Deep beam

Deep beams are structural elements loaded as simple beams in which a
significant amount of the load is carried to the supports by a compression force
combining the load and the reaction.
As a result, the strain distribution is no longer considered linear, and the shear
deformations become significant when compared to pure flexure.
Floor slabs under horizontal load, short span beams carrying heavy loads, and
transfer girders are examples of deep beams.

Two-Dimensional Action:because of the dimension of deep beam
they behave as two-dimensional action rather than one-dimensional
action.
Plane Section Do Not Remain Plane:the assumption of plane
section remain plane cannot be used in the deep beam design.
 The strain distribution is not longer linear.
Shear Deformation: the shear deformation cannot be neglected as in
the ordinary beam.

The stress distribution is not linear even in the elastic stage.
At the ultimate limit state the shape of concrete compressive stress block is not
parabolic shape.
The Design is based on the ACI Ultimate Strength Design
Method and applies to those flexural members having a clear span to depth ratio of
less than 4.0.
The flexural reinforcement is designed taking into account the reduced lever arm
due to the non-linearity of the strains' distribution.
Deep beams play a very significant role in design of mega and as well as small
structures.
To avoid this problem of construction of some very long span halls etc the concept
of deep beams is very effective and durable.

• The elementary theory of bending for simple beams may not be applicable to deep beams even
under the linear elastic assumption.
• A deep beam is in fact a vertical plate subjected to loading in its own plane. The strain or stress
distribution across the depth is no longer a straight line, and the variation is mainly dependent on
the aspect ratio of the beam.
• The analysis of a deep beam should therefore be treated as a two dimensional plane stress
problem, and two-dimensional stress analysis methods should be used in order to obtain a realistic
stress distribution in deep beams even for a linear elastic solution.

• span/depth ratio of
simply supported beam is < 2,
continuous beam < 2.5,
it is classified as deep beam.
• Such structures are found in transfer girders and in shear wall
structures that resist lateral forces in buildings. It is also found in some
of the industrial buildings.

• The traditional principles of stress analysis are neither suitable nor
adequate to determine the strength of reinforced concrete deep beams.
• In deep beams, the bending stress distribution across any transverse
section deviates appreciably from straight line distribution assumed in the
elementary beam theory.

• The behaviour of a deep beam depends also on how they are loaded & special
considerations should be given to this aspect in design.
• Here cracking will occur at one-third to one-half of the ultimate load.
• In the single span beam supporting a concentrated load at mid span, the compressive
stresses act roughly parallel to the lines joining the load and the supports and the tensile
stresses act parallel to the bottom of the beam.
• The flexural stresses at the bottom is constant over much of the span.
• The figure shows the crack pattern and the truss analogy of the same.

Each of the three tension AB, CD and EF ties have cracked and at failure shaded
region would crush or the anchorage zones at E and F would fail.
simplified truss model

• A single span beam supporting a uniform load acting on the top has the stress
trajectories , crack pattern and simplified truss as shown.

• A single span beam supporting a uniform load acting on the
lower face of the beam has the stress trajectories , crack pattern
and simplified truss as shown.

• The compression trajectories form an arch with the loads
hanging from it. The crack pattern shows that the load is
transferred upward by reinforcement until it acts on the
compression arch, which then transfers the load down to the
supports.
• The force in the longitudinal tension ties will be constant along
the length of the deep beam. This is the reason that the steel
must be anchored at the joints over the reaction, failure of
which is a major cause of distress

 Parameters influencing deep beam behavior are:
 Width of support = C
 Overall depth of beam = D
 Effective span = L
 Width / Thickness of beam = t
 Type of loading, uniform = w

The Min. thickness of deep beams should be based on two
considerations:
1. It should be thick enough to prevent buckling with respect to its
span & height i.e.
where t = thickness of beam.
2. The thickness should be such that the concrete itself should be able
to carry a good amount of the shear force that acts in the beam
without the assistance of any steel.
50&25 
t
L
t
D

• Z = 0.6L or 0.6D
i.e. Z = 0.6L when L/D < 1
& Z = 0.6D when L/D > 1

• From those values,
Mu = As.fs.Z where fs = 0.87 fy
• The greater value of As is taken as tension steel.
  
   Lfy
Mu
Lfy
Mu
A
fyD
Mu
Dfy
Mu
Zf
Mu
A
s
s
s
.
9.1
6.087.0
or
9.1
6.087.0.



Design procedure :
tftavDVc
fckft
D
av
Co
Dtft
D
av
CVc
VsVcVu
Dut
Vu
Tv
.)35.0(72.0
becomesequationtheHence,
strength.tensilethe,5.0
Depth
spanShear
concretewt.normalfor0.72toequaleff.C
where..35.01c)
b)
TTvwhere
.
ShearNominalDeterminea)
1
1
max














• When designing for shear, it is assumed that concrete itself should
carry at least 65% of the ultimate shear.
• This is ensured by choosing a suitable thk. of beam by the following
formula :
ftavD
Vu
t
)35.0(72.0
65.0



• Shear capacities of tension steel & nominal web steel should also be
taken into account in resisting the shear. Their shear capacity is
calculated as :
where,
C2 = 225 N/mm2 for Fe415
As = Area of tension steel provided.

n
D
y
AsCVs
1
2
2 Sin
1
. 

α = Angle between the bar considered & the critical diagonal crack.
y1= Depth from the top of the beam to the point where bar intersects the
critical diagonal crack line.
n = Number of bars including tension steel cut by the assumed crack line
D = Total depth of beam

• Vertical steel Av and Horizontal steel Ah
• Horizontal steel bars acts as shear reinforcement and also overcome the
effects of shrinkage & temperature.
• The amounts specified in IS:456-2000 are :
a) Vertical steel shall be 0.12% for Fe415, the bar diameter shall not be
more than 14mm and spacing not more than 3x thk. of beam or 450mm.

b) Horizontal steel shall be 0.20% for Fe415, the bar diameter shall not
be more than 16mm & spacing not more than 3x thk. of beam or
450mm.
c) Necessary side reinforcement should also be provided.

Detailing of tension steel:
ü In deep beams, the tension steel is placed in a zone of depth equal to
(0.25D-0.05L) adjacent to the face of beam.
ü No curtailment of the bars. It should be bent upwards at the ends to
obtain adequate anchorage & embedment .

1. Determine whether the given beam is deep or not.
2. Check its thickness.
3. Design for flexure.
4. Design for minimum web steel & its distribution in the beam.
5. Design for shear.
6. Check for bearing pressure at support & point loading for
local failures.
7. Detailing (BRITISH PRACTICE)

Thank you
Mr. VIKAS MEHTA
School of Mechanical and civil engineering
Shoolini University
Village Bajhol, Solan (H.P)
vikasmehta@shooliniuniversity.com
+91 9459268898

Deep beam

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Deep beam