Source: -
Date: 2022-11-28

Version of PRE-Stress: 6.7.028 (2022-10-28)

PRE-Stress-file is attached here.

The file used for handcalculations will not be available for public use.

If there are parameters used in both PRE-Stress and handcalculations there might be a postfix added (.PRE for PRE-Stress) or (.HC for hand calculations)

Codes and standards used

HandcalculationPRE-Stress
EN 1990 (2002-04-xx)SS-EN 1990 (2014-12-xx)
EN 1992-1-1:2004/A1:2014 (2014-12-xx)SS-EN 1992-1-1:2005/A1:2014 (2015-01-16)
EN 1168:2005+A3:2011EN 1168:2005+A3:2011
SS 21 25 53:2013SS 21 25 53:2013

Other documents

-

Prerequisites

Geometry and material

Hollowcore subjected to a uniform load.

  • Total length of the element Ltot = 8000 mm, theoretical span L0 = 7800 mm.
  • Exposure class XC1, Life class L50
Material  
ConcreteC40/50 
Prestressed reinforcementY1860S7

7-strand wire

øp = 12.9mm, cross section area = 100 mm2, relaxation class 2

Cross section

Handcalculation

The cross section is derived from among other things the following parameters:

  • Schematic of a cross sectionimage-20221205161002-7.png
    • H = 380 mm
    • B = 1197 mm
    • b = 1141 mm
    • ncores.outer = 2
    • bt1 = 213
    • bb1 = 213
    • h1 = 295
    • c1 = 45
    • rt1 = 143
    • rb1 = 130
    • zrt1 = c1 + rt1 = 188 mm
    • zrb1 = (H - c1 - h1) + rb1 = 170 mm
    • ncores.inner = 2
    • bt2 = 218 mm
    • bb2 =  218 mm
    • h2 = 295 mm
    • c2 = 45 mm
    • rt2 = 143 mm
    • rb2 = 130 mm
    • zrt2 = c2 + rt2 = 188 mm
    • zrb2 = (H - c2 - h2) + rb2 = 170 mm
  • Lifting indentations
    A formula to reduce the cross section due to lifting indentations is used
    image-20221206134637-1.png
    image-20221206134746-2.png

image-20221205142846-2.png

For the handcalculation a function of the width bw(y) is shown in the figure above, both without the reinforcement (blue) and with the reinforcement (black, Idealized cross section). Two vectors with the width at each y-coordinate is used in the calculation. One for the concrete cross section bw0 and one for the idealized cross section b.

image-20221205155550-5.png

image-20221205155615-6.png

Cross section area

The area of the cross section is calculated as the width at each level x 1mm height

Ac0.HC = 211 689.6 mm2

Acρ.HC = 215 321.8 mm2

Center of gravity

By integrating over the cross section a center of gravity is derived:

Yc0.HC = 193.16 mm

Ycρ.HC = 190.53 mm

Second moment of area (Moment of intertia)

By integrating over the cross section a center of gravity is derived:

Ic0.HC = 3867e6 mm4

Icρ.HC = 3954e6 mm4

image-20221212104033-1.png

PRE-Stress

image-20221205141246-1.png

Cross section area

Reinforcement is not considered in the section parameters shown when selecting the section parameters.

Ac.PRE = 214 300 mm2 (Reinforcement not considered)

  • Ac.PRE / Ac0.HC = 1.012

Center of gravity

Reinforcement is not considered in the section parameters shown when selecting the section parameters.

In the design the reinforcement is considered.

Yc0.PRE = 191 mm

Second moment of area (Moment of intertia)

Reinforcement is not considered in the section parameters shown when selecting the section parameters.

In the design the reinforcement is considered.

Ic0.PRE = 3.931e9 mm4

Design strengths

Strengths are calculated according to EN 1992-1-1, 3.1.6, 3.2.7, 3.3.6 and SS 21 25 53:2013

Concrete:
                      fck = 40 MPa
                      fcd = αcc * fckc = 1,0 * 40/1,5 = 26,67 MPa
                      fctk0,05 = 2,456 MPa
                      fctd = αct * fctk0,05c = 1,0 * 2,456/1,5 = 1,64 MPa
                      fctm = 3,509 MPa
                      Ecm = 35,22 GPa

           At release:
                      fck,i = 30 MPa
                      fctk0,05,i = 2,0 MPa
                      fctm,i = 2.9 MPa
                      Ecm,i = 33 GPa

Prestressing reinforcement:
                      7-strand wire
                      øp = 12.9 mm
                      Api = 100 mm2
                      fp0,1k = 1640 MPa
                      fpd = fp0,1ks = 1640/1,15 = 1426 MPa
                      fpuk = 1860 MPa
                      fpud = fpks = 1860 / 1,15 = 1617 MPa
                      Es = 195 GPa
                      εpuk = 3,15 * 10-2

Reinforcement

Coordinates - Handcalculation

No.x [mm]z [mm]Prestress [MPa]Diameter [mm]Area [mm2]Material
1037100012.9100Y1860S7
2037100012.9100Y1860S7
3037100012.9100Y1860S7
4037100012.9100Y1860S7
5037100012.9100Y1860S7
6037100012.9100Y1860S7
7037100012.9100Y1860S7
8037100012.9100Y1860S7

y-coordinates are not used, as an uneven placement (excentricity) is not considered in the hand calculation.

Coordinates - PRE-Stress

No.x (start) [mm]x (end) [mm]y [mm]z [mm]Prestress [MPa]Diameter [mm]Area [mm2]Material
1080004937100012.9100Y1860S7
20800027137100012.9100Y1860S7
30800036137100012.9100Y1860S7
40800055437100012.9100Y1860S7
50800064437100012.9100Y1860S7
60800083737100012.9100Y1860S7
70800092737100012.9100Y1860S7
808000114937100012.9100Y1860S7

Long term losses

Handcalculation

No losses (creep, shrinkage or relaxation) are considered for simplifying the calculations.

PRE-Stress

No losses (creep, shrinkage or relaxation) are considered to be able to compare with the handcalculations.

Manufacturing

Sudden release EN 1992-1-1 8.10.2.2, is not considered.

Design loads

Permanent loads  

Deadload hollowcore

Density of reinforced concrete (incl. reinforcement)

qG.HC

qG.PRE

ρc

5.12 kN/m

5.36 kN/m

24 kN/m3 + 1 kN/m3 = 25 kN/m3

Deadload joint concreteqG.joint 
Variable loads  
Live load

qd

ψ0

5 kN/m2

0.7

q(x)HC = 1.35 * qG + 1.5 * ψ0 * qd * 1.2 m2/m = 1.35 * 5.38 kN/m + 1.5 * 0.7 * 5kN/m2 * 1.2 m2/m = 13.568 kN/m

q(x)PRE = 1.35 * qG + 1.5 * ψ0 * qd * 1.2 m2/m = 1.35 * 5.36 kN/m + 1.5 * 0.7 * 5kN/m2 * 1.2 m2/m = 13.531 kN/m

Reactions

Handcalculation

VA = qG * Ltot / 2 = 21.53 kN (Deadload only)

VB = qG * Ltot / 2 = 21.53 kN (Deadload only)

VA = q(x) * Ltot / 2 = 54.27 kN (Design load)

VB = q(x) * Ltot / 2 = 54.27 kN (Design load)

PRE-Stress

image-20221215080500-3.png

VA = 21.43 kN (Deadload only)

VB = 21.43 kN (Deadload only)

VA = 54.12 kN (Design load)

VB = 54.12 kN (Design load)

Shear force

Handcalculation

image-20221215115337-4.png

PRE-Stress

image-20221215115427-5.png

Design

Critical point on line of failure

Handcalculation

image-20221215115739-6.png

The vector consits of the y-coordinate for each x-coordinate. Plotting the vector gives the line of failure.

PRE-Stress

PRE-Stress gives the angle 35 degrees from the support and looks at some points along the line where the critical value might be.

It is important to select the Advanced (EN1168 4.3.3.2.2.2)-option to get a comparable design.

image-20221216135122-24.png

Concrete compressive stress at height y and distance lx

image-20221215171422-7.png

Handcalculation

image-20221216100431-10.png

image-20221216100711-11.png

This will give a matrix with the stress in each x- and y-point of the beam.

image-20221216101231-12.png

From this matrix the values along the critical line is extracted into a vector, with a value for each x-value.

image-20221216101753-13.png

PRE-Stress

No values are extracted graphically.

Concrete shear stress due to transmission of prestress at height y and distance lx

image-20221215172114-8.png

Handcalculation

image-20221216103506-14.png

image-20221216111725-16.png

image-20221216111808-17.png

image-20221216111826-18.png

This will give a matrix with the shear stress in each x- and y-point of the beam.

image-20221216113549-19.png

From this matrix the values along the critical line is extracted into a vector, with a value for each x-value.

image-20221216113832-20.png

PRE-Stress

No values are extracted graphically.

Shear force capacity

image-20221215172359-9.png

Handcalculation

Using the input from previous calculations above we now put them into the final formula:

image-20221216125514-21.png

The result is a matrix with all possible Shear force capacities in the beam, but only the results along the critical line are relevant to look at.

By extracting those values we get a vector along the beam with the capacity for each x-coordinate:

image-20221216131504-22.png

Some values are not relevant, as they are not part of the design criterion according to EN 1168. Only values between the support and along the critical line are allowed.

So the final step is to find the lowest value of the shear capacity within the viable range.

image-20221216134749-23.png

VRdc = 181.7 kN

x = 235 mm from the end (or 135 mm from the support)

Concrete width at the critical point:

image-20221216142235-26.png

PRE-Stress

The capacity in PRE-Stress is shown as a range between coordinates.

Below is the capacity 188.26kN shown for range 0.10m-0.19m

image-20221216143507-27.png

Copyright 2020 StruSoft AB
PRE-Stress Documentation