Shear force capacity for hollowcores, EN 1168 4.3.3.2.2.2, Advanced method
Source: -
Date: 2022-11-28
Version of PRE-Stress: 6.7.028 (2022-10-28)
PRE-Stress-file is attached
.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
Handcalculation | PRE-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+A3:2011 | EN 1168:2005+A3:2011 |
SS 21 25 53:2013 | SS 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 | ||
Concrete | C40/50 | |
Prestressed reinforcement | Y1860S7 | 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 section
- 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
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 bwρ.
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
PRE-Stress
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 * fck/γc = 1,0 * 40/1,5 = 26,67 MPa
fctk0,05 = 2,456 MPa
fctd = αct * fctk0,05/γc = 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 = fp0,1k/γs = 1640/1,15 = 1426 MPa
fpuk = 1860 MPa
fpud = fpk/γs = 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 |
---|---|---|---|---|---|---|
1 | 0 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
2 | 0 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
3 | 0 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
4 | 0 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
5 | 0 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
6 | 0 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
7 | 0 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
8 | 0 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
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 |
---|---|---|---|---|---|---|---|---|
1 | 0 | 8000 | 49 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
2 | 0 | 8000 | 271 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
3 | 0 | 8000 | 361 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
4 | 0 | 8000 | 554 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
5 | 0 | 8000 | 644 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
6 | 0 | 8000 | 837 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
7 | 0 | 8000 | 927 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
8 | 0 | 8000 | 1149 | 37 | 1000 | 12.9 | 100 | Y1860S7 |
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 concrete | qG.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
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
PRE-Stress
Design
Critical point on line of failure
Handcalculation
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.
Concrete compressive stress at height y and distance lx
Handcalculation
This will give a matrix with the stress in each x- and y-point of the beam.
From this matrix the values along the critical line is extracted into a vector, with a value for each x-value.
PRE-Stress
No values are extracted graphically.
Concrete shear stress due to transmission of prestress at height y and distance lx
Handcalculation
This will give a matrix with the shear stress in each x- and y-point of the beam.
From this matrix the values along the critical line is extracted into a vector, with a value for each x-value.
PRE-Stress
No values are extracted graphically.
Shear force capacity
Handcalculation
Using the input from previous calculations above we now put them into the final formula:
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:
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.
VRdc = 181.7 kN
x = 235 mm from the end (or 135 mm from the support)
Concrete width at the critical point:
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