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Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
82
Roof Design Two Way Slab. Cl 13.8 Slab Systems As elastic Frames
1) Criteria For Equivalent Frame Method CSA S23.3a) Within a panel , the ratio of longer to shorter span, center to center of supports, is not
greater than 2.0
b) Slab systems with beams between supports the relative effective stiffness of beams inthe two directions is not less than 0.2 or greater than 5.0.
Not Applicable as the roof slab is a flat slab without beams.c) Column offsets are not greater than 20% of the span (indirection of offset) from either
axis between centerlines of successive columns.No offset column in the building.
d) The Reinforcement is placed in an orthogonal grid.Reinforcement will be placed in an orthogonal grid.
2) Slab Thickness With Out Drop Spans Cl 13.2.3
ln= clear span between columns. Will use the actual span length to be conservative and preventredesign of roof with changing column sizes.
.:. ln=5m 5000mm
Increase the minimum thickness by 10% due to the discontinuous edges. Cl13.2.3
3) Factored Design Loads.
Loading Based upon Roof Loads Cases and Computed In S frame model.
Center Span L=10m Edge Span L=5mDeadLoad:
4.00 kPa 40.0 kN/m 20.0 kN/m
Live Load: 1.00 kPa 10.0 kN/m 5.00 kN/m
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
83
SnowLoad:
2.72 kPa 27.2 kN/m 13.6 kN/m
Wind Load 0.68 kPa 6.80 kN/m 3.40 kN/m
Considered Patterned Loading Cl 13.8.4.2
Slab BeamMoment of Inertia
Central Span Beam Edge Span Beam
Column Moment of Inertia
Column Effective Moment of Inertia Cl13.8.3.3No beams therefore =0 and l2/l1=1 as a result =0.3
Summary Of Worst Load CaseCritical Design Case is 1.25D+1.5S+0.5LMf bottom = 460kNm Decrease Moment
Mf top = 272kNmVf= 297kN(Edge) and 475kN (Central)
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
84
4) Shear Design One Way Cl 11.1 11.3
=0.21 as hs=190mm<350mm Cl 11.3.6.2
c=0.65 =1 normal Density fc’=25MPa bw=10,000mm dv
dv=136.8mm Greater of 0.72*hs=0.72*190=136.8mm
0.9*d=0.9*135=121.5mm
bw=10,000mm as Vf based upon 10m Span Beam
.:. One way shear is ok. No reinforcement required for one way shear.
5) Two Way Shear
Shear Force
Central Column
Edge Column
A B C
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
85
Central Column
Shear Strain
Confirm fc’^0.5 is less than 8MPa Cl 13.3.4
Shear Resistance
Central(13 5) (13 6) (13 7)
=1.50MPa =1.63 MPa =1.24 MPa
Edge(13 5) (13 6) (13 7)
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
86
=1.50MPa =1.73 MPa =1.24 MPa
Corner(13 5) (13 6) (13 7)
=1.50MPa =1.81 MPa =1.24 MPa
Vf is greater than Vc therefore shear reinforcement required.
Check the max allowable shear for Stud Reinforcement.
The vmax < vf therefore shear reinforcement cannot be designed for this section of slab. Theissue is the length of span creates a large shear stress. Options to resolve this are largercolumns, more columns to decrease tributary area, drop panels, or increase the depth.
The column and beams have already been sized and spaced; to prevent redesign of thesemembers the roof slab will be depended. The choice to deepen the entire slab opposed tolocality with drop panels is that all columns require deepening.
Solve for a new depth using
. One Way shear will still be adequate.
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
87
Recalculate Shear Reinforcement.
Confirm fc’^0.5 is less than 8MPa Cl 13.3.4
Shear Resistance
Central vf=1.86 MPa
(13 5) (13 6) (13 7)
=1.64MPa =3.09 MPa =1.35 MPa
Edge vf=1.35 MPa(13 5) (13 6) (13 7)
=1.64MPa =3.33 MPa =1.35 MPa
Corner vf=1.10 MPa(13 5) (13 6) (13 7)
=1.64MPa =2.86 MPa =1.35 MPa
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
88
Design Reinforcement.
Cl 13.3.8.2
Stud Reinforcement:
Concrete Shear Stress is Stud Region Cl 13.3.8.3
Stud Spacing Cl 13.3.8.6
Stud Area Cl 13.3.8.5
Use 3/8” studs (9.5mm) area of Stud As=71mm2
in each direction
Layout of Stud rail “g”:
Spacing between rails:
Minimum length of stud rail: Cl 13.3.7.4
/and extend to where shear force is/
Length of rails based upon two rails per face with 7 studs
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
89
bo with rails
.
Final Stud Shear Resistance
Notes: the d/2 calculations for critical shear area were not revised upon deepening of the slab.As a result the “bo” values were not revised. As a result the shear stress for the two way shearwas designed with a larger value. The actual revised shear stress for the central column wouldbe:
RailLength
d/2=147.5mm
Column250x350
250mm
(11062+11062)0.5=1564mm
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
90
Shear Slab
Column Central Edge Cornerwf (kPa) 9.58d mm 135TA (m) 10x10 5x5 5x10Column (m) 0.350x0.250Shear Vf (kN) 956.2 477.5 238.2Shear stress vf (MPa) 1.86 1.35 1.10Concrete Resist vc(MPa)
1.00 1.35 1.35
Shear Steel vs (MPa) 1.16Use 30MPa ConcreteSlab Thickness: 350mmShear Studs at center column: Two Rails each face with 7 3/8” studs @ 145mm.End Distance to Stud 118mm
6) Design of Slab using Elastic Frames Cl 13.8
Criteria for Equivalent Frame Method
a) Within a panel , the ratio of longer to shorter span, center to center of supports, is notgreater than 2.0
b) Slab systems with beams between supports the relative effective stiffness of beams inthe two directions is not less than 0.2 or greater than 5.0.
Not Applicable as the roof slab is a flat slab without beams.c) Column offsets are not greater than 20% of the span (indirection of offset) from either
axis between centerlines of successive columns.No offset column in the building.
d) The Reinforcement is placed in an orthogonal grid.Reinforcement will be placed in an orthogonal grid.
Design Info:
Fy = 400 MPa f’c = 30 MPa hs = 350mm d = 295mm
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
91
7) Factored Design Loads.
Loading Based upon Roof Loads Cases and Computed In S frame model.
Center Span L=10m Edge Span L=5mDeadLoad:
4.00 kPa 40.0 kN/m 20.0 kN/m
Live Load: 1.00 kPa 10.0 kN/m 5.00 kN/mSnowLoad:
2.72 kPa 27.2 kN/m 13.6 kN/m
Wind Load 0.68 kPa 6.80 kN/m 3.40 kN/m
Consider Pattern Loading Cl 13.8.4.2
Slab BeamMoment of Inertia
Central Span Beam Edge Span Beam
Column Moment of Inertia
Column Effective Moment of Inertia Cl13.8.3.3No beams therefore =0 and l2/l1=1 as a result =0.3
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
92
Critical Design Case is 1.25D+1.5S+0.5L
Mf bottom = 460kNm Decrease Moment
Mf top = 272kNm
Vf= 297kN and 475kN
8) Treat the Frame System as a continuous Beam. This ignores the stiffness provided by the
Min Area of Steel Cl 7.8.1
Area of steel Required By Direct Procedure
A B C
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
93
Bottom Reinforcement Spacing for 15M rebar
Check against Spacing Limitations Cl 13.10.4
Outside of Band Width bb (1400mm)
Lesser of:
Within Band Width bb (1400mm)
Lesser of:
Band Width
Beam Strip
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
94
Exterior Midspan Interior Column
Steel Location Top Bottom TopMf (kNm) 12 272 400Column Strip Width (mm) 5000 5000 5000Within Band Width bbBand Width bb (mm) 1400 1400Moment 12 †1 400/3=133Reinforcement Required As (mm2) 118 1360Spacing Required (mm) 2350 200Max Spacing (mm) 250 250Bars 6 15M@250
for 10007 15M@200
†2Asmin (mm2) 980 980†3 Column WidthStrip Width 10000Moment 272Reinforcement Required As (mm2) 2690Spacing Required (mm) 744Max Spacing (mm) 500Bars 15M@ 400 †4
† 1 Cl 13.11.2.7 Interior Columns to support 1/3 of design moment
† 2 Cl 7.8.1 Min Area: Sample Calc. on previous Page
† 3 No Middle Strip as length and width of the spans are equal.
† 4 Spacing Reduced from 500mm to 400mm to provided additional strength allowing forconstruction Errors.
9) Slab Integrity Reinforcement Cl 13.10.6.1
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
95
10) Deflection Calculations
Deflection Calculations can be waived according to Cl 13.2.2 as the slab thickness (350mm) islarger than the minimum thickness (183mm) specified in Cl 13.2.3.
11) Development Length
Mid Span Bars
Tension Development Length is satisfactory for the mid span (bottom) bars as they run theentire 10m of slab. Compression Development is also satisfactory at the ends as the top steel isdesigned to take the entire moment load.
Center Column Cl 12.2.3
Table 12.1 is valid as
Point of inflection is 1.2m from column
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
96
Embedment length beyond inflection point Cl 12.12.2
Check the Maximum allowable Development Length Cl 12.11.3
The Length of Steel to either side of the central Column Center Line Must be
Edge Bars Hook Bars 90o
Note the Development Length a straight bar is the same as above 400mm
Use hook bars as there is insufficient bar length for full development Cl 12.5.2
Cover=40mm (outside)+10m(10M Column
Ties)=50mm
250
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
97
Point of inflection is 0.04m from edge.
Hook Length N12.5.2
Embedment length beyond inflection pointCl 12.12.2
Check the Maximum allowable Development Length Cl 12.11.3
Straight Length
Hook Design
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
126
Two Way Shear Cl 13.3.3.4.1
Determine the pressure on footing
Left=
Right= = Q Force= +Q Moment =
Slope
Shear Stress Cl 13.3.4.1
Where bo is the Critical Shear Failure around the Column
Continue with
70mm is the minimum Depth for equation (c ) as mentioned earlier the minimum Depth is 150.
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
127
Check Equations (a) and (b) of Cl 13.3.4.1 to determine if the resistance is greater than equation(c) Greater resistance means that the equation would not govern, if theresistance is lesser with a revised depth of 150mm.
Using d=150mm
Where
Note Equation (b) actually governed as without the increased in depth the resistance is lessthan 1.235MPa.
Actual Height of Footing
The actual height will be Depth, cover, and one layer of 25M
Oneway Shear Cl 11.3.4
Critical Shear Force Occurs at the a distance dv from pedestal.
180mm Governs
Distance is
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
128
Shear Resistance of Concrete
where
The concrete is adequate to carry shear load no Shear reinforcement required
Flexure Design
Treat the load as uniform form 0.35m to the end, this will over estimate the result.
Determine Area of Steel Required for Mr
Check Required Steel
Steel Bars
Spacing is the Length –End Spacing *2, divided by the number of spaces
Min Spacing Same as Pedestal, as a result it is adequate.
Max Spacing Cl 7.4.1.2 and Cl 13.10.4
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
129
500mm Spacing Governs. and 260mm is less .:. ok.
Bearing Between Footing and Pedestal Cl 10.8.1
Footing
Pedestal
Bearing Strength of Concrete is Adequate on Bearing Reinforcement Required.
Minimun Reinforcement Across Interface Cl 1.5.9.2.1
Four Bars
Bottom Hook
Note Hooks are not effective in compression (Cl 12.5.5) The hook Length is to provide length totie the bar to the Footings Flexural Steel
Development Length Cl 12.3
Final Report on the Design of aFire Testing & Research Facility
Lakehead University, Thunder Bay, Ontario
130
Development Length of Dowels is greater than footing Depth .:. Increase footing Height
SummaryDimensions 1.2mx1.2m Flexural Reinforcing 5 25M@ 260mm
Height 570mm
Dowels
4 25M 880mm lengthNo Shear Steel 300mm Hook
Cover 75mm All Faces Spliced to columnStarter Bars