Design of reinforced concrete beam

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1. Design in reinforcedconcrete
Prepared by: M.N.M Azeem Iqrah
B.Sc.Eng(Hons), C&G (Gdip)Skills College of Technology

2. Introduction
•Reinforced concrete is a composite material,
consisting of steel reinforcing bars embedded
inconcrete.
•Concrete has high compressive strengthbut
low tensilestrength.
•Steelbarscanresisthightensilestressesbut
willbucklewhensubjectedtocomparatively
lowcompressivestresses.

3. Introduction
•Steel bars are used in the zones within a
concrete member which will be subjected to
tensilestresses.
•Reinforced concrete is an economical
structural material which is both strong in
compression and intension.
•Concrete provides corrosion protectionand
fire resistance to the steelbars.

4. Basic ofdesign
•Two limit states design for reinforced concrete
in accordance to BS8110.
1.Ultimate limit state –considers the behaviour
of the element at failure due to bending,
shear and compression ortension.
2.The serviceability limit state considers the
behaviour of the member at working loads
and is concerned with deflection and
cracking.

5. Material properties -concrete
•The most important property is the compressive
strength. The strength may vary due to operation
such as transportation, compaction andcuring.
•Compressive strength is determined by
conducting compressive test on concrete
specimens after 28 days ofcasting.
•Two types of specimen: (1) 100 mm cube (BS
standard), and (2) 100 mm diameter by 200 mm
longcylinder.

6. Characteristic compressive strengthof
concrete
•Characteristic strength of concrete is defined
as the value below which no more than 5
percent of the test resultsfall.,

7. Characteristic compressive strength
(fcu) ofconcrete
Chanakya Arya, 2009. Design ofstructural
elements 3
rd edition, SponPress.
Cylinderstrength
Cubestrength
•Concrete strength classes in the range ofC20/25
and C50/60 can be designed using BS8110.

8. Stress-strain curve forconcrete
Stress strain curvefor
concretecylinder
(Chanakya Arya, 2009. Design of structural elements 3
rd
edition,
SponPress.)
Idealized stress strain curvefor
concrete in theBS8110

9. Material properties ofsteel
•Idealized stress-strain curve forsteel.
1.An elasticregion,
2.Perfectly plastic region (strain hardening of steelis
ignored)
BS 8110,1997

10. Durability (clause 3.1.5, BS8110)
•Durability of concrete structures is achieved
by:
1.The minimum strength class ofconcrete
2.The minimum cover toreinforcement
3.The minimum cementcontent
4.The maximum water/cementratio
5.The cement type orcombination
6.The maximum allowable surface crackwidth

11. Fire protection (clause 3.3.6,BS8110)
•Fire protection of reinforced concrete
members is largely by specifying limitsfor:
1.Nominal thickness of cover tothe
reinforcement,
2.Minimum dimensions ofmembers.

12. Concrete cover for fireresistance
BS 8110,1997

13. Minimum dimension forreinforced
concrete members for fireresistance
BS 8110,1997

14. Beams (clause 3.4,BS8110)
•Beams in reinforced concrete structures can
be defined accordingto:
1.Cross-section
2.Position ofreinforcement
3.Supportconditions

15. Beamdesign
•In ultimate limit state, bending is critical for
moderately loaded medium span beams.
Shear is critical for heavily loaded short span
beams.
•In service limit state, deflection will be
considered.
•Therefore, every beam must be design against
bending moment resistance, shear resistance
anddeflection.

16. Types of beam by crosssection
Rectangularsection L-section T-section
•L-and T-section beams are produced due to
monolithic construction between beam and slab. Part
of slab contributes to the resistance ofbeam.
•Under certain conditions, L-and T-beams aremore
economical than rectangular beams.

17. Types of beam byreinforcement
position
Singly reinforced Doublyreinforced
•Singly reinforced –reinforcement to resist tensilestress.
•Doubly reinforced –reinforcement to resist bothtensile
and compressivestress.
•Compressive reinforcement increases the moment
capacity of the beam and can be used to reducethe
depth ofbeams.

18. Notation for beam (clause 3.4.4.3, BS8110)
b
hd
d’
AS
A’S

19. Design forbending
M ≤Mu
Maximum moment on beam ≤ moment capacityof
thesection
The moment capacity of the beam is affectedby:
1.The effective depth,d
2.Amount ofreinforcement,
3.Strength of steelbars
4.Strength ofconcrete

20. Singly reinforcedbeam

21. Moment capacity of singlyreinforced
beam
Fcc
Fst
z
Forceequilibrium
Fst =Fcc
Fcc = stress xarea
=
Moment capacity of thesection

22. Singly reinforcedbeam
•If
Then the singly reinforced section is sufficient to
resistmoment.
Otherwise, the designer have to increase the
section size or design a doubly reinforced
section

23. Doubly reinforcedbeam
•If
The concrete will have insufficient strength in
compression. Steel reinforcement can be
provided in the compression zone to increase
compressiveforce.
Beams which contain tension and compression
reinforcement are termed doublyreinforced.

24. Doubly reinforcedbeam
M = Fsc (d-d’) + Fccz

25. Example 3.2 Singly reinforced beam
(Chanakya Arya,2009)
•A simply supported rectangular beam of 7 m span carries
characteristic dead (including self-weight of beam), gk and
imposed, qk, loads of 12 kN/m and 8 kN/m respectively.
Assuming the following material strengths, calculate thearea
of reinforcementrequired.

26. Example 3.2 Singly reinforced beam
(Chanakya Arya,2009)
Compression reinforcement is notrequired

27. Example 3.2 Singly reinforced beam
(Chanakya Arya,2009)
Provide 4H20, (As = 1260mm
2
)

28. Cross section area for steel bars(mm
2)

29. Example 3.7 Doubly reinforcedbeam
(Chanakya Arya,2009)
•The reinforced concrete beam has an effective span of 9m and
carries uniformly distributed dead load (including self weight
of beam) and imposed loads as shown in figure below. Design
the bendingreinforcement.

30. Example 3.7 Doubly reinforced beam(Chanakya
Arya,2009)

31. Example 3.7 Doubly reinforced beam(Chanakya
Arya,2009)
Compression reinforcement isrequired

32. Example 3.7 Doubly reinforced beam(Chanakya
Arya,2009)

33. Failure mode of beam inbeam
•The failure mode of beam in bending depends on
the amount ofreinforcement.
(1)under reinforced reinforced beam –the steel
yields and failure will occur due to crushing of
concrete. The beam will show considerable
deflection and severe cracking thus provide
warning sign beforefailure.
(2)over-reinforced –the steel does not yield and
failure is due to crushing of concrete. There is no
warning sign and cause sudden, catastrophic
collapse.

34. Shear (clause 3.4.5,BS8110)
•Two principal shear failuremode:
(a)diagonal tension –inclined crack develops and
splits the beam into two pieces. Shear link should
be provide to prevent thisfailure.
(b)diagonal compression –crushing of concrete.
The shear stress is limited to 5 N/mm
2
or
0.8(f
cu)
0.5
.

35. Shear (clause 3.4.5,BS8110)
•The shear stress is determinedby:
•The shear resistance in the beam is attributed
to (1) concrete in the compression zone, (2)
aggregate interlock across the crack zoneand
(3) dowel action of tensionreinforcement.

36. Shear (clause 3.4.5,BS8110)
•The shear resistance can be determined using
calculating the percentage of longitudinal
tension reinforcement (100As/bd) and
effectivedepth

37. Shear (clause 3.4.5,BS8110)
•The values in the table above are obtained
based on the characteristic strength of 25
N/mm
2. For other values of cube strength up
to maximum of 40 N/mm
2, the design shear
stresses can be determined by multiplying the
values in the table by the factor(f
cu/25)
1/3.

38. Shear (clause 3.4.5,BS8110)

39. Shear (clause 3.4.5,BS8110)
•When the shear stress exceeded the0.5c,
shear reinforcement should beprovided.
(1)Vertical shearlink
(2)A combination of vertical and inclinedbars.

40. Shear (clause 3.4.5,BS8110)
•Sv ≤0.75d

41. Example 3.3 Design of shearreinforcement
(Chanakya Arya,2009)
•Designtheshearreinforcementforthebeam
usinghighyieldsteelfy=500N/mm
2forthe
followingloadcases:
1.qk =0
2.qk = 10kN/m
3.qk = 45kN/m

42. Example 3.3 Design of shearreinforcement
(Chanakya Arya,2009)

43. Example 3.3 Design of shear reinforcement (Chanakya Arya,2009)

44. Example 3.3 Design of shear reinforcement (Chanakya Arya,2009)

45. Example 3.3 Design of shear reinforcement (Chanakya Arya,2009)
Provide nominal shearlink
=0.3

46. •The links spacing Sv should not exceed 0.75d
(0.75*547 = 410mm).
•Use H8 at 300 mmcentres.
Example 3.3 Design of shear reinforcement (Chanakya Arya,2009)

47. Example 3.3 Design of shear reinforcement (Chanakya Arya, 2009)
Case 3 (qk = 45kN/m)

48. Example 3.3 Design of shear reinforcement (Chanakya Arya,2009)
Provide H8 at 150 mmcentres.
Nominal shear links can be used from mid-span to position v = 1.05 N/mm
2
, to produce an
economicaldesign
Provide H8 at 300 mm centres. For 2.172 m
either side fromcentres.

49. Reinforcementdetailing.
Example 3.3 Design of shear reinforcement (Chanakya Arya,2009)

50. Deflection
•For rectangularbeam,
1.The final deflection should not exceedspan/250
2.Deflection after construction of finishes and
partitions should not exceed span/500 or
20mm, whichever is the lesser, for spans up to
10m.
BS 8110 uses an approximate method basedon
permissible ratios of the span/effectivedepth.

51. Deflection (clause3.4.6.3)
•This basic span/effective depth ratio is used in
determining the depth of the reinforced
concretebeam.

52. Reinforcement details (clause 3.12,BS
8110)
•The BS 8110 spell out a few rules to follow
regarding:
1.Maximum and minimum reinforcementarea
2.Spacing ofreinforcement
3.Curtailment and anchorage ofreinforcement
4.Lapping ofreinforcement

53. Reinforcement areas (clause3.12.5.3
and 3.12.6.1, BS8110)
•Minimum area of reinforcement is provided to
control cracking ofconcrete.
•Too large an area of reinforcement will hinder
proper placing and compaction of concrete
aroundreinforcement.
•For rectangular beam with b (width) and h
(depth), the area of tensile reinforcement, As
shouldlie:
•0.24% bh ≤As ≤ 4%bh
•0.13% bh ≤As ≤ 4%bh
for fy = 250 N/mm
2
for fy = 500N/mm
2

54. Spacing of reinforcement(clause
3.12.11.1, BS8110)
•The minimum spacing between tensile
reinforcement is provided to achieve good
compaction. Maximum spacing is specified to
controlcracking.
•For singly reinforcement simply supported beam
the clear horizontal distance between tension bars
shouldfollow:
•h
agg + 5 mm or bar size≤ s
b≤ 280 mm f
y = 250
N/mm
2
•h
agg + 5 mm or bar size≤ s
b≤ 155 mm f
y =500
N/mm
2 (h
agg is the maximum aggregatesize)

55. Curtailment (clause 3.12.9, BS8110)
•The area tensile reinforcement is calculated
based on the maximum bending moment at mid-
span. The bending moment reduces as it
approaches to the supports. The area of tensile
reinforcement could be reduced (curtailed) to
achieve economicdesign.

56. Curtailment (clause 3.12.9, BS8110)
Simply
supported
beam
Continuous
beam
(Chanakya Arya,2009)

57. Anchorage (clause 3.12.9, BS8110)
•At the end support, to achieve properanchorage
the tensile bar must extend a length equal to one
of thefollowing:
1.12 times the bar size beyond the centre lineof
thesupport
2.12times the bar size plus d/2 from thefaceof
support
(Chanakya Arya,2009)

58. Anchorage (clause 3.12.9, BS8110)
•In case of space limitation, hooks
or bends in the reinforcementcan
be use inanchorage.
•If the bends started after the
centre of support, the anchorage
length is at least 4but notgreater
than12.
•Ifthehookstartedbefored/2from
thefaceofsupport,theanchorage
lengthisat8rbutnotgreaterthan
24.

59. Continuous L and Tbeam
•For continuous beam, various loading
arrangement need to be considered to obtain
maximum design moment and shearforce.

60. Continuous L and Tbeam
•The analysis to calculate the bending moment
and shear forces can be carried outby
1.using moment distributionmethod
2.Providedtheconditionsinclause3.4.3ofBS
8110aresatisfied,designcoefficientscanbe
used.

61. Clause 3.4.3 of BS 8110: Uniformly-loaded continuous beams
with approximately equal spans: momentsand
shears

62. L-and T-beam
•Beam and slabs are cast monolithically, that is,
they are structurallytied.
•At mid-span, it is more economical to design
the beam as an L or T section by including the
adjacent areas of the slab. The actual width of
slab that acts together with the beam is
normally termed the effectiveflange.

64. L-andT-beam
•At the internal supports, the bending moment
is reversed and it should be noted that the
tensile reinforcement will occur in the top half
of the beam and compression reinforcement
in the bottom half of thebeam.

65. Clause 3.4.1.5: Effective widthof
flangedbeam
Effective span –for continuous beam the effective span
should normally taken as the distance between the centres of
supports

66. L-and T-beam
•The depth of neutral axis in relation to the
depth of the flange will influence the design
process.
•The neutralaxis
•When theneutral axis lies withinthe
flange, the breadth of the beam at mid-
span(b) is equal to the effective flange
width. At the support of a continuous beam,
the breadth is taken as the actual width of
thebeam.