Mathcad - Homework22

8/10/2019 Mathcad - Homework22

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Rak-83.3200 COMPOSITE Homework Nr. 1

INTRODUCTION

HOMEWORK Nr.2: Design of composite slab

This work shows the design of 3 span of a composite floor slab.

It is calculated for construction and composite stages.

In composite stage is considered that sheet profile is propped, with temporary supports

until concrete be cured.

The steel sheet profile used for this case is holorib.

M. ValenteID: 59082

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INPUTS

Partial factors

Partial factor for permanent loads G 1.35 EN 1990-1-1

Partial factor for variable loads Q 1.50

Partial factor for resistance of cross-sections M0 1.00

EN 1993-1-1

Partial factor for resistance of members to instability

assessed by member checksM1 1.00

Partial factor for ultimate limit state VS 1.25 EN 1994-1-1

Partial safety factor for concrete C 1.50EN 1992-1-1

Partial factor for reinforcing or prestressing steel S 1.15

Steel sheeting input

Profiled steel sheeting reference Holorib 51/150

Spacing between trough of steel sheeting profile btrough 150mm

Profile sheeting high hps 51mm

Steel sheet profile modulus of elasticity Esp 210000N

mm2

Profiled sheeting yield strenght fy.ps 350N

mm2

Lspan 2400 mm

Span of sheet profile

Profiled sheeting thickness tsp 0.86mm

Profiled sheeting effective area Asp 1562mm

2

m

Profiled sheeting second moment of area in yy axis Iyy.sp 620000mm

4

m

w

corr.ps

140mmWidth of corrugated in steel sheet profile

hcentr.ps 17mmHigh of centroidal axis of the profiled sheel sheeting

M. ValenteID: 59082

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Rak-83.3200 COMPOSITE Homework Nr. 1EN 1992-1-1Item: 3.2.3Compressive strength of concrete fcd

fck

C16.667

N

mm2

Distance from top of slab to profile sheet centroidal dp hth hcentr.ps 123 mm

Characteristic cylinder strength fctk.0.05 1.8N

mm2

actions input

Steel sheet profile self weight in construction stage gcns.ps 0.13kN

m2

Wet concrete self weight in construction stage to 140mm

thicknessgcns.wc 3.37

kN

m2

Distributed construction stage load qcns1 0.75kN

m2

Concentration of construction stage load in 3m2 qcns2

1.5kN

m2

Composite slab self weight (composite stage) gcmp.wcs 3.3kN

m2

Self weight of floor finishes gcmp.wff 1.2kN

m2

Imposed load qcmp.il 5.0kN

m2

M. ValenteID: 59082

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CONSTRUCTION STAGE / CONCREETING PHASE

Design values for load combinations

To help in this calculation, it was used a software to get the values of shear

forces and bending moments negative and positive. Software used is Autodesk

force effect.

Dead loads in construction stage for sagging bending moment

Shear ForceDiagram, ofsteel sheeting

profile

Momentdiagram,ofsteel sheetingprofile

Mpbm.ps 0.044kN m

M. ValenteID: 59082

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Shear ForceDiagram, ofwet concrete

to 140mmthickness

Momentdiagram, of wetconcrete to140mmthickness

Mpbm.wc 1.812kN m

Mpbm.g

Mpbm.ps Mpbm.wc

1m 1.856kN m

m

Live loads in construction stage for sagging bending moment

M. ValenteID: 59082

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Shear ForceDiagram, ofsteel sheetingprofile


Mnbm.ps 0.117kN m Fnbm.ps 0.204kN

M. ValenteID: 59082

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Shear ForceDiagram, ofsteel sheetingprofile


Mnbm.wc 2.329kN m Fnbm.wc 5.034kN

Mnbm.g

Mnbm.ps Mnbm.wc

1m2.446

kN m

m

Fnbm.g

Fnbm.ps Fnbm.wc

1m5.238

kN

m

M. ValenteID: 59082

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Rak-83.3200 COMPOSITE Homework Nr. 1Live loads in construction stage for hogging bending moment

Shear ForceDiagram, ofdistributedconstructionload

Momentdiagram, ofdistributedconstructionload

Mnbm.dcl 0.121kN m Fnbm.dcl 0.507kN

Mnbm.ccl 0.76kN m Fnbm.ccl 1.871kN

M. ValenteID: 59082

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Mnbm.q

Mnbm.dcl Mnbm.ccl

1m0.881

kN m

m

Fnbm.q

Fnbm.dcl Fnbm.ccl

1m2.378

kN

m

Mnbm.Ed G Mnbm.g Q Mnbm.q 4.624kN m

m

Fnbm.Ed G Fnbm.g Q Fnbm.q 10.638kN

m

Design check

Positive Bending moment or Sagging bending moment

Mpbm.Rd

Mpbm.Rk

M0

6.1kN m

m Mpbm.Ed 3.716

kN m

m OK

Negative Bending moment or Hogging bending moment

Mnbm.Rd

Mnbm.Rk

M06.3

kN m

m Mnbm.Ed 4.624

kN m

m OK

Support reaction

RRd

R

wkM0

37 kNm Fnbm.Ed 10.638 kNm OK

Combine moment and support reaction

Mnbm.Ed

Mnbm.Rd

Fnbm.Ed

Rwk 1.021 1.25 OK

Serviceability limit state

According with Eurocode, deflection should not exceedLspan

180

According to input we already know that there is no local buckling, so no need to verify!!

sp.wc

2.65 gcns.ps 3.4 gcns.wc Lspan4

384 Esp Iyy.sp

sp.wc 7.832 mm sp.wc.maxLspan

18013.333 mm OK

M. ValenteID: 59082

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Since deflection of steel sheet profile with wet concrete is less than 1/10 of slab

depth, no need to take account ponding effect.

The sheeting can work as shuttering in construction stage.

Verifification of composite slab in Ultimate Limit State

IMAGE

MEd.cmp

G gcmp.wcs gcmp.wff Q qcmp.il Lspan2

89.774

kN m

m

VEd

G gcmp.wcs gcmp.wff Q qcmp.il Lspan

216.29

kN

m

Ls

Lspan

4600 mm

V1.Rd

Wsl dp

VS 1m( )2

msp Asp 1m2

Wsl Lsksp 1m

57.284

kN

m

VEd 16.29kN

m V1.Rd 57.284

kN

m

So is possible to use m-k method

Design bending moment

Nc.f Asp fy.ps 1m 546.7 kN

M. ValenteID: 59082

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pl

Nc.f

0.85 Wsl fcd38.591 mm

In case of full shear connection

Mpl.Rd Asp fy.ps dp

pl

2

56.695 kN MEd.cmp 9.774 kN OK

LxNc.f

Wsl u.Rd1.952 103 mm

Nc u.Rd Wsl Lx Nc.f

This value means that Lxis the minimum distance from support that will obtain a full shear connection.

M. ValenteID: 59082

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M x( )G gcmp.wcs gcmp.wff Q qcmp.il x Lx x

2

y x( )msp

1m

Asp

1000 x

ksp

1m

Lx 1.952m

xi 0 m

xf 2 m

yi 0

kN m

m

yf 10kN m

m

0 0.5 1 1.5 2

2000

4000

6000

8000

10000

moment

abcd

12345

y x( )

M x( )

x

M. ValenteID: 59082

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10 5 0 5 100

2 103

4 103

6 103

8 103

1 104

y x( )

x

Design Vertical Shear

CRd.c0.18

C0.12

1200 1mm

dp 2.275

bw

wcorr.ps ncorr.ps 1000 mm

wps 1 m 918.033

mm

m

I min 0.02Asp

bw dp

0.014

1 0.15

c.p 0

Vv.Rd CRd.c 100I 25 13

1 c.p

bw dpkN 10

3

m2

100.44kN

m

Minimum of Shear Resistance

min 0.035 1.5

250.5

0.601

VV.R.d.min min 1 c.p bw dpkN 10

3

m2

67.814kN

m

M. ValenteID: 59082

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VV.R.d.min 67.814kN

m Vv.Rd 100.44

kN

m

VEd 16.29kN

m

Vv.Rd 100.44kN

m

Verifification of composite slab in Serviceability Limit State

Cracking of concrete

As 0.004 Wsl ht 356mmm

2

m

drebar 10mm

Arebar

drebar2

478.54 mm2

minimum of rebars in a meterAs

Arebar4.533

To use rebar of 10mm of diameter the spacing should be 200mm

Deflection

Ec1

2

Ecm

Ecm

3

2.067 104

N

mm2

Esp

Ec10.161

c

Asp

Wsl1

2 Wsl dp

Asp 1

c 48.99mm

M. ValenteID: 59082

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IWsl c

3

3

Asp 1m dp c

2 Iyy.sp 1m 1.303 10

7 m

mm4

m

b0

u

Wsl

h

t2

2

b0 hsp hth

h

sp2

Asp dp

Wsl hc b0 hp Asp

b0

Ibu

Wsl hc3

12

Wsl hc

u

hc

2

2

b0 hp

3

12

b0 hp

hth uhsp

2

2

Asp dp u 2

Isp u

Ib

I Ibu

2

Ibu

After remove all temporary supports

Grts gcmp.wcs

Lspan

2 3.96

kN

m

c.G.prop

0.01146Gprop Lspan3

Esp Ib

Ib

Composite slab without any temporary supports and with weight of f loor finishes

c.wff

0.0068 gcmp.wff Lspan4

Esp Ib Ib

Composite slab without any temporary supports and with weight of f loor finishes

c.il

0.00991 qcmp.il Lspan4

Esp Ib

Ib

T c.G.prop c.il c.wff c.G.prop Lspan

2509.6 mm

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