beam_design_spreadsheet

8/7/2019 Beam_Design_Spreadsheet

http://slidepdf.com/reader/full/beamdesignspreadsheet 1/31



Caculation Sheet

Project Title: Designed by: Rob Lane

Checked by: Maire Greene Sheet: of:

Project No: Approved by:

Element: Post Tensioned Concrete Beam File Ref: Rev:

Package: Package No: Date:

Item Output

2.0 Material Properties

2.1Concrete Unit Weight 24

45

fcm 53

Assuming transfer at day 5

t = 5

0.711

fcm (5) 37.663

fck (5) 29.663

fctm 3.795

fctm (5) 2.697

fct 17.798 fcw 27

ftt -2.697 ftw 0

ymc 1.5

2.2

Steel Tendon Type EN10138 7 wire steel strand, Y1770S7

fpk 1770

kN/m3

CharacteristicStrength (fck) N/mm2

N/mm2

Time factor (β)

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2



Caculation Sheet






Item Output

fp0.1k 1520

Area 140 each

Diameter 15.2 mm

Weight kN/m

Ep 195

yms 1.15

3.0 Section Properties

3.1 0.4 m

0.039

Zt 0.099

Zb 0.099

4.0 Loading

Q (live load) 12 kN/m

G (dead load) 4 kN/m

3.6 kN/m

Self Weight 13.44 kN/m

17.44 kN/m

29.44 kN/m

N/mm2

mm2

kN/mm2

Depth to NeutralAxis

Second Momentof Area m4

(provided boxsection and void islocated centrally)

m3

m3

Quasi-permanent liveload

Transfer Loading

Total unfactoredSLS Loading



Caculation Sheet






Item Output

5.0 Analysis

5.1

Elastic

Bending

Moments

BMD Span 1

Mmax (sag) 33 kNm

8.13 m

Mmax (hog) 37.5 kNm

QSE Results for loading of 1kN/m

Dis fromSupport1



Caculation Sheet






Item Output

Mmax (sag) 0.78 kNm

28.75 m

Mmax (hog) 37.5 kNm

5.2

Elastic

Shear

Forces

-8.13 kN

11.9 kN

Dis fromSupport1

Shear force atsupport 1

Shear force at

support 2



Caculation Sheet






Item Output

-8.75 kN

1.25 kN

Multiply results above by the relevent load to obtain design moments

Summary

Assumed Losses

@ Transfer 0.9

Mmi 575.52 kNm

Msi -654 kNm

0.7

Mmw 971.52 kNmMsw -1104 kNm



@ WorkingConditions



Caculation Sheet






Item Output

6.0 Magnel Inequalities

Zt/A 176.190 mm

Zb/A 176.190 mm

6.1

Mid Eqn 1

Span

Eco < 9.35E+08 + 176.19

P

Eqn 2

Eco < ### - 176.19

P

Eqn3

Eco > ### + 176.19

P

Eqn 4

Eco > ### - 176.19

P



Caculation Sheet






Item Output

6.2

Support Eqn 5

Section

Eco < -2.68E+09 + 176.19

P

Eqn 6

Eco < -1.02E+09 - 176.19

P

Eqn 7

Eco > -1.58E+09 + 176.19

P

Eqn 8

Eco > ### - 176.19

P

7.0 Eccentricity

100 mm

eco 500 mm

Cover to CoG of P



Caculation Sheet






Item Output

Read 1/P from Magnel Diagrams

1/P 0 N-1

P 1443 kN

1054.83

No 7.53 no.

==> 8 no.

Ap 1120

1532.16 kN

& Check if e is ok!

#.0 Prestress Losses

#.1

Loss μ 0.2 (friction coefficient)

Data k 0.01 (wobble coefficient)

Draw-in 3 mm

195

P 1,445 kN

Area of TendonsRequired mm2

mm2

Pprovided

SketchArrangement

Etendon kN/mm2



Caculation Sheet






Item Output

1,120

#.2 Friction Losses

Single End x 10 m distance for which P is being calculated

Jacking ∑θ 0.1 rads cumulative change in slope of the tendon between en

P(x) 1388.34 kN

57 kN

%Loss 3.92 % at x NB Check with Assumptions

Draw-in Losses (assuming fricting between tendon and duct)

m 5.67 kN/m lossess per metre run of tendon

Ld 10.75 m

121.86 kN

P(0) 1,323 kN

%Loss 8.43 % At free end

Mid Span draw in 10 m

Double End P(x) 1379.8 kN

Long Term assume short term + 20%

P(x) LT 1103.84 kN

Aprestress mm2

ΔP

ΔP



Caculation Sheet






Item Output

#.0 ULS Design Checks

Must Satisfy

1 Equilibrium

2 Compatibility

3 Plane sections remain plane

Safety Factors 1.5

γd 1.35

#.1

Choose MID SPAN

Section

e 500 mm

d 1000 mm

Ap 1540

1547 kN

Take Simplified Approach (No Ult Strain Limit ) and Use EC2 Simplified Stress Block

γl

mm2

Long Term

Prestress



Caculation Sheet






Item Output

0.02

Ec 0

fp0.1k/yms 1321.74

Es1 0.01

Fs 2035.48 kN

Fc 2035.48 kN

From Simplified Stress Block

Fc = 0.567*fck*0.8x*b x=depth to NA

Ac 79775.75

Aflange 200000

Yes

If Yes:

x 99.72 mm

Strain Es2 0.03

Yes

If Yes:

Mur = Fc * z z = lever arm

Mur = 1954.29 kNm

Ult Load 36.14 kN/m

Assume steelyields @ strain= 0.02

N/mm2

Strain in steel from Prestress

mm2

mm2

Is Ac fullyinside Flange?

HasReinforcementYielded?



Caculation Sheet






Item Output

Ult Moment 1807.2 kNm

Ok? Yes

Design Margin



an



5 10 15 20

-800

-600

-400

-200

200

400

600

800

1000



25 30

SPAN Upp

SPAN Low

SUPPORT Upp

SUPPORT Low

emaxtop

emaxbottomLinear Transformation

Eco

e(x)



Limit Kern

Span Support

Kb 380 mm Kb 275.2 mm a

Kt 169.4 mm Kt 253 mm b

transfer uwi 9.84 kN/m P

work udl ww 25.84 kN/m

left hand Rai 80 Raw 210.08

right han Rci 12.3 Rcw 32.3

x 0 2 4 6 8 10 12

M(x)i 0 140.32 241.28 302.88 325.11 307.99 251.51

M(x)w 0 368.48 633.6 795.36 853.75 808.79 660.47

Mi/ap 0 62.36 107.23 134.61 144.49 136.89 111.78

Mw/bp 0 210.56 362.06 454.49 487.86 462.17 377.41

eupp 380 442.36 487.23 514.61 524.49 516.89 491.78

elow -169.4 41.16 192.66 285.09 318.46 292.77 208.01

eupp 275.2 485.76 637.26 729.69 763.06 737.37 652.61

elow -253 -190.64 -145.77 -118.39 -108.51 -116.11 -141.22



0.9

0.7

2500 kN

14 16 18 20 22 24 26 28

155.67 20.47 -154.09 -368.02 -216.48 -103.32 -29.52 4.92

408.79 53.75 -404.65 -966.42 -568.48 -271.32 -77.52 12.92

69.19 9.1 -68.49 -163.56 -96.21 -45.92 -13.12 2.19

233.59 30.71 -231.23 -552.24 -324.85 -155.04 -44.3 7.38

449.19 389.1 311.51 216.44 283.79 334.08 366.88 382.19

64.19 -138.69 -400.63 -721.64 -494.25 -324.44 -213.7 -162.02

508.79 305.91 43.97 -277.04 -49.65 120.16 230.9 282.58

-183.81 -243.9 -321.49 -416.56 -349.21 -298.92 -266.12 -250.81



30

0

0

0

0

380 SPAN

-169.4SPAN

275.2SUPPORT

-253 SUPPORT

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