Design of R.C.C Beam

F O R S H E A R A N D F L E X T U R E .
DESIGN OF R.C.C. BEAM
 BEAM
 TYPES OF BEAMS
 SINGLY REINFORCED BEAM
(FLEXURE AND SHEAR)
 DOUBLY REINFORCED BEAM
(FLEXURE AND SHEAR)
AAKANSHA 1216512101
ANKITHA 1216512103
ARUNDATHI 1216512104
ASHOK SAHOO 1216512105

Beam is a horizontal member of structure carrying transverse loads.
 Beam is rectangular in cross-section.
 Beams carry the floor slab or roof slab.
 Beams transfers all the loads including its self weight to the
columns or walls.
R.C.C. BEAM
RCC beam is subjected to bending moments and shear.
 Due to the vertical external load, bending compresses the top fibers
of the beam and elongates the bottom fibers.
 The strength of the RCC beam depends upon the composite action
of concrete and steel.
BEAM

WORKING STRESS METHOD
•The Stresses in an element is obtained from the working loads and compared
with permissible stresses.
•The method follows linear stress-strain behavior of both the materials.
•Modular ratio can be used to determine allowable stresses.
•Material capabilities are under estimated to large extent. Factor of safety are
used in working stress method.
•The member is considered as working stress.
•Ultimate load carrying capacity cannot be predicted accurately.
•The main drawback of this method is that it results in an uneconomical
section

LIMIT STATE METHOD
• The stresses are obtained from design loads and compared
with design strength.
• In this method, it follows linear strain relationship but not
linear stress relationship (one of the major difference between
the two methods of design).
• The ultimate stresses of materials itself are used as allowable
stresses.
• The material capabilities are not under estimated as much as
they are in working stress method. Partial safety factors are
used in limit state method.

LOAD ACTING ON A STRUCTURE:
DEAD LOAD:
 DEAD Load is self-weight of the various components in the building.
LIVE LOAD:
 LIVE Load is the external superimposed load on a structure.
 Uniformly distributed load.
 Uniformly varying load.
 Concentrated load.
 Arbitrary load.

TYPES OF BEAMS:
Simply Supported Beam.
 Fixed Beam.
 Cantilever Beam.
 Continuous Beam.
 Overhanging Beam.
 Cantilever, Simply supported beam

FIXED BEAM:
SIMPLY SUPPORTED BEAM:
It is a beam that is freely supported at two ends on walls or columns.
 In actual practice no beam rests freely on the supports
( columns or walls )
 In this beam both ends of the beam are rigidly fixed into the supports.
 Main reinforcement bars and stirrups are also provided.

CANTILEVER BEAM:
One end of the beam is fixed to wall or column and the other end is free.
 It has tension on top and compression on bottom.
CONTINIOUS BEAM:
 A continuous beam is a statically indeterminate multi
span beam on hinged support.
 The end spans may be cantilever, may be freely
supported or fixed supported. At least one of the supports
of a continuous beam must be able to develop a reaction
along the beam axis.

OVERHANGING BEAM:
 In overhanging beam its end extends beyond column or wall support.
 Overhanging of the beam is the unsupported portion of the beam, it may be
on side or both the sides.
TYPES OF RCC BEAMS:
 SINGLY REINFORCED BEAM:
•Singly reinforcement beam have steel provided only one side tension an
another side compression. tension takes steel load or tensile load and
compression takes concrete or compressive load.
 DOUBLY REINFORCED BEAM:
•Doubly reinforced sections contain reinforcement both at the tension and
at the compression face, usually at the support section only.

SINGLY REINFORCED BEAM
 Determine the moment of resistance for the section shown in figure.
(i) fck = 20 N/mm , fy = 415 N/mm
Solution:
(i) fck = 20 N/mm , fy = 415 N/mm
breadth (b) = 250 mm
effective depth (d) = 310 mm
effective cover = 40 mm
Force of compression = 0.36 fck b x
= 0.36 X 20 X 250x
= 1800x N
Area of tension steel At = 3 X 113 mm
Force of Tension = 0.87 fy At
= 0.87 X 415
X 3 X 113
= 122400 N
 Force of Tension = Force of
compression
 122400 = 1800x
 x = 68 mm
 xm = 0.48d
 = 0.48 X
310
 = 148.8 mm
 148.8 mm > 68 mm
 Therefore,
 Depth of neutral axis = 68 mm

SINGLY REINFORCED BEAM
Lever arm z = d – 0.42x
= 310 – 0.42 X 68
= 281 mm
As x < xm ( It is under reinforced )
Since this is an under reinforced section,
moment of resistance is governed by steel.
Moment of resistance w.r.t steel = tensile force X z
Mu = 0.87fy At z
= 0.87 X 415 X 3 X 113 X 281
Mu = 34.40kNm

DESIGN FOR SHEAR
• Question : Design a rectangular beam to resist a bending moment equal to 45 kNm using (i) M15
mix and mild steel
• Solution :
• The beam will be designed so that under the applied moment both materials reach their
maximum stresses.
• Assume ratio of overall depth to breadth of the beam equal to 2.
Breadth of the beam = b
Overall depth of beam = D
therefore , D/b = 2
For a balanced design,
Factored BM = moment of resistance with respect to concrete
= moment of resistance with respect to steel
= load factor X B.M
= 1.5 X 45
= 67.5 kNm

DESIGN FOR SHEAR(CONT.)
For balanced section,
Moment of resistance Mu = 0.36 fck b xm(d - 0.42 xm)
Grade for mild steel is Fe250
For Fe250 steel,
xm = 0.53d
Mu = 0.36 fck b (0.53 d) (1 – 0.42 X 0.53) d
= 2.22bd
Since D/b =2 or, d/b = 2 or, b=d/2
Mu = 1.11 d
Mu = 67.5 X 10 Nmm
d=394 mm and b= 200mm

• Adopt D = 450 mm
• b = 250 mm
• d = 415mm
 Area of tensile steel At =
 =
= 962 mm
= 9.62 cm
 Minimum area of steel Ao= 0.85

=
= 353 mm
353 mm < 962 mm
In beams the diameter of main reinforced bars is usually selected
between 12 mm and 25 mm.
Provide 2-20mm and 1-22mm bars giving total area
= 6.28 + 3.80
= 10.08 cm > 9.62 cm

DESIGN PROCEDURE FOR DOUBLY
REINFORCED BEAM
DESIGNING DOUBLY REINFORCED BEAM
FOR SHEAR STRESS
Step 1: Determining nominal shear stress
The nominal shear stress in beams of uniform depth shall be obtained by the
following equation.
Ʈv = Vu / bd
Where,
Vu = shear force due to design load
b = breadth of the member, which for flanged section shall be is taken
as the breadth of the web, bw, and
d = effective depth

FOR SHEAR STRESS
For solid slabs, the design shear strength
for concrete shall be Ʈck, where k has
values given below:
NOTE: This provision shall not apply to
flat slabs
Under no circumstances even with the
shear reinforcement, shall the nominal
shear stress in beams Ʈv exceed Ʈcmax given
in table 20 of IS 456: 2000
Overall
depth of
slab, mm
300 or
more
275 250 225 200 175 150
or
less
k 1.00 1.05 1.10 1.15 1.20 1.25 1.30
minimum shear reinforcement
When Ʈvis less than Ʈc given in table 19 of IS
456:2000, minimum shear reinforcement shall
be provided
design of shear reinforcement
When Ʈvexceeds Ʈv given in table 19, shear
reinforcement shall be provided in any of the
following forms:
•Vertical stirrups,
•Bent-up bars along with stirrups, &
•Inclined stirrups
Shear reinforcement shall be provide to carry a
shear equal to
Vus= Vu – Ʈc bd

STRENGTH OF SHEAR REINFORCEMENT
• The strength of shear reinforcement Vusshall be calculated as below:
• For vertical stirrups:
• Vus= 0.87fyAsvd / sv
• For inclined stirrups or a series of bars bent up at different cross sections:
• Vus= (0.87fyAsvd / sv)(sin α + cos α)
• For single bar or single group of parallel bars, all bent up at the cross-section:
• Vus = 0.87fyAsvsin α
• Where,
• Asv = sv = Ʈv =
• Ʈc = b = fy =
• α = d =

Design of R.C.C Beam

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