforcement Y (mm²/m) 0Linear Shear X (MPa) 0.323vc (MPa) 0.362


vc (MPa) 0.360Cost 3908.40

3.60

X

Y

Y

3.0

0

0.70

0.50

PMx

1.0

5

Hx

0.70

1.20

241.11 kN/m²

3.60

X

Y

Y

3.0

0

0.70

0.50

PMx

1.0

5

Hx

0.70

1.20

365.31 kN/m²



Load Case:1

BS8110 - 1997

14 of 45

SheetJob Number

Job Title

Client











vc (MPa) 0.357Cost 3435.84

3.60

X

Y

Y

3.0

0

0.70

0.50

PMx

1.0

5

Hx

0.70

1.20

48.92 kN/m²

3.60

X

Y

Y

3.0

0

0.70

0.50

PMx

1.0

5

Hx

0.70

1.20

68.49 kN/m²



Load Case:2

BS8110 - 1997

15 of 45

SheetJob Number

Job Title

Client











vc (MPa) 0.357Cost 3522.28

3.60

X

Y

Y

3.0

0

0.70

0.50

PMx

1.0

5

Hx

0.70

1.20

80.66 kN/m²

3.60

X

Y

Y

3.0

0

0.70

0.50

PMx

1.0

5

Hx

0.70

1.20

112.92 kN/m²



Load Case:3

BS8110 - 1997

16 of 45

SheetJob Number

Job Title

Client











vc (MPa) 0.357Cost 3591.03

3.60

X

Y

Y

3.0

0

0.70

0.50

PMx

1.0

5

Hx

0.70

1.20

126.05 kN/m²

3.60

X

Y

Y

3.0

0

0.70

0.50

PMx

1.0

5

Hx

0.70

1.20

158.58 kN/m²



Load Case:4

BS8110 - 1997

17 of 45

SheetJob Number

Job Title

Client











vc (MPa) 0.357Cost 3690.36

3.60

X

Y

Y

3.0

0

0.70

0.50

PMx

1.0

5

Hx

0.70

1.20

177.12 kN/m²

3.60

X

Y

Y

3.0

0

0.70

0.50

PMx

1.0

5

Hx

0.70

1.20

217.28 kN/m²



Load Case:5

BS8110 - 1997

18 of 45

SheetJob Number

Job Title

Client




19Y20-B-200 (B2)

15Y20-A-200 (B1)

19Y20-D-200 ABR (T2)

15Y20-C-200 ABR (T1)

col1

PLAN

SECTION

B B B B B B B B B B B B B B B B B B

3R10-H

R10-H

2Y25-G2Y32-F +4Y32-E +

E

E

E

E

F F

G

G

SECTION: col1

19 of 45

SheetJob Number

Job Title

Client




Input Data





1.71.5

Col 1 Col 2

.7

.5

1.2.41.0525

18220.575

7575750.9

1.425011

3030460

Unfactored Loads

Load Case

Colno.

LFULSovt

LFULS

P(kN)

Hx(kN)

Hy(kN)

Mx(kNm)

My(kNm)

1 1 1.5 1.4 95 4 1 1.5 1.4 18 6 1 1.5 1.6 43 13

2 1 1.5 1.4 95 4 1 1.5 1.4 18 6 1 1.5 1.4 -48 -21

3 1 1.5 1.4 95 4 1 1.5 1.4 18 6 1 1.5 1.4 -56 -6

4 1 1.5 1.2 95 4 1 1.5 1.2 18 6 1 1.5 1.2 43 13

1 1.5 1.2 -48 -21 5 1 1.5 1.2 15 4 1 1.5 1.2 18 6

1 1.5 1.2 43 13 1 1.5 1.2 -56 -6

A

X

Y

Y

B

C1

D1

PMx

Z

Hx

Y

X

BS8110 - 1997

Sketch of Base

20 of 45

SheetJob Number

Job Title

Client








Design moment X (kNm/m) 0.00Reinforcement X (mm²/m) 0Design moment Y (kNm/m) 0.00Reinforcement Y (mm²/m) 0Linear Shear X (MPa) 0.084vc (MPa) 0.376

Linear Shear Y (MPa) 0.050vc (MPa) 0.376Linear Shear Other (MPa) 0.000Punching Shear (MPa) N.A.

vc (MPa) N.A.Cost 481.58

1.70

X

Y

Y

1.5

0

0.70

0.50

PMx

1.0

5

Hx

0.40

1.20

142.52 kN/m²

1.70

X

Y

Y

1.5

0

0.70

0.50

PMx

1.0

5

Hx

0.40

1.20

208.66 kN/m²



Load Case:1

BS8110 - 1997

21 of 45

SheetJob Number

Job Title

Client












1.70

X

Y

Y

1.5

0

0.70

0.50

PMx

1.0

5

Hx

0.40

1.20

80.27 kN/m²

1.70

X

Y

Y

1.5

0

0.70

0.50

PMx

1.0

5

Hx

0.40

1.20

112.38 kN/m²



Load Case:2

BS8110 - 1997

22 of 45

SheetJob Number

Job Title

Client












1.70

X

Y

Y

1.5

0

0.70

0.50

PMx

1.0

5

Hx

0.40

1.20

61.63 kN/m²

1.70

X

Y

Y

1.5

0

0.70

0.50

PMx

1.0

5

Hx

0.40

1.20

86.29 kN/m²



Load Case:3

BS8110 - 1997

23 of 45

SheetJob Number

Job Title

Client












1.70

X

Y

Y

1.5

0

0.70

0.50

PMx

1.0

5

Hx

0.40

1.20

77.20 kN/m²

1.70

X

Y

Y

1.5

0

0.70

0.50

PMx

1.0

5

Hx

0.40

1.20

98.73 kN/m²



Load Case:4

BS8110 - 1997

24 of 45

SheetJob Number

Job Title

Client












1.70

X

Y

Y

1.5

0

0.70

0.50

PMx

1.0

5

Hx

0.40

1.20

75.91 kN/m²

1.70

X

Y

Y

1.5

0

0.70

0.50

PMx

1.0

5

Hx

0.40

1.20

97.17 kN/m²



Load Case:5

BS8110 - 1997

25 of 45

SheetJob Number

Job Title

Client




9Y16-B-200 (B2)

8Y16-A-200 (B1)

9Y16-D-200 ABR (T2)

8Y16-C-200 ABR (T1)

col1

PLAN

SECTION

B B B B B B B B B

3R10-H

R10-H

2Y20-G2Y20-F +4Y20-E +

E

E

E

E

F F

G

G

SECTION: col1

26 of 45

SheetJob Number

Job Title

Client




Input Data





3.503.50

Col 1 Col 2

.7

.5

1.20.501.0525

18220.575

7575750.9

1.425011

3030460

Unfactored Loads

Load Case

Colno.

LFULSovt

LFULS

P(kN)

Hx(kN)

Hy(kN)

Mx(kNm)

My(kNm)

1 1 1.5 1.4 120 24 1 1.5 1.4 44 28 1 1.5 1.6 105 66

2 1 1.5 1.4 120 24 1 1.5 1.4 44 28 1 1.5 1.4 -122 -84

3 1 1.5 1.4 120 24 1 1.5 1.4 44 28 1 1.5 1.4 -129 -68

4 1 1.5 1.2 120 24 1 1.5 1.2 44 28 1 1.5 1.2 105 66

1 1.5 1.2 -122 -84 5 1 1.5 1.2 120 24 1 1.5 1.2 44 28

1 1.5 1.2 105 66 1 1.5 1.2 -129 -68 6 1 1.5 1.4 120 24 1 1.5 1.4 44 28 1 1.5 1.4 -207 -179 95 7 1 1.5 1.4 120 24

1 1.5 1.4 44 28 1 1.5 1.4 -214 -163 95 8 1 1.5 1.2 120 24 1 1.5 1.2 44 28 1 1.5 1.2 105 66 1 1.5 1.2 -207 -179 -95

9 1 1.5 1.2 120 24 1 1.5 1.2 44 28 1 1.5 1.2 105 66 1 1.5 1.2 -214 -163 -95

27 of 45

SheetJob Number

Job Title

Client



A

X

Y

Y

B

C1

D1

PMx

Z

Hx

Y

X

BS8110 - 1997

Sketch of Base








Linear Shear Y (MPa) 0.081vc (MPa) 0.357Linear Shear Other (MPa) 0.000Punching Shear (MPa) 0.120vc (MPa) 0.357Cost 3027.33

28 of 45

SheetJob Number

Job Title

Client



3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

81.74 kN/m²

3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

119.29 kN/m²



Load Case:1

BS8110 - 1997









vc (MPa) 0.357Cost 2807.06

29 of 45

SheetJob Number

Job Title

Client



3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

42.76 kN/m²

3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

59.86 kN/m²



Load Case:2

BS8110 - 1997









vc (MPa) 0.357Cost 2792.08

30 of 45

SheetJob Number

Job Title

Client



3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

38.38 kN/m²

3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

53.73 kN/m²



Load Case:3

BS8110 - 1997









vc (MPa) 0.357Cost 2860.12

31 of 45

SheetJob Number

Job Title

Client



3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

51.80 kN/m²

3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

68.51 kN/m²



Load Case:4

BS8110 - 1997









vc (MPa) 0.357Cost 2865.11

32 of 45

SheetJob Number

Job Title

Client



3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

55.04 kN/m²

3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

72.39 kN/m²



Load Case:5

BS8110 - 1997



SF overturning (SLS) 2.24SF overturning (ULS) 1.23Safety Factor slip (ULS) 1.66Safety Factor uplift (ULS) 5.42




Design moment Y (kNm/m) -24.58Reinforcement Y (mm²/m) 139Linear Shear X (MPa) 0.072vc (MPa) 0.357


vc (MPa) 0.357Cost 2910.75

33 of 45

SheetJob Number

Job Title

Client



3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

87.69 kN/m²

3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

122.76 kN/m²



Load Case:6

BS8110 - 1997



SF overturning (SLS) 2.39SF overturning (ULS) 1.29Safety Factor slip (ULS) 1.78Safety Factor uplift (ULS) 4.66






vc (MPa) 0.357Cost 2892.27

34 of 45

SheetJob Number

Job Title

Client



3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

81.46 kN/m²

3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

114.04 kN/m²



Load Case:7

BS8110 - 1997









vc (MPa) 0.357Cost 2886.73

35 of 45

SheetJob Number

Job Title

Client



3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

74.79 kN/m²

3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

95.00 kN/m²



Load Case:8

BS8110 - 1997









vc (MPa) 0.357Cost 2873.89

36 of 45

SheetJob Number

Job Title

Client



3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

69.51 kN/m²

3.50

X

Y

Y

3.5

0

0.70

0.50

PMx

1.0

5

Hx

0.50

1.20

89.75 kN/m²



Load Case:9

BS8110 - 1997

37 of 45

SheetJob Number

Job Title

Client




18Y16-B-200 (B2)

18Y16-A-200 (B1)

18Y16-D-200 ABR (T2)

18Y16-C-200 ABR (T1)

col1

PLAN

SECTION

B B B B B B B B B B B B B B B B B B

3R10-H

R10-H

4Y20-G4Y20-F +4Y20-E +

E

E

E

E

F F

F F

G

G

G

G

SECTION: col1

38 of 45

Project Job Ref.

Section Sheet no./rev.

1

Calc. by

ADate

4/25/2012Chk'd by Date App'd by Date

RC BEAM DESIGN (BS8110);CONCRETE RECTANGULAR BEAM DESIGN (CL 3.4.4.4)

BEAM DEFINITION

; Beam width; b = 300 mm

; Overall beam depth ; h = 600 mm

; Nominal cover to all reinforcement including links; cnom = 75 mm

; Tension bar diameter (try); Dtry = 32 mm

; Link bar diameter (try if applicable); Ldia_try = 10 mm

Depth to tension steel; d = h - cnom - Ldia_try - Dtry/2 = 499 mm

; Characteristic strength of reinforcement; fy = 460 N/mm2

; Characteristic strength of concrete; fcu = 30 N/mm2

; Clear span of beam; L = 9500 mm

The beam is not a deep beam - calculations OK

BS8110 - DESIGN MOMENTS AND SHEARS (SAGGING)M = 180.0 kNm

V = 100.0 kN

CONCRETE RECTANGULAR BEAM COMPRESSION STEEL REQUIRED? (CL 3.4.4.4)

Calculations also valid for flanged beams with neutral axis in flange

; Design ultimate moment; M = 180 kNm

; Moment redistribution factor; βb = 1.00

Reinforcement required

;;; K = abs(M) / ( b × d2 × fcu ) = 0.080

K' = min (0.156 , (0.402 × (βb - 0.4)) - (0.18 × (βb - 0.4)2 )) = 0.156

Compression steel not required

Beam requiring tension steel only

;; z = min (( 0.95 × d),(d×(0.5+√(0.25-K/0.9)))) = 450 mm

;;; As_req = abs(M) / (1/γms × fy × z) = 914 mm2

Tension steel

;;Use 3 No. 32 dia bar(s); As_prov = Ast = 2410 mm2

Area of tension steelprovided sufficient

Check min and max areas of tension steelTotal area of concrete; Ac = b × h = 180000 mm2

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; Minimum percentage of tension steel; kt = 0.13 %

Ast_min = kt × Ac = 234 mm2

Ast_max = 4 % × Ac = 7200 mm2

;Area of tension steel provided; As_prov = 2410 mm2

Area of tension steelprovided OK

NOTIONAL COMPRESSION STEEL;;

;Provide 1 No. 6 dia bar(s) ; As'prov = Asc = 28 mm 2

SHEAR RESISTANCE OF CONCRETE BEAMS CLOSE TO SUPPORTS - AV < 2D (CL 3.4.5.8)

; Length of member traversed by a shear failure plane; av = 500 mm

;; Breadth of beam (average web width of flanged section); bv = 300 mm

av < 2d - calculations valid

; Effective area of tension reinforcement - at section x-x; As_shear = 2410 mm2

; Design ultimate shear force; V = 100 kN

Applied shear stress

v = V / (bv × d) = 0.668 N/mm2

Check shear stress to clause 3.4.5.2

vallowable = min ((0.8 N1/2/mm) × √(fcu ), 5 N/mm2 ) = 4.382 N/mm2

Shear stress OK

Shear stresses to clause 3.4.5.4

It is assumed that nominal shear reinforcement is provided and reinforcement provided by bent up bars is not considered.

Design shear stress

vc = 1.57 N/mm2

0.5 × vc = 0.79 N/mm2

Applied shear stress; v = 0.67 N/mm2

Note - shear reinforcement not necessarily required - provide nominal links

The shear stress component resisted by shear reinforcement

vsv = max (abs(v) - vc , 0.4 N/mm2 ) = 0.400 N/mm2

Reinforcement Requirements

; Characteristic strength of shear reinforcement; fyv = 460 N/mm2

The link requirements will be determined allowing for the code requirement that the calculated reinforcement should be

provided within the middle three-quarters of the length av.

cl. 3.4.5.9

;Estimated ratio; Asv_to_sv_reqd = bv × vsv/ (0.95 × fyv × 0.75) = 0.366 mm

Define Links Provided;;

Provide 10 dia links in 2s @ 200 centres ;Ratio provided; Asv_to_sv = 1.571 mm ; Link spacing; sv = 200 mm ; Link diameter; Ldia = 10 mm

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No of links in each group; Ln = 2 ; Area of steel per link group; Asv = 314 mm2

Check that the chosen link spacing provides sufficient total steel within the middle three-quarters of av:

Asv_reqd = av × bv × vsv / (0.95 × fyv) = 137 mm2

No. of link groups within middle three-quarters of length av; Ng = Quotient( 0.75 × av, sv ) = 1

Asv_prov = Ng × Asv = 314 mm2

Area of shear steel provided sufficient

SPACING OF SHEAR LINKS (CL 3.4.5.5)

; Shear steel; Link spacing; sv = 200 mm

; Max spacing; slimit = 0.75 × d = 374.3 mm

Shear link spacing OK

CONCRETE BEAM DEFLECTION CHECK (CL 3.4.6)

; Design ultimate moment; M = 180 kNm

Modification Factors

;Basic span / effective depth ratio (Table 3.10); ratiospan_depth = 20

The modification factor for spans in excess of 10m (ref. cl 3.4.6.4) has not been included.

;fs = fy × As_req / (1.4 × γms × As_prov × βb ) = 118.7 N/mm2

factortens = min ( 2 , 0.55 + ( 477 N/mm2 - fs ) / ( 120 × ( 0.9 N/mm2 + abs(M) / (b×d2)))) = 1.452

factorcomp = min ( 1.5 , 1 + (100×As'prov/(b×d)) / (3 + (100×As'prov/(b×d)))) = 1.006

Calculate Maximum Span

This is a simplified approach and further attention should be given where special circumstances exist. Refer to clauses3.4.6.4 and 3.4.6.7.

Maximum span; Lmax = ratiospan_depth × factortens × factorcomp × d = 14.58 m

Check the actual beam span

Actual span/depth ratio; L / d = 19.04

Span depth limit; ratiospan_depth × factortens × factorcomp = 29.23

Span/Depth ratio checksatisfied

CLEAR DISTANCE BETWEEN BARS IN TENSION (CL 3.12.11.2.4)

ACTUAL CLEAR DISTANCE BETWEEN TENSION BARS

; Diameter of tension bars; Dt = 32 mm

; Number of tension bars; Lnt = 3

; Diameter of shear links; Ldia = 10 mm

Nominal cover

Nominal cover to steel (links if present); cnom = h - d - Dt/2 - Ldia = 75 mm

Actual clear distance

Clear distance between bars; spacingbars = ( b - 2×( cnom + Ldia) - Dt ) / (Lnt - 1) - Dt = 17.0 mm

Calculate maximum allowable clear distance

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Tension steel

; Characteristic strength of reinforcement; fy = 460 N/mm2

; Moment Redistribution Factor; βb = 1.00

Approx Service Stress

; fs = fy × As_req / (1.4 × γms× As_prov × βb ) = 118.7 N/mm2

Maximum allowable clear distance between tension bars;

spacingmax = min ((47000 N/mm) / fs , 300 mm) = 300 mm

Max distance between bars check - OK

Minimum clear distance between tension bars

; Assumed aggregate size; hagg = 20 mm

spacingmin = hagg + 5 mm = 25 mm

Min distance between bars check - NOT Satisfied

CLEAR DISTANCE BETWEEN FACE OF BEAM AND NEAREST LONGITUDINAL BAR IN TENSION (CL 3.12.11.2.5)

Distance from tension bar to face of beam

Distface = cnom + Ldia + Dt/2 = 101.0 mm

Distmax = spacingmax / 2 = 150.0 mm

Max distance to beam face check - OK

CHECK OF NOMINAL COVER - (BS8110:PT 1, TABLE 3.4); Diameter of tension reinforcement; Dt = 32 mm

; Diameter of links; Ldia = 10 mm

Cover to tension reinforcement

cten = h - d - Dt / 2 = 85.0 mm

Nominal cover to links steel

cnom = cten - Ldia = 75.0 mm

Permissable minimum nominal cover to all reinforcement (Table 3.4)

; cmin = 35 mm

Cover OK

SERVICEABILITY LIMIT STATE - CRACKING OF BEAMS

(BS8110:Pt 2, Cl. 3.8 & BS8007 Cl 2.6 & Appendix B)

; Design serviceability moment; MSLS = 120 kNm

; Diameter of links; Ldia = 10 mm

; Diameter of tension reinforcement; Dt = 32 mm

; Number of tension reinforcement bars; Lnt = 3

Area of tension reinforcement; Ast = π × Dt2 /4 × Lnt = 2413 mm2

Cover to tension reinforcement

cten = h - d - Dt / 2 = 85.0 mm

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cnom = cten - Ldia = 75.0 mm

Tension bar centres

barcrs = (b - 2×(cnom + Ldia) - Dt ) / (Lnt - 1) = 49.0 mm

MODULAR RATIO

Modulus of elasticity for reinforcement; Es = 200 kN/mm2

BS8110:Pt 1:Cl 2.5.4

Modulus of elasticity for concrete (half the instanteneous)

Ec = ((20 kN/mm2) + 200×fcu) / 2 = 13 kN/mm2

BS8110:Pt 2:Equation 17

Modular ratio; m = Es / Ec = 15.385

NEUTRAL AXIS POSITION

For equilibrium; Fst equates Fc

Therefore: m × Ast × [ fc×(d-x)/x ] equates to 0.5 × fc × b × x

Solving for x gives the position of the neutral axis in the section:-

x = d × [ -1×Es×Ast/(Ec×b×d) + √( Es×Ast/(Ec×b×d) × (2+Es×Ast/(Ec×b×d)))] = 248.8 mm

Depth of concrete in compression

x = 248.8 mm

CONCRETE AND STEEL STRESSES

The serviceability limit state moment; MSLS = 120 kNm

Taking moments about the centreline of the reinforcement:-

Moment of resistance of concrete is 0.5 × fc × b × x × (d - x/3)

Solving for concrete stress fc gives;

fc = 2 × abs(MSLS) / ( b × x × (d - x/3)) = 7.73 N/mm2

Allowable stress; 0.45 × fcu = 13.50 N/mm2

Concrete stress OK

Taking moments about the centre of action of the concrete force:-

Moment of resistance of steel is fst × As × (d - x/3)

Solving for steel stress fst gives;

fst = abs(MSLS) / ( Ast × (d - x/3)) = 119.54 N/mm2

CONCRETE AND STEEL STRAINS

Strain in the reinforcement

εs = fst / Es = 597.7××××10-6

Allowable steel strain; 0.8 × fy / Es = 1.840××××10-3

Steel strain OKBS8007:App B.4

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; Allowable crack width; CrackAllowable = 0.2 mm

BS8007:Cl 2.2.3.3

Factor for stiffening based on limiting crack width

factor = if(CrackAllowable >= (0.2 mm), (1.0 N/mm2), (1.5 N/mm2)) = 1 N/mm2

Breadth of tension face; bt = b = 300 mm

Strain in the concrete at the level at which crack widths are required

Tension face of beam

Level of crack; a'1 = h = 600 mm

ε11 = εs × (a'1 - x)/(d - x) = 839.0××××10-6

Strain in the concrete at the level at which crack width is required adjusted for stiffening of the concrete tension zone

εm1 = min( ε11 ,max(0 , ε11 - [ factor × bt× (h - x) × (a'1 - x) / (3×Es× Ast ×(d - x))])) = 736.8××××10-6

BS8007:App B.3

Distance from tension bar to crack in tension face between tension bars

acrt1 = √ ( (barcrs/2)2 + (cnom + Ldia + Dt/2)2) - Dt/2 = 87.9 mm

Distance from tension bar to crack in tension face at corner of beam

acrt2 = √(2) × (cnom + Ldia + Dt/2 ) - Dt/2 = 126.8 mm

Critical distance from tension bar

acr1 = max(acrt1, acrt2 ) = 126.8 mm

Design crack width in tension face

Crackdesign1 = 3 × acr1 × εm1 /(1 + 2×(acr1 - cten)/(h - x)) = 0.226 mm

BS8007:App B.2

Side of beam mid way between NA and tension steel

Level of crack; a'2 = x + (d - x)/2 = 374 mm

ε12 = εs × (a'2 - x)/(d - x) = 298.9××××10-6

Strain in the concrete at the level at which crack width is required adjusted for stiffening of the concrete tension zone

εm2 = min( ε12 , max(0 , ε12 - [ factor × bt× (h - x) × (a'2 - x) / (3×Es× Ast ×(d - x))])) = 262.5××××10-6

BS8007:App B.3

Distance from tension bar to crack in side face mid way between NA and tension steel

acr2 = √( ((d - x)/2)2 + (cnom + Ldia + Dt/2)2) - Dt/2 = 144.8 mm

Design crack width in side of beam

Crackdesign2 = 3 × acr2 × εm2 /(1 + 2×(acr2 - cten)/(h - x)) = 0.085 mm

BS8007:App B.2

Design crack width

Crackdesign = max(Crackdesign1 , Crackdesign2 ) = 0.226 mm

Max allowable crack width

CrackAllowable = 0.20 mm

BS8007:Cl 2.2.3.3

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Allowable crack width exceeded - FAIL

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