csi etabs & safe manual: slab analysis and design to ec2

CSI ETABS & SAFE MANUAL

Part‐III: Model Analysis & Design of Slabs

According to Eurocode 2

AUTHOR: VALENTINOS NEOPHYTOU BEng (Hons), MSc

REVISION 2: August, 2014

2

ABOUT THIS DOCUMENT

This document presents an example of analysis design of slab using ETABS. This example examines a simple single story building, which is regular in plan and elevation. It is examining and compares the calculated ultimate moment from CSI ETABS & SAFE with hand calculation. Moment coefficients were used to calculate the ultimate moment. However it is good practice that such hand analysis methods are used to verify the output of more sophisticated methods.

Also, this document contains simple procedure (step-by-step) of how to design solid slab according to Eurocode 2.The process of designing elements will not be revolutionised as a result of using Eurocode 2.

Due to time constraints and knowledge, I may not be able to address the whole issues.

Please send me your suggestions for improvement. Anyone interested to share his/her knowledge or willing to contribute either totally a new section about ETABS or within this section is encouraged.

For further details:

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Email: [email protected]

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mailto:[email protected]

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3

TABLE OF CONTENTS

1. SLAB MODELING .................................................................................... 4

2. THEORETICAL CALCULATION OF ULTIMATE MOMENTS ......... 5

3. DESIGN OF SLAB ACCORDING TO EUROCODE 2 ........................... 7

4. WORKED EXAMPLE : ANALYSIS AND DESIGN OF RC SLAB

USING CSI ETABS AND SAFE .............................................................. 11

5. ANALYSIS RESULTS ............................................................................. 17

6. DESIGN THE SLAB FOR FLEXURAL USING MOMENT CAPACITY

VALUES .................................................................................................... 19

ANNEX A - EXAMPLE OF HOW TO DETERMINE THE DESIGN BENDING

MOMENT USING MOMENT COEFFICIENTS...…………………….22

ANNEX B - EXAMPLE OF HOW TO DETERMINE THE MOMENT CAPACITY

OF RC SLAB………………………………………………………..…….28

ANNEX C - EXAMPLE OF DESIGN SLAB PANEL WITH TWO

DISCONTINUOUS EDGES…………..…..………………………..…….32

ANNEX D - EXAMPLE OF DESIGN SLAB PANEL WITH ONE

DISCONTINUOUS EDGES………………………………………..…….48

ANNEX E - EXAMPLE OF DESIGN INTERIOR PANEL SLAB..…………..…….65

4

1. SLAB MODELING

1.1 ASSUMPTIONS

In preparing this document a number of assumptions have been made to avoid over

complication; the assumptions and their implications are as follows.

a) Element type : SHELL

b) Meshing (Sizing of element) : Size= min{Lmax/10 or l000mm}

c) Element shape : Ratio= Lmax/Lmin = 1 ≤ ratio ≤ 2

d) Acceptable error : 20%

1.2 INITIAL STEP BEFORE RUN THE ANALYSIS

a) Sketch out by hand the expected results before carrying out the analysis.

b) Calculate by hand the total applied loads and compare these with the sum of

the reactions from the model results.

5

2. THEORETICAL CALCULATION OF ULTIMATE MOMENTS

Maximum moments of two-way slabs

If ly/lx<2: Design as a Two-way slab

If lx/ly> 2: Deisgn as a One-way slab

Note: lx is the longer span

ly is the shorter span

Msx= asxnlx2 in

direction of span lx

n: is the ultimate load m2

Msy= asynlx2 in

direction of span ly


Bending moment coefficient for simply supported slab

ly/lx 1.0 1.1 1.2 1.3 1.4 1.5 1.75 2.0

asx 0.062 0.074 0.084 0.093 0.099 0.104 0.113 0.118

asy 0.062 0.061 0.059 0.055 0.051 0.046 0.037 0.029

Maximum moment of Simply supported (pinned) two-way slab

Maximum moment of Restrained supported (fixed) two-way slab

Msx= asxnlx2 in

direction of span lx


Msy= asynlx2 in

direction of span ly


Bending moment coefficient for two way rectangular slab supported by beams

(Manual of EC2 ,Table 5.3)

Type of panel and moment

considered

Short span coefficient for value of Ly/Lx Long-span coefficients for all

values of Ly/Lx 1.0 1.25 1.5 1.75 2.0

Interior panels

Negative moment at continuous edge 0.031 0.044 0.053 0.059 0.063 0.032

Positive moment at midspan 0.024 0.034 0.040 0.044 0.048 0.024

One short edge discontinuous



One long edge discontinuous



Two adjacent edges discontinuous



6

L: is the effective span

Maximum moments of one-way slabs

If ly/lx<2: Design as a Two-way slab

If lx/ly> 2: Deisgn as a One-way slab

Note: lxis the longer span

lyis the shorter span

MEd= 0.086FL

F: is the total ultimate

load =1.35Gk+1.5Qk


Note: Allowance has been made in the coefficients in

Table 5.2 for 20% redistribution of moments.

Maximum moment of Simply supported (pinned)

one-way slab

(Manual of EC2, Table 5.2)

Maximum moment of continuous supported one-

way slab


Uniformly distributed loads

End support condition Moment

End support support MEd =-0.040FL

End span MEd =0.075FL

Penultimate support MEd= -0.086FL

Interior spans MEd =0.063FL

Interior supports MEd =-0.063FL

F: total design ultimate load on span


Note: Allowance has been made in the coefficients in

Table 5.2 for 20% redistribution of moments.

7

3. DESIGN OF SLAB ACCORDING TO EUROCODE 2

𝑓𝑦𝑑 =𝑓𝑦𝑘𝛾𝑠

Determine design yield strength of reinforcement

FLEXURAL DESIGN

(EN1992-1-1,cl. 6.1)

𝐾 =𝑀𝐸𝑑

𝑏𝑑2𝑓𝑐𝑘

𝐾′ = 0.6𝛿 − 0.18𝛿2 − 0.21

Determine K from:

K<K′ (no compression reinforcement required)

Obtain lever arm z:𝑧 =𝑑

2 1 + 1 − 3.53𝐾 ≤ 0.95𝑑

K>K′(then compression reinforcement required –

not recommended for typical slab)

Obtain lever arm z:𝑧 =𝑑

2 1 + 1 − 3.53𝐾′ ≤ 0.95𝑑

δ=1.0 for no redistribution

δ=0.85 for 15% redistribution

δ=0.7 for 30% redistribution

𝐴𝑠.𝑟𝑒𝑞 =𝑀𝐸𝑑

𝑓𝑦𝑑 𝑧

𝐴𝑠𝑥 .𝑟𝑒𝑞 =𝑀𝐸𝑑 ,𝑠𝑥

𝑓𝑦𝑑 𝑧

𝐴𝑠𝑦 .𝑟𝑒𝑞 =𝑀𝐸𝑑 ,𝑠𝑦

𝑓𝑦𝑑 𝑧

Area of steel reinforcement required:

One way solid slab Two way solid slab

For slabs, provide group of bars with area As.prov per meter width

Spacing of bars (mm)

75 100 125 150 175 200 225 250 275 300

Bar

Diameter

(mm)

8 670 503 402 335 287 251 223 201 183 168

10 1047 785 628 524 449 393 349 314 286 262

12 1508 1131 905 754 646 565 503 452 411 377

16 2681 2011 1608 1340 1149 1005 894 804 731 670

20 4189 3142 2513 2094 1795 1571 1396 1257 1142 1047

25 6545 4909 3927 3272 2805 2454 2182 1963 1785 1636

32 10723 8042 6434 5362 4596 4021 3574 3217 2925 2681

For beams, provide group of bars with area As. prov

Number of bars

1 2 3 4 5 6 7 8 9 10

Bar

Diameter

(mm)

8 50 101 151 201 251 302 352 402 452 503

10 79 157 236 314 393 471 550 628 707 785

12 113 226 339 452 565 679 792 905 1018 1131

16 201 402 603 804 1005 1206 1407 1608 1810 2011

20 314 628 942 1257 1571 1885 2199 2513 2827 3142

25 491 982 1473 1963 2454 2945 3436 3927 4418 4909

32 804 1608 2413 3217 4021 4825 5630 6434 7238 8042

𝐴𝑠,𝑚𝑖𝑛 =0.26𝑓𝑐𝑡𝑚 𝑏𝑑

𝑓𝑦𝑘≥ 0.0013𝑏𝑑 ≤ 𝐴𝑠,𝑝𝑟𝑜𝑣 ≤ 𝐴𝑠,𝑚𝑎𝑥 = 0.04𝐴𝑐

Check of the amount of reinforcement provided above the “minimum/maximum amount of

reinforcement “limit

(CYS NA EN1992-1-1, cl. NA 2.49(1)(3))

8

SHEAR FORCE DESIGN

(EN1992-1-1,cl 6.2)

MEd= 0.4F

F: is the total ultimate

load =1.35Gk+1.5Qk

Maximum moment of Simply supported (pinned)

one-way slab

(Manual of EC2, Table 5.2)

Maximum shear force of continuous supported

one-way slab


Uniformly distributed loads

End support condition Moment

End support support MEd =0.046F

Penultimate support MEd= 0.6F

Interior supports MEd =0.5F

F: total design ultimate load on span

Determine design shear stress, vEd

vEd=VEd/b·d

Reinforcement ratio, ρ1 (EN1992-1-1, cl 6.2.2(1)) ρ1=As/b·d

𝑘 = 1 + 200

𝑑≤ 2,0with 𝑑 in mm

𝑉𝑅𝑑 .𝑐 = 0.18

𝛾𝑐𝑘 100𝜌1𝑓𝑐𝑘

1

3 + 𝑘1𝜎𝑐𝑝 𝑏𝑑

𝑉𝑅𝑑 .𝑐 .𝑚𝑖𝑛 = 0.0035 𝑓𝑐𝑘𝑘1.5 + 𝑘1𝜎𝑐𝑝 𝑏𝑑

Design shear resistance

Alternative value of design shear resistance, VRd.c (Concrete centre) (ΜΡa) ρI =

As/(bd)

Effective depth, d (mm)

≤200 225 250 275 300 350 400 450 500 600 750

0.25% 0.54 0.52 0.50 0.48 0.47 0.45 0.43 0.41 0.40 0.38 0.36

0.50% 0.59 0.57 0.56 0.55 0.54 0.52 0.51 0.49 0.48 0.47 0.45

0.75% 0.68 0.66 0.64 0.63 0.62 0.59 0.58 0.56 0.55 0.53 0.51

1.00% 0.75 0.72 0.71 0.69 0.68 0.65 0.64 0.62 0.61 0.59 0.57

1.25% 0.80 0.78 0.76 0.74 0.73 0.71 0.69 0.67 0.66 0.63 0.61

1.50% 0.85 0.83 0.81 0.79 0.78 0.75 0.73 0.71 0.70 0.67 0.65

1.75% 0.90 0.87 0.85 0.83 0.82 0.79 0.77 0.75 0.73 0.71 0.68

≥2.00% 0.94 0.91 0.89 0.87 0.85 0.82 0.80 0.78 0.77 0.74 0.71

k 2.000 1.943 1.894 1.853 1.816 1.756 1.707 1.667 1.632 1.577 1.516

Table derived from: vRd.c=0.12k(100ρIfck)1/3≥0.035k1.5fck

0.5

where k=1+(200/d)0.5≤0.02

If VRdc≥VEd≥VRdc.min, Concrete strut is adequate in resisting shear stress

Shear reinforcement is not required in slabs

9

DESIGN FOR CRACKING

(EN1992-1-1,cl.7.3)

Asmin<As.prov

𝐴𝑠.𝑚𝑖𝑛 =𝑘𝑘𝑐𝑓𝑐𝑡 ,𝑒𝑓𝑓𝐴𝑐𝑡

𝜎𝑠

Minimum area of reinforcement steel

within tensile zone

(EN1992-1-1,Eq. 7.1)

Chart to calculate unmodified steel stress σsu

(Concrete Centre - www.concretecentre.com)

Crack widths have an influence on the durability of the RC member. Maximum crack width sizes can be determined from the table below (knowing σs, bar diameter, and spacing).

Maximum bar diameter and maximum spacing to limit crack widths

(EN1992-1-1,table7.2N&7.3N)

σs

(N/mm2)

Maximum bar diameter and spacing for

maximum crack width of:

0.2mm 0.3mm 0.4mm

160 25 200 32 300 40 300

200 16 150 25 250 32 300

240 12 100 16 200 20 250

280 8 50 12 150 16 200

300 6 - 10 100 12 150

Note. The table demonstrates that cracks widths can be reduced if;

σs is reduced Bar diameter is reduced. This mean that spacing is reduced if As.provis to be the

same. Spacing is reduced

kc=0.4 for bending k=1 for web

width < 300mm or k=0.65for web >

800mm fct,eff= fctm = tensile strength after 28

days Act=Area of concrete in tension=b (h-

(2.5(d-z))) σs=max stress in steel

immediately after crack initiation

𝜎𝑠 = 𝜎𝑠𝑢 𝐴𝑠.𝑟𝑒𝑞

𝐴𝑠.𝑝𝑟𝑜𝑣

1

𝛿 or 𝜎𝑠 = 0.62

𝐴𝑠.𝑟𝑒𝑞

𝐴𝑠.𝑝𝑟𝑜𝑣𝑓𝑦𝑘

10

DESIGN FOR DEFLECTION

(EN1992-1-1,cl.7.4)

Simplified Calculation approach

𝑙

𝑑= 𝐾 11 + 1.5 𝑓𝑐𝑘

𝜌0

𝜌+ 3.2 𝑓𝑐𝑘

𝜌0

𝜌− 1

1.5

𝑖𝑓𝜌 ≤ 𝜌0

𝑙

𝑑= 𝐾 11 + 1.5 𝑓𝑐𝑘

𝜌0

𝜌 − 𝜌′+

1

12 𝑓𝑐𝑘

𝜌,

𝜌0

𝑖𝑓𝜌 > 𝜌0

Span/effective depth ratio

(EN1992-1-1, Eq. 7.16a and 7.16b)

The effect of cracking complicacies the deflection calculations of the RC member under service load. To avoid such complicate calculations, a limit placed upon the span/effective

depth ration.

Note: The span-to-depth ratios should ensure that deflection is limited to span/250

Structural system modification factor

(CY NA EN1992-1-1,NA. table 7.4N)

The values of K may be reduced to account for long span as follow:

In beams and slabs where the span>7.0m, multiply by leff/7

Type of member K

Cantilever 0.4

Flat slab 1.2

Simply supported 1.0

Continuous end

span

1.3

Continuous interior

span

1.5

𝜌0 = 0.001 𝑓𝑐𝑘

Reference reinforcement

ratio

(EN1992-1-1,cl. 7.4.2(2))

𝜌 =𝐴𝑠.𝑟𝑒𝑞

𝑏𝑑

Tension reinforcement ratio

(EN1992-1-1,cl. 7.4.2(2))

11

4. WORKED EXAMPLE : ANALYSIS AND DESIGN OF RC SLAB USING

CSI ETABS AND SAFE

4.1 DIMENSIONS:

Depth of slab, h: h=170mm

Length in longitudinal direction, Ly: Ly=5m

Length in transverse direction, Lx: Lx=5m

Number of slab panels: N=3x3

4.2 LOADS:

Dead load:

Self weight, gk.s: gk.s=4.25kN/m2

Extra dead load, gk.e: gk.e=2.00kN/m2

Total dead load, Gk: Gk=6.25kN/m2

Live load:

Live load, qk: gk=2.00kN/m2

Total live load, Qk: Qk=2.00kN/m2

4.3 LOAD COMBINATION:

Total load on slab: 1.35Gk+1.5Qk=

ULS: 1.35*6.25+1.5*2.00=11.4kN/m2

Total load on slab: 1.35Gk+1.5Qk=

SLS: 1.00*6.25+1.00*2.00=8.25kN/m2

12

4.4 LAYOUT OF MODEL:

Figure 1: Layout of the model

13

4.5 PROCEDURE FOR EXPORTING ETABS MODEL TO SAFE

A very useful and powerful way to start a model in SAFE is to import the model

from ETABS. Floor slabs or basemats that have been modeled in ETABS can be

exported from ETABS.

From that form, the appropriate floor load option can be selected, along with the

desired load cases. After the model has been exported as an .f2k text file, the same

file can then be imported into SAFE using the File menu > Import command.

Using the export and import steps will complete the transfer of the slab geometry,

section properties, and loading for the selected load cases. The design strips need

to be added to the imported model since design strips are not defined as part of the

ETABS model.

ETABS: File > Export > Storey as SAFE

Text File commands saves the specified story level as a SAFE.f2k text input file.

You can later import this file/model into SAFE.

Figure 2: Load to Export to SAFE

Notes:

Model must be analyzed and locked to export.

The export floor loads only option is for individual floor plate design.

The export floor loads and loads from above is used to design foundation.

The export floor loads plus Column and Wall Distortions is necessary only when

displacement compatibility could govern and needs to be checked floor slab

design.(Effects punching shear and flexural reinforcement design).

14

Figure 3: Load cases selection

Figure 4: Load combination selection

15

4.6 DRAW DESIGN STRIPS

Use the Draw menu > Draw Design Strips command to add design strips to the

model. Design strips are drawn as lines, but have a width associated with them.

Design strips are typically drawn over support locations (e.g., columns), with a

width equal to the distance between midspan in the transverse direction.

Design strips determine how reinforcing will be calculated and positioned in the

slab. Forces are integrated across the design strips and used to calculate the

required reinforcing.

Typically design strips are positioned in two principal directions: Layer A and

Layer B.

Select the Auto option. The added design strips will automatically adjust their

width to align with adjacent strips.

Figure 5: Design strip for x direction

16

Figure 6: Design strip for y direction

Figure 7: Model after drawing design strip

17

5. ANALYSIS RESULTS

Figure 8: Maximum hogging and Sagging moment at Short span direction Lx

Figure 9: Maximum Shear Force at Short span direction Lx

18

Figure 10: Maximum hogging and Sagging moment at Long span direction

Ly

Figure 11: Maximum Shear Force at Short span direction Ly

19

6. DESIGN THE SLAB FOR FLEXURAL USING MOMENT CAPACITY

VALUES

SAFE: Display > Show slab forces/stresses

20

Figure 12: Bending moment for M11 (Mx – direction) contours displayed

The figure above indicates that the proposed bending reinforcements are adequate to

resist the design moment (hogging & sagging moments).

21

Figure13: Bending moment for M22 (My – direction) contours displayed

The figure above indicates that the proposed bending reinforcements are adequate to

resist the design moment (hogging & sagging moments).

22

ANNEX A - EXAMPLE OF HOW TO DETERMINE THE DESIGN

BENDING MOMENT USING MOMENT COEFFICIENTS

CALUCLATIION SHEET

BEAM FLEXURAL AND SHEAR CAPACITY CHECK

Date:01/09/2014Rev:B

Calculated by:VNChecked by:IK

BENDING MOMENT COEFFICIENTS FOR TWO-WAY SPANNING RECTANGULAR SLABS (Table 5.3, Manual to EC2 - IStrucTE)

GEOMETRICAL DATA:

Shorter effective span of panel (clear span): lx 5000mm

Longer effective span of panel: ly 5000mm

Type of panel and moment considered: Slab_type:= "Interior panel"Slab_type:= "One short edge discontinuous"Slab_type:= "One long edge discontinuous"Slab_type:= "Two adjacent edges discontinuous"

Slab_type "Two adjacent edges discontinuous"

Ratio of Ly/Lx: Ratioly

lx1

LOADINGS:

Characteistic permanent action: Gk 6.25kN m2

Characteistic variable action: Qk 2kN m2

PARTIAL FACTOR FOR LOADS:

Permanent action (dead load) - Ultimate limit state (ULS): γGk.ULS 1.35

Variable action (live load) - Ultimate limit state (ULS): γQk.ULS 1.50

Permanent action (dead load) - Ultimate limit state (SLS): γGk.SLS 1.00

Variable action (live load) - Ultimate limit state (SLS): γQk.SLS 1.00

DESIGN LOADS:

Ultimate design load (ULS): FEd.ULS γGk.ULS Gk γQk.ULS Qk 11.438 kN m2

Ultimate design load (SLS): FEd.SLS γGk.SLS Gk γQk.SLS Qk 8.25 kN m2

MOMENT COEFFICIENT:

Short span - Bending moment coefficient for negative moment (hogging moment) atcontinuous edge

SEISMIC ASSESSMENT OF EXISTING RC BUILDING

of 27

CALUCLATIION SHEET




βsx.support 0.031lx

ly1.0 Slab_type "Interior panel"=if

0.044 1.0ly

lx 1.25 Slab_type "Interior panel"=if

0.053 1.25ly


0.059 1.5ly


0.063 1.75ly


0.039lx

ly1.0 Slab_type "One short edge discontinuous"=if

0.050 1.0ly

lx 1.25 Slab_type "One short edge discontinuous"=if

0.058 1.25ly


0.063 1.5ly


0.067 1.75ly


0.039lx

ly1.0 Slab_type "One long edge discontinuous"=if

0.059 1.0ly

lx 1.25 Slab_type "One long edge discontinuous"=if

0.073 1.25ly


0.082 1.5ly


0.089 1.75ly


0.047lx

ly1.0 Slab_type "Two adjacent edges discontinuous"=if

0.066 1.0ly

lx 1.25 Slab_type "Two adjacent edges discontinuous"=if

l


of 27

CALUCLATIION SHEET




0.078 1.25ly


0.087 1.5ly


0.093 1.75ly


Short span - Bending moment coefficient for positive moment (sagging moment) atcontinuous edge

βsx.midspan 0.024lx

ly1.0 Slab_type "Interior panel"=if

0.034 1.0ly


0.040 1.25ly


0.044 1.5ly


0.048 1.75ly


0.029lx

ly1.0 Slab_type "One short edge discontinuous"=if

0.038 1.0ly


0.043 1.25ly


0.047 1.5ly


0.050 1.75ly


0.030lx

ly1.0 Slab_type "One long edge discontinuous"=if

0.045 1.0ly


0.055 1.25ly


l


of 27

CALUCLATIION SHEET




0.062 1.5ly


0.067 1.75ly


0.036lx

ly1.0 Slab_type "Two adjacent edges discontinuous"=if

0.049 1.0ly


0.059 1.25ly


0.065 1.5ly


0.070 1.75ly


Long span - Bending moment coefficient for negative moment (hogging moment) atcontinuous edge

βsy.support 0.032 Slab_type "Interior panel"=if

0.037 Slab_type "One short edge discontinuous"=if

0.037 Slab_type "One long edge discontinuous"=if

0.045 Slab_type "Two adjacent edges discontinuous"=if

Long span - Bending moment coefficient for positive moment (sagging moment) atcontinuous edge

βsy.midspan 0.024 Slab_type "Interior panel"=if

0.028 Slab_type "One short edge discontinuous"=if

0.028 Slab_type "One long edge discontinuous"=if

0.034 Slab_type "Two adjacent edges discontinuous"=if

Summary of moment coefficient:

Short span - Moment coefficient - support: βsx.support 0.047

Short span - Moment coefficient - midspan: βsx.midspan 0.036

Long span - Moment coefficient - support: βsy.support 0.045

Long span - Moment coefficient - midspan: βsy.midspan 0.034


of 27

CALUCLATIION SHEET




BENDING MOMENT RESULTS:

Note: Bending moment per unit width.

Short span - Bending moment at support: MEd.sx.sup βsx.support FEd.ULS lx2

13.439 kN

Short span - Bending moment at midspan: MEd.sx.mid βsx.midspan FEd.ULS lx2

10.294 kN

Long span - Bending moment at support: MEd.sy.sup βsy.support FEd.ULS lx2

12.867 kN

Long span - Bending moment at midspan: MEd.sy.mid βsy.midspan FEd.ULS lx2

9.722 kN


of 27

28

ANNEX B - EXAMPLE OF HOW TO DETERMINE THE MOMENT

CAPACITY OF RC SLAB

CALUCLATIION SHEET

BEAM FLEXURAL CAPACITY CHECK


Calculated by:VNChecked by:VN

REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2

Note: The following colour key is a guide to using the full calculation page.

INPUT DTATA

COMPUTED OUTPUT

DATA TO BE CHECKED

STANDARD DATA

Figure 1: Analysis of rectangular section - stress strain

ASSUMPTIONS:

GEOMETRICAL DATA:

Concrete cover: cnom 25mm

Breadth of the section (assumed 1m strip): b 1m

Depth of the section: h 170mm

Longitudinal diameter (tension zone - bottom): dt 10mm

Longitudinal diameter (compression zone - top): dc 12mm

Spacing of steel reinforcement: sp 200mm

Area of steel reinforcement provided: As.prov.t πdt

2

4

m

sp 392.699 mm

2

Area of steel reinforcement provided: As.prov.c πdc

2

4

m

sp 565.487 mm

2

Effective depth of the section. d: d h cnomdt

2 140 mm

Effective depth of the section. d2: d2 cnom

dc

2 31 mm

MATERIAL PROPERTIES:

Mean characteristic compressive

SLAB DESIGN TO EUROCODE 2 of 31

CALUCLATIION SHEET




cylinder strength of concrete(Laboratory results): fck 30N mm

2

Characteristic yield strength of steel reinforcement:

fyk 500N mm2

PARTIAL SAFETY FACTOR (CYS NA EN1992-1-1,Table 2.1):

Partial factor for reinforcement steel (NA CYS EN 1992-1-1:2004, Table 2.1)): γs 1.15

Partial factor for concrete (NA CYS EN 1992-1-1:2004, Table 2.1)): γc 1.5

DESIGN STRENGTHS OF MATERIAL(EN1992-1-1,cl.3.1.6):

Design yield strength of reinforcement(EN1992-1-1,Fig.3.8): fyd

fyk

γs434.783 N mm

2

Coefficient value for compressive strength(NA CYS EN 1992-1-1:2004, cl. NA 2.8): αcc 1

Design value of concrete compressive strength(EN 1992-1-1:2004, Equation 3.15):

fcd

αcc fck

γc20 N mm

2

RECTANGULAR STRESS BLOCK FACTORS:

λ 0.8 fck 50MPaif

0.8fck 50MPa

400MPa

fck 50MPaif

0.8Factor, λ(EN1992-1-1,Eq.3.19&3.20)

η 1.0 fck 50MPaif

1.0fck 50MPa

200MPa

fck 50MPaif

1Factor, η(EN1992-1-1,Eq.3.21&3.22)

BENDING MOMENT CAPACITY (AT MIDSPAN) FOR A SINGLY REINFORCED SECTION

Figure 2: Detail of reinforcement slab at midspan

For equilibrium, the ultimate design moment, must be balanced by the moment of resistanceof the section (figure 1):

Fc Fst Fst

Fst fyd As.prov.t 170.739 kN

Fc fcd b λ x kN x

Therefore depth of stress block is:


CALUCLATIION SHEET




sfyd As.prov.t

fcd b8.537 mm

xs

λ10.671 mm

To ensure rotation of the plastic hinge with sufficient yielding of the tension steel and also toallow for other factors such as the strain hardening of the steel, EC2 limit the depth of neutralaxis to:

Check if x 0.45d "PASS" "FAIL"( ) "PASS"

z ds

2 135.732 mm

Moment capacity: MRd fyd As.prov.t z 23.175 kN m

BENDING CAPACITY (AT SUPPORTS) OF SECTION WITH COMPRESSION REINFORCEMENT AT ULTIMATE LIMIT STATE

Figure 3: Detail of reinforcement slab at support

For equilibrium, the ultimate design moment, must be balanced by the moment of resistanceof the section (figure 1):

Fst Fc Fsc Fc

Fsc fyd As.prov.c 245.864 kN

Fst fyd As.prov.t 170.739 kN

Fc fcd b λ x

Therefore depth of stress block is:

sfyd As.prov.c As.prov.t

fcd b3.756 mm

xs

λ10.671 mm

Check if x 0.45d "PASS" "FAIL"( ) "PASS"

To ensure rotation of the plastic hinge with sufficient yielding of the tension steel and also toallow for other factors such as the strain hardening of the steel, EC2 limit the depth of neutralaxis to:

Moment capacity: MRd. fcd b s ds

2

fyd As.prov.c d d2 37.176 kN m


32

ANNEX C - EXAMPLE OF DESIGN SLAB PANEL WITH TWO

DISCONTINUOUS EDGES

CALUCLATIION SHEET

REINFORCED CONCRETE SOLID SLAB DESIGN TO

EUROCODE 2





INPUT DTATAASSUMPTIONS:

1. Fire resistance 1hour (REI 60).2. Exposure class of concrete XC1.3. No redistribution of bending moment made.

COMPUTED OUTPUT

DATA TO BE CHECKED

STANDARD DATA

GEOMETRICAL DATA:

Structural_system:= "Simply supported" "End span of continuous slab" "Interior span" "Flat slab" "Cantilever"

Structural system:

Structural_system "End span of continous slab"

Depth of slab: h 170mm

Strip width: b 1000mm



Type of slab:Type_slab "Two way slab"

ly

lx2.0if

"One way slab"ly

lx2.0if

"Two way slab"

ANALYSIS & LOADING RESULTS:

TWO DISCONTINOUS EDGE of 48

CALUCLATIION SHEET


EUROCODE 2



Figure 1: Bending moment diagram for x - direction

Figure 2: Bending moment diagram for y - direction


CALUCLATIION SHEET


EUROCODE 2



Figure 3: Shear force diagram for x - direction


CALUCLATIION SHEET


EUROCODE 2



Figure 4: Shear force diagram for y - direction

Loads:



Quasi-permanent value of variable action: ψ2 0.3

Short span:

Design bending moment at short span - continuous support: Mx.1 21.14kN m

Design bending moment at short span - middle: Mx.m 12.35kN m

Design shear force at short span - continous support: Vx.1 21kN

Design shear force at short span - discontinous support: Vx.2 13kN

Long span:

Design bending moment at long span - continous support: My.1 10.52kN m

Design bending moment at long span - middle: My.m 11.86kN m

Design shear force at long span - continous support: Vy.1 18kN


CALUCLATIION SHEET


EUROCODE 2



Design shear force at long span - discontinous support: Vy.2 13kN

STEEL REINFORCEMENT PROPERTIES:

Bars diameter for short/long span-midspan: ϕy.p 10mm

Characteristic yield strength of steel reinforcement: fyk 500N mm

2

CONCRETE PROPERTIES:

Characteristic compressive cylinderstrength of concrete: fck 30N mm

2

Mean value of compressive sylinderstrength(EN 1992-1-1:2004, table 3.1): fctm 0.3

fck

MPa

0.667

MPa 2.9 N mm2

PARTIAL SAFETY FACTORS:





fyk

γs434.783 N mm

2



fcd

αcc fck

γc20 N mm

2

CONCRETE COVER TO REINFORCEMENT:

Allowance in design for deviation(Assuming no measurement of cover)(EN1992-1-1,cl.4.4.1.3(3):

Δcdev 10mm

Minimum cover due to bond(Diameter of bar)(EN1992-1-1,Table 4.2):

cmin.b ϕy.p 10 mm

Minimum cover due to environmental condition (Condition :XC1)("How to design to Eurocode 2",Table 8):

cmin.dur 15mm

Minimum concrete cover(EN1992-1-1,Eq.4.2):

cmin max cmin.b cmin.dur 10mm 15 mm

Nominal cover(EN1992-1-1,Eq.4.1):

cnom cmin Δcdev 25 mm


CALUCLATIION SHEET


EUROCODE 2



FIRE DESIGN CHECK:

Minimum slab thickness(EN1992-1-2,Table 5.8):

hs.min 80mm

Fire_resistance if h hs.min "OK" "NOT OK" "OK"

Axis distance to top and bottom reinforcement, a(EN1992-1-2,Table 5.8):

amin 20mm

Minimum distance to top and bottomreinforcement:

aprov cnom

ϕy.p

2 30 mm

Fire_resistance if aprov amin "OK" "NOT OK" "OK"

REINFORCEMENT DESIGN AT MID-SPAN IN SHORT SPAN DIRECTION:

Actual bar size: ϕx.m 10mm

Actual bar spacing: sx.m 200mm

Area of reinforcement provided: Asx.m πϕx.m

2

4

m

sx.m 392.699 mm

2

dx.m h cnomϕx.m

2 140 mm

Values for Klim

(Assumed no redistribution):

KMx.m

b dx.m2

fck0.021 Klim 0.22

Compression if K Klim "NOT REQUIRED" "REQUIRED" "NOT REQUIRED"

Level arm:z min

dx.m

21 1 3.53 K

0.95dx.m

133 mm

Area of reinforcement required forbending:

Asx.p.m

Mx.m

fyd z213.571 mm

2

Minimumreinforcement(EN1992-1-1,Eq.9.1N):

As.min max 0.26fctm

fyk b dx.m 0.0013 b dx.m

211.102 m

Maximum reinforcement(EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04 b dx.m 5.6 10

3 mm

2

Check_steel_1 if Asx.p.m Asx.m As.min Asx.m As.max "OK" "NOT OK" "OK"

Ratio_1max As.min Asx.p.m

Asx.m0.544

Stress in the reinforcement(IStrucTE EC2 Manual)

σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsx.p.m

Asx.m1

141.617 N mm2


CALUCLATIION SHEET


EUROCODE 2



Maximum spacing (for wk=0.3mm)

(EN1992-1-1,Table 7.3N:

smax 300mm σs 160MPaif

275mm 160MPa σs 180MPaif










300 mm

Maximum spacing of bars(EN1992-1-1,cl.9.3.1.1(3):

smax. min 3 h 400mm smax 300 mm

Spacing_1 if sx.m smax. "OK" "NOT OK" "OK"

Ratio_s_1sx.m

smax0.667

REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT IN SHORT SPAN DIRECTION:

Actual bar size: ϕx.1 12mm

Actual bar spacing: sx.1 200mm

Area of reinforcement provided: Asx.1 πϕx.1

2

4

m

sx.1 565.487 mm

2

dx.1 h cnomϕx.1

2 139 mm

Values for Klim


KMx.1

b dx.12

fck0.036 Klim 0.22


Level arm:z min

dx.1

21 1 3.53 K

0.95dx.1

132.05 mm


Asx.n.1

Mx.1

fyd z368.209 mm

2


As.min max 0.26fctm

fyk b dx.1 0.0013 b dx.1

209.594 mm

Maximum reinforcement(EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04 b dx.1 5.56 10

3 mm

2


CALUCLATIION SHEET


EUROCODE 2



Check_steel_2 if Asx.n.1 Asx.1 As.min Asx.1 As.max "OK" "NOT OK" "OK"

Ratio_2max As.min Asx.n.1

Asx.10.651


σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsx.n.1

Asx.11

169.552 N mm2


(EN1992-1-1,Table 7.3N:












275 mm



Spacing_2 if sx.1 smax. "OK" "NOT OK" "OK"

Ratio_s_2sx.1

smax0.727

REINFORCEMENT DESIGN AT MID-SPAN IN LONG SPAN DIRECTION:

Actual bar size: ϕy.m 10mm

Actual bar spacing: sy.m 200mm

Area of reinforcement provided: Asy.m πϕy.m

2

4

m

sy.m 392.699 mm

2

dy.m h cnomϕy.m

2 140 mm

Values for Klim


KMy.m

b dy.m2

fck0.02 Klim 0.22



CALUCLATIION SHEET


EUROCODE 2



Level arm:z min

dy.m

21 1 3.53 K

0.95dy.m

133 mm


Asy.p.m

My.m

fyd z205.098 mm

2


As.min max 0.26fctm

fyk b dy.m 0.0013 b dy.m

211.102 mm

Maximum reinforcement(EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04 b dy.m 5.6 10

3 mm

2

Check_steel_3 if Asy.p.m Asy.m As.min Asy.m As.max "OK" "NOT OK" "OK"

Ratio_3max As.min Asy.p.m

Asy.m0.538


σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsy.p.m

Asy.m1

135.998 N mm2


(EN1992-1-1,Table 7.3N:












0.3 m



Spacing_3 if sy.m smax. "OK" "NOT OK" "OK"

Ratio_s_3sy.m

smax0.667

REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT IN LONG SPAN DIRECTION:

Actual bar size: ϕy.1 10mm

Actual bar spacing: sy.1 200mm

Area of reinforcement provided: Asy.1 πϕy.1

2

4

m

sy.1 392.699 mm

2


CALUCLATIION SHEET


EUROCODE 2



dy.1 h cnomϕy.1

2 140 mm

Values for Klim


KMy.1

b dy.12

fck0.018 Klim 0.22


Level arm:z min

dy.1

21 1 3.53 K

0.95dy.1

133 mm


Asy.n.1

My.1

fyd z181.925 mm

2


As.min max 0.26fctm

fyk b dy.1 0.0013 b dy.1

211.102 mm

Maximum reinforcement(EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04 b dy.1 5.6 10

3 mm

2

Check_steel_4 if Asy.n.1 Asy.1 As.min Asy.1 As.max "OK" "NOT OK" "OK"

Ratio_4max As.min Asy.n.1

Asy.10.538


σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsy.n.1

Asy.11

120.632 N mm2


(EN1992-1-1,Table 7.3N:












300 mm




Ratio_s_4sy.m

smax0.667


CALUCLATIION SHEET


EUROCODE 2



SHEAR CAPACITY CHECK AT SHORT SPAN CONTINUOUS SUPPORT:

Effective depth factor(EN1992-1-1,cl.6.2.2): k min 2.0 1

200mm

dx.1

0.5

2

Reinforcement ratio: ρ1 min 0.02Asx.1

b dx.1

4.068 103

Minimum shear resistance(EN1992-1-1,Eq.6.3N &6.2b): VRd.c.min 0.035 k

fck

MPa

0.5

b dx.1

N mm2

53.293 kN

Shear resistance(EN1992-1-1,Eq.6.2a):

VRd.c.x.1 max VRd.c.min0.18MPa

γc

k 100 ρ1fck

MPa

0.333

b dx.1

76.743 k

Shear_1 if Vx.1 VRd.c.x.1 "NO SHEAR REQUIRED" "SHEAR REQUIRED"

Shear_1 "NO SHEAR REQUIRED"

Ratio1Vx.1

VRd.c.x.10.274

SHEAR CAPACITY CHECK AT SHORT SPAN DISCONTINUOUS SUPPORT:

Flexural reinforcement at discontinuous supportEN1992-1-1,cl.9.3.1.2(2):

As.req Asx.m 0.25 98.175 mm2


Bar spacing: sx.2 sx.m 200 mm


2

4

m

sx.2 251.327 mm

2

Effective depth:dx.2 h cnom

ϕx.2

2 141 mm


200mm

dx.2

0.5

2


b dx.2

1.782 103


fck

MPa

0.5

b dx.2

N mm2

54.06 kN



γc

k 100 ρ1fck

MPa

0.333

b dx.2

59.143 k




CALUCLATIION SHEET


EUROCODE 2



Ratio2Vx.2

VRd.c.x.20.22

SHEAR CAPACITY CHECK AT LONG SPAN CONTINUOUS SUPPORT:


200mm

dy.1

0.5

2

Reinforcement ratio: ρ1 min 0.02Asy.1

b dy.1

2.805 103


fck

MPa

0.5

b dy.1

N mm2

53.677 kN


VRd.c.y.1 max VRd.c.min0.18MPa

γc

k 100 ρ1fck

MPa

0.333

b dy.1

68.294 kN

Shear_3 if Vy.1 VRd.c.y.1 "NO SHEAR REQUIRED" "SHEAR REQUIRED"


Ratio3Vy.1

VRd.c.y.10.264

SHEAR CAPACITY CHECK AT LONG SPAN DISCONTINUOUS SUPPORT:


As.req Asy.m 0.25 98.175 mm2


Bar spacing: sy.2 sy.m 200 mm


2

4

m

sy.2 251.327 mm

2

Effective depth:dy.2 h cnom

ϕy.2

2 141 mm


200mm

dy.2

0.5

2


b dy.2

1.782 103


fck

MPa

0.5

b dy.2

N mm2

54.06 kN



γc

k 100 ρ1fck

MPa

0.333

b dy.2

59.143 kN


CALUCLATIION SHEET


EUROCODE 2





Ratio4Vy.2

VRd.c.y.20.22

BASIC SPAN-TO-DEPTH DEFLECTION RATIO CHECK:

Reference reinforcement ratio: ρo 0.001fck

MPa

0.5

5.477 103

Required compression reinforcement(at mid-span - short span): ρc 0

Required tension reinforcement(at mid-span - short span):

ρt max 0.0035Asx.m

b dx.m

3.5 103

Structural system factor(EN1992-1-1,Table 7.4N):

Kδ 1.0 Structural_system "Simply supported"=if

1.3 Structural_system "End span of continous slab"=if

1.5 Structural_system "Interior span"=if

1.2 Structural_system "Flat slab"=if

0.4 Structural_system "Cantilever"=if

1.3

Basic limit span-to-depth ratio(EN1992-1-1,Eq.7.16a&7.16b):

Limx.bas Kδ 11 1.5fck

MPa

0.5

ρo

ρt 3.2

fck

MPa

0.5

ρo

ρt1

1.5

ρt ρoif

Kδ 11 1.5fck

MPa

0.5

ρo

ρt ρc

1

12

fck

MPa

0.5

ρc

ρo

ρt ρoif

40.689

Actual span to effective depth ratio: Ratioact

lx

dx.m35.714

Deflection if Ratioact Limx.bas "OK" "NOT OK" "OK"

RatioRatioact

Limx.bas0.878

CALCULATION SUMMARY RESULTS:

Short span - Bending capacity: PASS/FAIL: Ratio:

Check bending capacity at midspan: Check_steel_1 "OK" Ratio_1 0.544

Spacing at midspan reinforcement: Spacing_1 "OK" Ratio_s_1 0.667

Check bending capacity at support 1: Check_steel_2 "OK" Ratio_2 0.651

Spacing at support 1 reinforcement: Spacing_2 "OK" Ratio_s_2 0.727


CALUCLATIION SHEET


EUROCODE 2



Long span - Bending capacity: PASS/FAIL: Ratio:





Short span - Shear capacity: PASS/FAIL: Ratio:

Check shear capacity at support 1: Shear_1 "NO SHEAR REQUIRED" Ratio1 0.274


Long span - Shear capacity: PASS/FAIL: Ratio:



Deflection: PASS/FAIL: Ratio:

Check deflection of panel: Deflection "OK" Ratio 0.878

RENFORCEMENT SUMMARY:

Short span:

Midspan in short span direction: ϕx.m 10 mm sx.m 200 mmat C/CContinuous support 1 in short span direction: ϕx.1 12 mm sx.1 200 mmat C/CDiscontinuous support 2 in short span direction: ϕx.2 8 mm sx.2 200 mmat C/C

Long span:

Midspan in short span direction: ϕy.m 10 mm sy.m 200 mmat C/CContinuous support 1 in long span direction: ϕy.1 10 mm sy.1 200 mmat C/CDiscontinuous support 2 in long span direction: ϕy.2 8 mm sy.2 200 mmat C/C


CALUCLATIION SHEET


EUROCODE 2



ϕy.2 8 mm sy.2 200 mm

ϕx.2 8 mm sx.2 200 mmϕx.1 12 mm sx.1 200 mm

ϕx.m 10 mm sx.m 200 mm

ϕy.m 10 mm sy.m 200 mm

ϕy.1 10 mm sy.1 200 mm


CALUCLATIION SHEET


EUROCODE 2



mm2


48

ANNEX D - EXAMPLE OF DESIGN SLAB PANEL WITH ONE

DISCONTINUOUS EDGES

CALUCLATIION SHEET


EUROCODE 2







COMPUTED OUTPUT

DATA TO BE CHECKED

STANDARD DATA

GEOMETRICAL DATA:


Structural system:

Structural_system "End span of continous slab"






ly

lx2.0if

"One way slab"ly

lx2.0if

"Two way slab"


ONE DISCONTINUOUS EDGE Page 49 of 64

CALUCLATIION SHEET


EUROCODE 2






CALUCLATIION SHEET


EUROCODE 2




Loads:




Short span:

Design bending moment at short span - continuous support: Mx.1 21kN m

Design bending moment at short span - middle: Mx.m 7kN m




Long span:

Design bending moment at long span - continous support: My.1 20kN m

Design bending moment at long span - middle: My.m 12kN m


CALUCLATIION SHEET


EUROCODE 2








2



2


fck

MPa

0.667

MPa 2.9 N mm2






fyk

γs434.783 N mm

2



fcd

αcc fck

γc20 N mm

2



Δcdev 10mm


cmin.b ϕy.p 10 mm


cmin.dur 15mm




CALUCLATIION SHEET


EUROCODE 2





FIRE DESIGN CHECK:


hs.min 80mm



amin 20mm


aprov cnom

ϕy.p

2 30 mm






2

4

m

sx.m 392.699 mm

2

dx.m h cnomϕx.m

2 140 mm

Values for Klim


KMx.m

b dx.m2

fck0.012 Klim 0.22


Level arm:z min

dx.m

21 1 3.53 K

0.95dx.m

133 mm


Asx.p.m

Mx.m

fyd z121.053 mm

2


As.min max 0.26fctm


211.102 mm


3 mm

2



Asx.m0.538


CALUCLATIION SHEET


EUROCODE 2




σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsx.p.m

Asx.m1

80.269 N mm2


(EN1992-1-1,Table 7.3N:












300 mm




Ratio_s_1sx.m

smax0.667

REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT 1 IN SHORT SPAN DIRECTION:




2

4

m

sx.1 565.487 mm

2

dx.1 h cnomϕx.1

2 139 mm

Values for Klim


KMx.1

b dx.12

fck0.036 Klim 0.22


Level arm:z min

dx.1

21 1 3.53 K

0.95dx.1

132.05 mm


Asx.n.1

Mx.1

fyd z365.771 mm

2


CALUCLATIION SHEET


EUROCODE 2




As.min max 0.26fctm

fyk b dx.1 0.0013 b dx.1

209.594 mm


3 mm

2



Asx.10.647


σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsx.n.1

Asx.11

168.429 N mm2


(EN1992-1-1,Table 7.3N:












275 mm




Ratio_s_2sx.1

smax0.727





2

4

m

sx.2 565.487 mm

2


CALUCLATIION SHEET


EUROCODE 2



dx.2 h cnomϕx.2

2 139 mm

Values for Klim


KMx.2

b dx.22

fck0.036 Klim 0.22


Level arm:z min

dx.2

21 1 3.53 K

0.95dx.2

132.05 mm


Asx.n.2

Mx.2

fyd z365.771 mm

2


As.min max 0.26fctm

fyk b dx.2 0.0013 b dx.2

209.594 mm


3 mm

2



Asx.20.647


σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsx.n.2

Asx.21

168.429 N mm2


(EN1992-1-1,Table 7.3N:












275 mm




Ratio_s_3sx.2

smax0.727


CALUCLATIION SHEET


EUROCODE 2







2

4

m

sy.m 392.699 mm

2

dy.m h cnomϕy.m

2 140 mm

Values for Klim


KMy.m

b dy.m2

fck0.02 Klim 0.22


Level arm:z min

dy.m

21 1 3.53 K

0.95dy.m

133 mm


Asy.p.m

My.m

fyd z207.519 mm

2


As.min max 0.26fctm


211.102 mm


3 mm

2



Asy.m0.538


σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsy.p.m

Asy.m1

137.603 N mm2


(EN1992-1-1,Table 7.3N:












0.3 m


CALUCLATIION SHEET


EUROCODE 2






Ratio_s_4sy.m

smax0.667

REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT IN LONG SPAN DIRECTION:




2

4

m

sy.1 565.487 mm

2

dy.1 h cnomϕy.1

2 139 mm

Values for Klim


KMy.1

b dy.12

fck0.035 Klim 0.22


Level arm:z min

dy.1

21 1 3.53 K

0.95dy.1

132.05 mm


Asy.n.1

My.1

fyd z348.353 mm

2


As.min max 0.26fctm

fyk b dy.1 0.0013 b dy.1

209.594 mm


3 mm

2



Asy.10.616


σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsy.n.1

Asy.11

160.409 N mm2


CALUCLATIION SHEET


EUROCODE 2




(EN1992-1-1,Table 7.3N:












275 mm



Spacing_5 if sy.1 smax. "OK" "NOT OK" "OK"

Ratio_s_5sy.1

smax0.727

SHEAR CAPACITY CHECK AT SHORT SPAN CONTINUOUS SUPPORT 1:


200mm

dx.1

0.5

2


b dx.1

4.068 103


fck

MPa

0.5

b dx.1

N mm2

53.293 kN



γc

k 100 ρ1fck

MPa

0.333

b dx.1

76.743 k



Ratio1Vx.1

VRd.c.x.10.287



200mm

dx.2

0.5

2


CALUCLATIION SHEET


EUROCODE 2




b dx.2

4.068 103


fck

MPa

0.5

b dx.2

N mm2

53.293 kN



γc

k 100 ρ1fck

MPa

0.333

b dx.2

76.743 k



Ratio2Vx.2

VRd.c.x.20.235

SHEAR CAPACITY CHECK AT LONG SPAN CONTINUOUS SUPPORT:


200mm

dy.1

0.5

2


b dy.1

4.068 103


fck

MPa

0.5

b dy.1

N mm2

53.293 kN



γc

k 100 ρ1fck

MPa

0.333

b dy.1

76.743 kN



Ratio3Vy.1

VRd.c.y.10.274

SHEAR CAPACITY CHECK AT LONG SPAN DISCONTINUOUS SUPPORT:


As.req Asy.m 0.25 98.175 mm2


Bar spacing: sy.2 sy.m 200 mm


2

4

m

sy.2 251.327 mm

2

Effective depth:dy.2 h cnom

ϕy.2

2 141 mm


CALUCLATIION SHEET


EUROCODE 2




200mm

dy.2

0.5

2


b dy.2

1.782 103


fck

MPa

0.5

b dy.2

N mm2

54.06 kN



γc

k 100 ρ1fck

MPa

0.333

b dy.2

59.143 kN



Ratio4Vy.2

VRd.c.y.20.22



MPa

0.5

5.477 103



ρt max 0.0035Asx.m

b dx.m

3.5 103







1.3



MPa

0.5

ρo

ρt 3.2

fck

MPa

0.5

ρo

ρt1

1.5

ρt ρoif

Kδ 11 1.5fck

MPa

0.5

ρo

ρt ρc

1

12

fck

MPa

0.5

ρc

ρo

ρt ρoif

40.689


lx

dx.m35.714



CALUCLATIION SHEET


EUROCODE 2



RatioRatioact

Limx.bas0.878























Short span:

Midspan in short span direction: ϕx.m 10 mm sx.m 200 mmat C/CContinuous support 1 in short span direction: ϕx.1 12 mm sx.1 200 mmat C/CDiscontinuous support 2 in short span direction: ϕx.2 12 mm sx.2 200 mmat C/C

Long span:

Midspan in short span direction: ϕy.m 10 mm sy.m 200 mmat C/C


CALUCLATIION SHEET


EUROCODE 2



Continuous support 1 in long span direction: ϕy.1 12 mm sy.1 200 mmat C/CDiscontinuous support 2 in long span direction: ϕy.2 8 mm sy.2 200 mmat C/C

ϕy.2 8 mm sy.2 200 mm

ϕx.2 12 mm sx.2 200 mm ϕx.1 12 mm sx.1 200 mm



ϕy.1 12 mm sy.1 200 mm


65

ANNEX E - EXAMPLE OF DESIGN INTERIOR PANEL SLAB

CALUCLATIION SHEET


EUROCODE 2







COMPUTED OUTPUT

DATA TO BE CHECKED

STANDARD DATA

GEOMETRICAL DATA:


Structural system:

Structural_system "Interior span"






ly

lx2.0if

"One way slab"ly

lx2.0if

"Two way slab"


INTERIOR PANEL Page 66 of 82

CALUCLATIION SHEET


EUROCODE 2






CALUCLATIION SHEET


EUROCODE 2



Loads:




Short span:


Design bending moment at short span - middle: Mx.m 6kN m



Design shear force at short span - discontinous support: Vx.2 21kN

Long span:


Design bending moment at long span - middle: My.m 6kN m







2



2


fck

MPa

0.667

MPa 2.9 N mm2



CALUCLATIION SHEET


EUROCODE 2







fyk

γs434.783 N mm

2



fcd

αcc fck

γc20 N mm

2



Δcdev 10mm


cmin.b ϕy.p 10 mm


cmin.dur 15mm





FIRE DESIGN CHECK:


hs.min 80mm



amin 20mm


aprov cnom

ϕy.p

2 30 mm





CALUCLATIION SHEET


EUROCODE 2





2

4

m

sx.m 392.699 mm

2

dx.m h cnomϕx.m

2 140 mm

Values for Klim


KMx.m

b dx.m2

fck0.01 Klim 0.22


Level arm:z min

dx.m

21 1 3.53 K

0.95dx.m

133 mm


Asx.p.m

Mx.m

fyd z103.759 mm

2


As.min max 0.26fctm


211.102 mm


3 mm

2



Asx.m0.538


σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsx.p.m

Asx.m1

68.802 N mm2


(EN1992-1-1,Table 7.3N:












300 mm




CALUCLATIION SHEET


EUROCODE 2




Ratio_s_1sx.m

smax0.667





2

4

m

sx.1 565.487 mm

2

dx.1 h cnomϕx.1

2 139 mm

Values for Klim


KMx.1

b dx.12

fck0.036 Klim 0.22


Level arm:z min

dx.1

21 1 3.53 K

0.95dx.1

132.05 mm


Asx.n.1

Mx.1

fyd z365.771 mm

2


As.min max 0.26fctm

fyk b dx.1 0.0013 b dx.1

209.594 mm


3 mm

2



Asx.10.647


σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsx.n.1

Asx.11

168.429 N mm2


CALUCLATIION SHEET


EUROCODE 2




(EN1992-1-1,Table 7.3N:












275 mm




Ratio_s_2sx.1

smax0.727





2

4

m

sx.2 565.487 mm

2

dx.2 h cnomϕx.2

2 139 mm

Values for Klim


KMx.2

b dx.22

fck0.036 Klim 0.22


Level arm:z min

dx.2

21 1 3.53 K

0.95dx.2

132.05 mm


Asx.n.2

Mx.2

fyd z365.771 mm

2


As.min max 0.26fctm

fyk b dx.2 0.0013 b dx.2

209.594 mm


3 mm

2


CALUCLATIION SHEET


EUROCODE 2





Asx.20.647


σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsx.n.2

Asx.21

168.429 N mm2


(EN1992-1-1,Table 7.3N:












275 mm




Ratio_s_3sx.2

smax0.727





2

4

m

sy.m 392.699 mm

2

dy.m h cnomϕy.m

2 140 mm

Values for Klim


KMy.m

b dy.m2

fck0.01 Klim 0.22



CALUCLATIION SHEET


EUROCODE 2



Level arm:z min

dy.m

21 1 3.53 K

0.95dy.m

133 mm


Asy.p.m

My.m

fyd z103.759 mm

2


As.min max 0.26fctm


211.102 mm


3 mm

2



Asy.m0.538


σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsy.p.m

Asy.m1

68.802 N mm2


(EN1992-1-1,Table 7.3N:












0.3 m




Ratio_s_4sy.m

smax0.667

REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT 1 IN LONG SPAN DIRECTION:




2

4

m

sy.1 565.487 mm

2


CALUCLATIION SHEET


EUROCODE 2



dy.1 h cnomϕy.1

2 139 mm

Values for Klim


KMy.1

b dy.12

fck0.036 Klim 0.22


Level arm:z min

dy.1

21 1 3.53 K

0.95dy.1

132.05 mm


Asy.n.1

My.1

fyd z365.771 mm

2


As.min max 0.26fctm

fyk b dy.1 0.0013 b dy.1

209.594 mm


3 mm

2



Asy.10.647


σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsy.n.1

Asy.11

168.429 N mm2


(EN1992-1-1,Table 7.3N:












275 mm




Ratio_s_5sy.1

smax0.727


CALUCLATIION SHEET


EUROCODE 2



REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT 2 IN LONG SPAN DIRECTION:




2

4

m

sy.2 565.487 mm

2

dy.2 h cnomϕy.2

2 139 mm

Values for Klim


KMy.2

b dy.22

fck0.036 Klim 0.22


Level arm:z min

dy.2

21 1 3.53 K

0.95dy.2

132.05 mm


Asy.n.2

My.2

fyd z365.771 mm

2


As.min max 0.26fctm

fyk b dy.2 0.0013 b dy.2

209.594 mm2


3 mm

2



Asy.20.647


σs

fyk

γs

ψ2 Qk Gk

1.5 Qk 1.35 Gk

minAsy.n.2

Asy.21

168.429 N mm2


(EN1992-1-1,Table 7.3N:












275 mm


CALUCLATIION SHEET


EUROCODE 2






Ratio_s_6sy.2

smax0.727



200mm

dx.1

0.5

2


b dx.1

4.068 103


fck

MPa

0.5

b dx.1

N mm2

53.293 kN



γc

k 100 ρ1fck

MPa

0.333

b dx.1

76.743 k



Ratio1Vx.1

VRd.c.x.10.274



200mm

dx.2

0.5

2


b dx.2

4.068 103


fck

MPa

0.5

b dx.2

N mm2

53.293 kN



γc

k 100 ρ1fck

MPa

0.333

b dx.2

76.743 k



Ratio2Vx.2

VRd.c.x.20.274

SHEAR CAPACITY CHECK AT LONG SPAN CONTINUOUS SUPPORT 1:


CALUCLATIION SHEET


EUROCODE 2




200mm

dy.1

0.5

2


b dy.1

4.068 103


fck

MPa

0.5

b dy.1

N mm2

53.293 kN



γc

k 100 ρ1fck

MPa

0.333

b dy.1

76.743 kN



Ratio3Vy.1

VRd.c.y.10.274

SHEAR CAPACITY CHECK AT LONG SPAN CONTINUOUS SUPPORT 2:


200mm

dy.2

0.5

2


b dy.2

4.068 103


fck

MPa

0.5

b dy.2

N mm2

53.293 kN



γc

k 100 ρ1fck

MPa

0.333

b dy.2

76.743 kN



Ratio4Vy.2

VRd.c.y.20.274



MPa

0.5

5.477 103



ρt max 0.0035Asx.m

b dx.m

3.5 103


CALUCLATIION SHEET


EUROCODE 2









1.5



MPa

0.5

ρo

ρt 3.2

fck

MPa

0.5

ρo

ρt1

1.5

ρt ρoif

Kδ 11 1.5fck

MPa

0.5

ρo

ρt ρc

1

12

fck

MPa

0.5

ρc

ρo

ρt ρoif

46.949


lx

dx.m35.714


RatioRatioact

Limx.bas0.761

















CALUCLATIION SHEET


EUROCODE 2












Short span:

Midspan in short span direction: ϕx.m 10 mm sx.m 200 mmat C/CContinuous support 1 in short span direction: ϕx.1 12 mm sx.1 200 mmat C/CContinuous support 2 in short span direction: ϕx.2 12 mm sx.2 200 mmat C/C

Long span:

Midspan in short span direction: ϕy.m 10 mm sy.m 200 mmat C/CContinuous support 1 in long span direction: ϕy.1 12 mm sy.1 200 mmat C/CContinuous support 2 in long span direction: ϕy.2 12 mm sy.2 200 mmat C/C


CALUCLATIION SHEET


EUROCODE 2



ϕy.2 12 mm sy.2 200 mm

ϕx.2 12 mm sx.2 200 mm ϕx.1 12 mm sx.1 200 mm



ϕy.1 12 mm sy.1 200 mm


csi etabs & safe manual: slab analysis and design to ec2

Engineering