Design of reinforced concrete beam

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

Introduction
• Reinforced concrete is a composite material,
consisting of steel reinforcing bars embedded
in concrete.
• Concrete has high compressive strength but
low tensile strength.
• Steel bars can resist high tensile stresses but
will buckle when subjected to comparatively
low compressive stresses.

Introduction
• Steel bars are used in the zones within a
concrete member which will be subjected to
tensile stresses.
• Reinforced concrete is an economical
structural material which is both strong in
compression and in tension.
• Concrete provides corrosion protection and
fire resistance to the steel bars.

Basic of design
• Two limit states design for reinforced concrete
in accordance to BS 8110.
1. Ultimate limit state – considers the behaviour
of the element at failure due to bending,
shear and compression or tension.
2. The serviceability limit state considers the
behaviour of the member at working loads
and is concerned with deflection and
cracking.

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

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

Characteristic compressive strength
(fcu) of concrete
Chanakya Arya, 2009. Design of structural
elements 3rd edition, Spon Press.
Cylinder strength
Cube strength
• Concrete strength classes in the range of C20/25
and C50/60 can be designed using BS 8110.

Stress-strain curve for concrete
Stress strain curve for
concrete cylinder
(Chanakya Arya, 2009. Design of structural elements 3rd edition,
SponPress.)
Idealized stress strain curve for
concrete in the BS8110

Material properties of steel
• Idealized stress-strain curve for steel.
1. An elastic region,
2. Perfectly plastic region (strain hardening of steel is
ignored)
BS 8110, 1997

Durability (clause 3.1.5, BS 8110)
• Durability of concrete structures is achieved
by:
1. The minimum strength class of concrete
2. The minimum cover to reinforcement
3. The minimum cement content
4. The maximum water/cement ratio
5. The cement type or combination
6. The maximum allowable surface crack width

Fire protection (clause 3.3.6, BS8110)
• Fire protection of reinforced concrete
members is largely by specifying limits for:
1. Nominal thickness of cover to the
reinforcement,
2. Minimum dimensions of members.

Concrete cover for fire resistance
BS 8110, 1997

Minimum dimension for reinforced
concrete members for fire resistance
BS 8110, 1997

Beams (clause 3.4, BS8110)
• Beams in reinforced concrete structures can
be defined according to:
1. Cross-section
2. Position of reinforcement
3. Support conditions

Beam design
• 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
and deflection.

Types of beam by cross section
Rectangular section 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 of beam.
•Under certain conditions, L- and T-beams are more
economical than rectangular beams.

Types of beam by reinforcement
position
Singly reinforced Doubly reinforced
• Singly reinforced – reinforcement to resist tensile stress.
• Doubly reinforced – reinforcement to resist both tensile
and compressive stress.
• Compressive reinforcement increases the moment
capacity of the beam and can be used to reducethe
depth of beams.

Notation for beam (clause 3.4.4.3, BS 8110)
b
hd
d’
AS
A’S

Design for bending
M ≤ Mu
Maximum moment on beam ≤ moment capacity of
the section
The moment capacity of the beam is affected by:
1. The effective depth, d
2. Amount of reinforcement,
3. Strength of steel bars
4. Strength of concrete

Moment capacity of singly reinforced
beam
Fcc
Fst
z
Force equilibrium
Fst =Fcc
Fcc = stress xarea
=
Moment capacity of the section

Singly reinforced beam
• If
Then the singly reinforced section is sufficient to
resist moment.
Otherwise, the designer have to increase the
section size or design a doubly reinforced
section

Doubly reinforced beam
• If
The concrete will have insufficient strength in
compression. Steel reinforcement can be
provided in the compression zone to increase
compressive force.
Beams which contain tension and compression
reinforcement are termed doubly reinforced.

Doubly reinforced beam
M = Fsc (d-d’) + Fccz

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 the area
of reinforcement required.

Compression reinforcement is not required

Provide 4H20, (As = 1260 mm2)

Cross section area for steel bars (mm2)

Example 3.7 Doubly reinforced beam
• 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 bending reinforcement.

Example 3.7 Doubly reinforced beam (Chanakya
Arya, 2009)

Example 3.7 Doubly reinforced beam (Chanakya
Arya, 2009)
Compression reinforcement is required

Failure mode of beam in beam
• The failure mode of beam in bending depends on
the amount of reinforcement.
(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 before failure.
(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.

Shear (clause 3.4.5, BS8110)
• Two principal shear failure mode:
(a)diagonal tension – inclined crack develops and
splits the beam into two pieces. Shear link should
be provide to prevent this failure.
(b)diagonal compression – crushing of concrete.
The shear stress is limited to 5 N/mm2 or
0.8(fcu)0.5.

• The shear stress is determined by:
• The shear resistance in the beam is attributed
to (1) concrete in the compression zone, (2)
aggregate interlock across the crack zone and
(3) dowel action of tension reinforcement.

• The shear resistance can be determined using
calculating the percentage of longitudinal
tension reinforcement (100As/bd) and
effective depth

• The values in the table above are obtained
based on the characteristic strength of 25
N/mm2. For other values of cube strength up
to maximum of 40 N/mm2, the design shear
stresses can be determined by multiplying the
values in the table by the factor (fcu/25)1/3.

• When the shear stress exceeded the 0.5c,
shear reinforcement should be provided.
(1) Vertical shear link
(2) A combination of vertical and inclined bars.

• Sv ≤ 0.75d

Example 3.3 Design of shear reinforcement
• Design the shear reinforcement for the beam
using high yield steel fy = 500 N/mm2 for the
following load cases:
1. qk = 0
2. qk = 10 kN/m
3. qk = 45 kN/m

Example 3.3 Design of shear reinforcement

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

Provide nominal shear link
= 0.3

• The links spacing Sv should not exceed 0.75d
(0.75*547 = 410 mm).
• Use H8 at 300 mm centres.

Case 3 (qk = 45 kN/m)

Provide H8 at 150 mm centres.
Nominal shear links can be used from mid-span to position v = 1.05 N/mm2, to produce an
economical design
Provide H8 at 300 mm centres. For 2.172 m
either side from centres.

Reinforcement detailing.

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

Deflection (clause 3.4.6.3)
• This basic span/effective depth ratio is used in
determining the depth of the reinforced
concrete beam.

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

Reinforcement areas (clause 3.12.5.3
and 3.12.6.1, BS 8110)
• Minimum area of reinforcement is provided to
control cracking of concrete.
• Too large an area of reinforcement will hinder
proper placing and compaction of concrete
around reinforcement.
• For rectangular beam with b (width) and h
(depth), the area of tensile reinforcement, As
should lie:
• 0.24% bh ≤As ≤ 4% bh
• 0.13% bh ≤As ≤ 4% bh
for fy = 250 N/mm2
for fy = 500 N/mm2

Spacing of reinforcement (clause
3.12.11.1, BS 8110)
• The minimum spacing between tensile
reinforcement is provided to achieve good
compaction. Maximum spacing is specified to
control cracking.
• For singly reinforcement simply supported beam
the clear horizontal distance between tension bars
should follow:
• hagg + 5 mm or bar size≤ sb≤ 280 mm fy = 250
N/mm2
• hagg + 5 mm or bar size≤ sb≤ 155 mm fy = 500
N/mm2 (hagg is the maximum aggregate size)

Curtailment (clause 3.12.9, BS 8110)
• 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 economic design.

Curtailment (clause 3.12.9, BS 8110)
Simply
supported
beam
Continuous
beam

Anchorage (clause 3.12.9, BS 8110)
• At the end support, to achieve proper anchorage
the tensile bar must extend a length equal to one
of the following:
1. 12 times the bar size beyond the centre line of
the support
2. 12 times the bar size plus d/2 from the face of
support

Anchorage (clause 3.12.9, BS 8110)
• In case of space limitation, hooks
or bends in the reinforcementcan
be use in anchorage.
• If the bends started after the
centre of support, the anchorage
length is at least 4 but not greater
than 12.
• If the hook started before d/2 from
the face of support, the anchorage
length is at 8r but not greater than
24.

Continuous L and T beam
• For continuous beam, various loading
arrangement need to be considered to obtain
maximum design moment and shear force.

Continuous L and T beam
• The analysis to calculate the bending moment
and shear forces can be carried out by
1. using moment distribution method
2. Provided the conditions in clause 3.4.3 of BS
8110 are satisfied, design coefficients can be
used.

Clause 3.4.3 of BS 8110: Uniformly-loaded continuous beams
with approximately equal spans: moments and
shears

L- and T- beam
• Beam and slabs are cast monolithically, that is,
they are structurally tied.
• 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 effective flange.

L- and T-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 the beam.

Clause 3.4.1.5: Effective width of
flanged beam
Effective span – for continuous beam the effective span
should normally taken as the distance between the centres of
supports

L- and T- beam
• The depth of neutral axis in relation to the
depth of the flange will influence the design
process.
• The neutral axis
• When the neutral axis lies within the
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
the beam.

Design of reinforced concrete beam

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