1. Plain & Reinforced Concrete-1 CE3601
Lecture # 13, 14 &15 13th to 20th April 2012
Flexural Analysis and
Design of Beams (Ultimate Strength Design of Beams)

2. Plain & Reinforced Concrete-1
Load Carried by the Beam
Beam Supporting One-way Slab
(ly/lx > 2)
Exterior Beam
Interior Beam lx lx ly
Width of slab supported by interior beam = lx
Width of slab supported by exterior beam = lx/2 + Cantilever width

3. Plain & Reinforced Concrete-1
Load Carrie by the Beam
Beam Supporting Two-way Slab (ly/lx≤ 2)
Exterior Long Beam
45o
Exterior Short Beam lx
Interior Long Beam lx ly ly
Interior Short Beam

4. Plain & Reinforced Concrete-1
Load Carrie by the Beam
Beam Supporting Two-way Slab (ly/lx≤ 2) contd…
Shorter Beams
For simplification this triangular load on both the sides is to be replaced by equivalent UDL, which gives same Mmax as for the actual triangular load.
lx/2
45o
lx/2
Area of Square

5. Plain & Reinforced Concrete-1
Load Carried by the Beam
Beam Supporting Two-way Slab (ly/lx≤ 2) contd…
Equivalent Rectangular Area
45o
45o lx
Factor of 4/3 convert this VDL into UDL.
Equivalent width supported by interior short beam
Equivalent width supported by exterior short beam
Cantilever

6. Plain & Reinforced Concrete-1
Load Carried by the Beam
Beam Supporting Two-way Slab (ly/lx≤ 2)contd…
Exterior Long Beam
lx/2
ly - lx
lx/2
Supported Area lx lx ly

7. Plain & Reinforced Concrete-1
Load Carried by the Beam
Beam Supporting Two-way Slab (ly/lx≤ 2)contd…
Exterior Long Beam
Factor F converts trapezoidal load into equivalent UDL for maximum B.M. at center of simply supported beam.
where
For Square panel
R = 1 and F = 4/3

8. Plain & Reinforced Concrete-1
Load Carried by the Beam
Beam Supporting Two-way Slab (ly/lx≤ 2)contd…
Exterior Long Beam
lx/2
ly - lx
lx/2
Equivalent width
Equivalent width ly
+ Cantilever (if present)

9. Plain & Reinforced Concrete-1
Load Carried by the Beam
Beam Supporting Two-way Slab (ly/lx≤ 2) contd…
Interior Long Beam
lx/2
ly - lx
lx/2
Equivalent width
Equivalent width ly

10. Plain & Reinforced Concrete-1
Wall Load (if present) on Beam
tw (mm)
UDL on beam
H (m)
(kN/m)

11. Plain & Reinforced Concrete-1
Wall Load on the Lintel
Equivalent UDL on lintel if height of slab above lintel is greater than 0.866L
0.866L
60o
60o
kN/m L
tw = wall thickness in “mm”
L = Opening size in “m”
If the height of slab above lintel is less than 0.866L
Total Wall Load + Load from slab in case of load bearing wall
UDL = (Equivalent width of slab supported) x (Slab load per unit area)
= m x kN/m2 = kN/m

12. Plain & Reinforced Concrete-1
Slab Load per Unit Area
Top Roof
Slab Thickness = 125 mm
Earth Filling = 100 mm
Brick Tiles = 38 mm
Dead Load
Self wt. of R.C. slab
Earth Filling
Brick Tiles
Total Dead Load, Wd =
554 kg/m2

13. Plain & Reinforced Concrete-1
Slab Load per Unit Area (contd…)
Top Roof
Live Load
WL = 200 kg/m2
Total Factored Load, Wu

14. Plain & Reinforced Concrete-1
Slab Load per Unit Area (contd…)
Intermediate Floor
Slab Thickness = 150 mm
Screed (brick ballast + 25% sand) = 75 mm
P.C.C = 40 mm
Terrazzo Floor = 20 mm
Dead Load
Self wt. of R.C. slab
Screed
Terrazzo + P.C.C
Total Dead Load, Wd =
633 kg/m2

15. Plain & Reinforced Concrete-1
Slab Load per Unit Area (contd…)
Intermediate Floor
Live Load
Occupancy Live Load = 250 kg/m2
Moveable Partition Load = 150 kg/m2
WL = = 400 kg/m2
Total Factored Load, Wu

16. Plain & Reinforced Concrete-1
Slab Load per Unit Area (contd…)
Self Weight of Beam
Service Self Wight of Beam = b x h x 1m x 2400
Kg/m
Factored Self Wight of Beam
kN/m
Self weight of beam is required to be calculated in at the stage of analysis, when the beam sizes are not yet decided, so approximate self weight is computed using above formula.

17. Plain & Reinforced Concrete-1
Bar Bending Schedule
Serial #
Bar
Designation
Number of Bars
Length of one Bar
Dia
of bar
Weight of Steel Required
Shape of Bar
#10
#13
#15
#19
#25 1
M-1 2
S-1 3
H-1 Σ
Total weight of steel = 1.05Σ , 5% increase, for wastage during cutting and bending

18. Plain & Reinforced Concrete-1
Bar Bending Schedule (contd…)
Bent-up Bar h h
45o L
Additional Length = h
Total Length = L h

19. Plain & Reinforced Concrete-1
Bar Bending Schedule (contd…)
90o-Standard Hooks (ACI) L db
R = 4db for bar up-to #25
R = 12db
R = 5db for bar #29 & #36
Total Length = L + 18db
For R 4db

20. Plain & Reinforced Concrete-1
Bar Bending Schedule (contd…)
180o-Standard Hooks (ACI) L db
Same as 90o hook
4db
Total Length = L + 20db

21. Plain & Reinforced Concrete-1
Bar Bending Schedule (contd…)
Example: Prepare bar bending schedule for the given beam. Clear cover = 40 mm
2-#10
180 c/c
1-# 15
2-#20
570
2-#20 +1-#15
4000
Longitudinal Section
228

22. Plain & Reinforced Concrete-1
Bar Bending Schedule (contd…)
Example: Prepare bar bending schedule for the given beam. Clear cover = 40 mm
2-#10
(H-1)
180 c/c
375
(S-1)
2-#20
(M-1)
1-# 15
(M-2)
228
Cross Section

23. Plain & Reinforced Concrete-1
Bar Bending Schedule (contd…)
Example:
M-1 = x 228 – 2 x x (18 x 20)
= 5096
M-1
M-2
h = 375 – 2 x 40 – 2 x 10 – 2 (15/2) = 260 h
M-2 = x 228 – 2 x 40 + (0.414 x 260) x 2
= 5091
H-1
H-1 = x 228 – 2 x 40
= 4376

24. Plain & Reinforced Concrete-1
Bar Bending Schedule (contd…)
Example: Prepare bar bending schedule for the given beam. Clear cover = 40 mm
Shear stirrups a
Number of Bars = 4000 / = 24
Round-up
a = 375 – 2 x 40 – 10 = 285 mm
b = 228– 2 x 40 – 10 =138 mm b
Total length of S-1 = 2 ( x 10) = 1206 mm

25. Plain & Reinforced Concrete-1
Bar Bending Schedule
Serial #
Bar
Designation
Number of Bars
Length of one Bar
(m)
Dia
of bar
Weight of Steel Bars
Shape of Bar
#10
#15
#20 1
M-1 2
5.096 20 24
M-2
4.591 15
7.2 3
H-1
4.376 10
6.9 4
S-1
1.206
22.7
1.05 Σ
31.1
7.6
25.2
4376
4376
4376
138
285
Total Weight = 64 kg

26. Plain & Reinforced Concrete-1
Design of Singly Reinforced Beam by Strength Method (for flexure only)
Data:
Load, Span (SFD, BMD)
fc’, fy, Es
Architectural depth, if any
Required:
Dimensions, b & h
Area of steel
Detailing (bar bending schedule)

27. Plain & Reinforced Concrete-1
Design of Singly Reinforced Beam by Strength Method (contd…)
Procedure:
Select reasonable steel ratio between ρmin and ρmax. Then find b, h and As.
Select reasonable values of b, h and then calculate ρ and As.

28. Plain & Reinforced Concrete-1
Design of Singly Reinforced Beam by Strength Method (contd…)
Using Trial Dimensions
Calculate loads acting on the beam.
Calculate total factored loads and plot SFD and BMD. Determine Vumax and Mumax.
Select suitable value of beam width ‘b’. Usually between L/20 to L/15. preferably a multiple of 75mm or 114 mm.
Calculate dmin.
hmin = dmin + 60 mm for single layer of steel
hmin = dmin + 75mm for double layer of steel
Round to upper 75 mm

29. Plain & Reinforced Concrete-1
Design of Singly Reinforced Beam by Strength Method (contd…)
Decide the final depth.
For strength
For deflection
Architectural depth
Preferably “h” should be multiple of 75mm.
Recalculate “d” for the new value of “h”

30. Plain & Reinforced Concrete-1
Design of Singly Reinforced Beam by Strength Method (contd…)
Calculate “ρ” and “As”.
Four methods a) b)
Design Table
Design curves
Using trial Method c) d)

31. Plain & Reinforced Concrete-1
Design of Singly Reinforced Beam by Strength Method (contd…)
Check As ≥ As min. As min = ρmin bd (ρmin = 1.4/fy to fc’ ≤ 30 MPa)
Carry out detailing
Prepare detailed sketches/drawings.
Prepare bar bending schedule.

32. Plain & Reinforced Concrete-1
Design of Singly Reinforced Beam by Strength Method (contd…)
Using Steel Ratio
Step I and II are same as in previous method.
Calculate ρmax and ρmin & select some suitable “ρ”.
Calculate bd2 from the formula of moment
Select such values of “b” and “d” that “bd2” value is satisfied.
Calculate As.
Remaining steps are same as of previous method.

33. Concluded