Plain & Reinforced Concrete-1 CE3601 Lecture # 25 , 26 & 27 20th April to 8th May 2012 Analysis and Design of Slabs

Plain & Reinforced Concrete-1 Isolated One Way Slab

Plain & Reinforced Concrete-1 Continuous One Way Slab

Plain & Reinforced Concrete-1 Negative Moment Positive Moment Continuous One Way Slab

Plain & Reinforced Concrete-1 Minor Bending Continuous One Way Slab

Plain & Reinforced Concrete-1 Example: Design a cantilever projecting out from a room slab extending 1.0m and to be used as balcony (LL = 300 kg/m2). A brick wall of 250 mm thickness including plaster of 1m height is provided at the end of cantilever. fc’ = 17.25 MPa fy = 300 MPa Slab thickness of room = 125 mm. Slab bottom steel 1in the direction of cantilever is # 13 @ 190 mm c/c.

Plain & Reinforced Concrete-1 Solution: cantilever 125 mm 1m

Plain & Reinforced Concrete-1 Solution: (contd…) Let we use the same thickness as of the room d Main steel in cantilever is at the top

Plain & Reinforced Concrete-1 Solution: (contd…) Slab Load Self weight of slab 75 mm brick ballast/ screed 60 mm floor finishes Total dead load

Plain & Reinforced Concrete-1 Solution: (contd…) Slab Load Live Load For a unit strip

Plain & Reinforced Concrete-1 Solution: (contd…) 1.063m Per meter width

Plain & Reinforced Concrete-1 Solution: (contd…) d # 13 @ 380 mm c/c already available in the form half the bent up bar from the room slab

Plain & Reinforced Concrete-1 Solution: (contd…) Remaining steel required at the top Use Distribution steel

Plain & Reinforced Concrete-1 Solution: #13 @ 380 c/c Slab bottom steel 1500 mm #10 @ 280 c/c #10 @ 380 c/c

Plain & Reinforced Concrete-1 Two-Way Edge Supported Slabs

Plain & Reinforced Concrete-1 Two-Way Slabs Slab resting on walls or sufficiently deep and rigid beams on all sides. Other options are column supported slab e.g. Flat slab, waffle slab. Two-way slabs have two way bending unlike one-way slab.

Plain & Reinforced Concrete-1 Isolated Two Way Slab

Plain & Reinforced Concrete-1 Positive Moment Negative Moment Continuous Two Way Slab

Plain & Reinforced Concrete-1 Design Methods ACI co-efficient method Direct design method Equivalent frame method Finite element method Notes In two-way slabs shorter direction strip carry greater %age of load. Steel will be more in shorter direction. Shorter direction steel will be placed near the outer edge to get more “d” means more lever arm to get more flexural capacity. Ly Lx

Plain & Reinforced Concrete-1 ACI Co-efficient Method Unit width strip is taken in both directions. The strip is designed separately for +ve and –ve moment. C = ACI co-efficient ωu = Slab load “C” depends upon the end conditions of slab and the aspect ratio. Three tables are available for “C” Dead load positive moment Live load positive moment -ve moment M+ coefficients are increased by 25 % and M- coefficients are reduced by 10 % to get the result more closer to accurate solution.

Plain & Reinforced Concrete-1 Minimum Depth of 2-Way Slab for Deflection Control According to ACI-318-1963 hmin = (inner perimeter of slab panel)/180 ≥ 90 mm For fy = 300 MPa For fy = 420 MPa According to ACI-318-2008 Ln = clear span in short direction

Plain & Reinforced Concrete-1 Example: Design the 4 marked slab panels of an ordinary house. Use US customary bars. fc’= 17.25 MPa fy = 300 MPa 1 2 4500 x 7000 6000 x 7000 Wall thickness = 228 mm 3 4 6000 x 6000 3500 x 6000

Plain & Reinforced Concrete-1 Solution: Panel Edge Conditions Panel # 1 Lx = 4.5m , Ly = 7.0m m = 0.64 > 0.5, 2-way slab Panel # 2 Lx = 6.0m , Ly = 7.0m m = 0.86> 0.5, 2-way slab Panel # 3 Lx = 3.5m , Ly = 6.0m m = 0.58 > 0.5, 2-way slab Panel # 4 Lx = 6.0m , Ly = 6.0m m = 1 > 0.5, 2-way slab

Plain & Reinforced Concrete-1 Solution: (contd…) Slab Thickness Generally same depth is preferred for one monolith slab. Calculate hmin for all the panels and select the largest value. Panel # 1 Panel # 2

Plain & Reinforced Concrete-1 Solution: (contd…) Panel # 3 Panel # 4

Plain & Reinforced Concrete-1 Solution: (contd…) Effective depth d2 d1 Long direction steel Short direction steel For short direction steel For longer direction steel

Plain & Reinforced Concrete-1 Solution: (contd…) Slab Load Self weight of slab 75 mm brick ballast/ screed 60 mm floor finishes Total dead load

Plain & Reinforced Concrete-1 Solution: (contd…) Slab Load Live Load

Plain & Reinforced Concrete-1 Solution: (contd…) Minimum Steel For a unit strip

Concluded