8/10/2019 Mathcad - Homework22
1/17
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
Page nr. 1 of 21
8/10/2019 Mathcad - Homework22
2/17
Rak-83.3200 COMPOSITE Homework Nr. 1
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
Page nr. 2 of 21
8/10/2019 Mathcad - Homework22
3/17
8/10/2019 Mathcad - Homework22
4/17
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
Page nr. 4 of 21
8/10/2019 Mathcad - Homework22
5/17
Rak-83.3200 COMPOSITE Homework Nr. 1
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
Page nr. 5 of 21
8/10/2019 Mathcad - Homework22
6/17
Rak-83.3200 COMPOSITE Homework Nr. 1
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
Page nr. 6 of 21
8/10/2019 Mathcad - Homework22
7/17
8/10/2019 Mathcad - Homework22
8/17
Rak-83.3200 COMPOSITE Homework Nr. 1
Shear ForceDiagram, ofsteel sheetingprofile
Momentdiagram,ofsteel sheetingprofile
Mnbm.ps 0.117kN m Fnbm.ps 0.204kN
M. ValenteID: 59082
Page nr. 8 of 21
8/10/2019 Mathcad - Homework22
9/17
Rak-83.3200 COMPOSITE Homework Nr. 1
Shear ForceDiagram, ofsteel sheetingprofile
Momentdiagram,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
Page nr. 9 of 21
8/10/2019 Mathcad - Homework22
10/17
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
Page nr. 10 of 21
8/10/2019 Mathcad - Homework22
11/17
Rak-83.3200 COMPOSITE Homework Nr. 1
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
Page nr. 11 of 21
8/10/2019 Mathcad - Homework22
12/17
Rak-83.3200 COMPOSITE Homework Nr. 1
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
Page nr. 12 of 21
8/10/2019 Mathcad - Homework22
13/17
Rak-83.3200 COMPOSITE Homework Nr. 1
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
Page nr. 13 of 21
8/10/2019 Mathcad - Homework22
14/17
Rak-83.3200 COMPOSITE Homework Nr. 1
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
Page nr. 14 of 21
8/10/2019 Mathcad - Homework22
15/17
Rak-83.3200 COMPOSITE Homework Nr. 1
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
Page nr. 15 of 21
8/10/2019 Mathcad - Homework22
16/17
Rak-83.3200 COMPOSITE Homework Nr. 1
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
Page nr. 16 of 21
8/10/2019 Mathcad - Homework22
17/17
Rak-83.3200 COMPOSITE Homework Nr. 1
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