T-Beams - Limit State Method - Building Construction

Analyze T-beams using the Limit State Method, emphasizing flexural strength, reinforcement detailing, load distribution, and structural efficiency.

1. T BEAM
DONE BY: GROUP 3
ROLL NO.93,94,102,109,119

2. INTRODUCTION
●A T-beam (or tee beam
[1]
), used in
construction, is a load-bearingstructureof
reinforced concrete, woodor metal, with a T-
shaped cross section.
●The top of the T-shaped cross section serves
as a flangeor compression memberin
resisting compressivestresses.
●The web (vertical section) of the beambelow
the compression flange serves to resist shear
stressand to provide greater separation for
the coupled forces of bending

3. ADVANTAGES OF T BEAM
●T-beam casting with slab as we know so Its flange takes
compressive stress and that mean It will resist more sagging
moment of beam.
●Depth of beam is reduced as compared to ordinary beam so better
headroom advantage.
●Over longer span T-beam is used rather than ordinary beam for
reducing the deflection of beam

4. DISADVANTAGES OF T BEAMS
●There is a considerable increase in the shear stress at the junction of
the flange and the web of the beam due to the change in cross section.
●Since the beam slab is monolithic ,it becomes ,it becomes very weak in
resisting lateral shear forces. Therefore in earthquake prone zones
using t beams for high rise buildings is reinforced with mechanical
stiffeners in the junction.

5. Effective Flange Width
●The effective flange width (b
e) of a
T-beam needs to be determined in
order to begin the design process.
In Figure-1, the flange of the
isolated T-beam is a little bit wider
than the T-beam stem, and the
entire flange is effective in resisting
compression.
●However, in Figure-2, the
flange width is large; hence,
parts of the flanges situated at
a distance from the stem do
not take their full share in
resisting compression, and
the stresses keep varying.
•The variation of stresses
leads to tedious calculations;
that is why a uniform stress
distribution is considered
over a smaller width of the
effective flange, see
Figure-3.
Figure-1: Effective
Flange Width of an
Isolated T-beam
Figure-2: Effective Flange
Width of an Interior T-beam
Figure-3: Theoretical Stress Distribution and
Simplified or Rectangular Stress Distribution
Over the Width of a Flange of T-beam

6. According to ACI 318-19, the effective flange width of a T-
beam can be found as follows:
1.Isolated Beams
For isolated beams, in which the flange is only used to provide an additional
compression area, the flange should have a thickness greater than or equal to
1/2b
w,and an effective width less than or equal to 4b
w.
2. Internal T-beams
According to 318-19, the effective flange width of an internal T-beam should not
exceed the smallest of:
1-One-fourth the clear span length of the beam, L/4.
2-Width of web plus 16 times slab thickness, b
w+16h
f.
3-Center-to-centerspacing of beams
3. Edge Beam (L-Shape)
According to 318-19, the effective flange width of an edge beam should not
exceed the smallest of:
1-Effective flange width (b
e) equal to or smaller than(b
w+(Clear span/4))
2-Effective flange width (b
e) equal to or smaller than(b
w+(6h
f)
3-Effective flange width (b
e) equal to or smaller than(b
w+halfclear distance to
the next clear web beam)

7. LIMIT STATE METHOD
●Thisis the most rational method which takes into account the ultimate
strength of the structure and also the serviceability requirements.
●It is a judicious combination of working stress and ultimate load methods of
design.
●The acceptable limits of safety and serviceability requirements before failure
occurs are called a limit state.
●This method is based on the concept of safety at ultimate loads (ultimate load
method) and serviceability at working loads (working stress method).
●The two important limit states to be considered in design are
(i) Limit state of collapse.
(ii) Limit state of serviceability

8. Types of limit states:
Limit State of Collapse:-This limit state
corresponds to the strength of the structure
and categorized into following types:
(a)Limit state of collapse: Flexure.
(b) Limit state of collapse: Shear and bond.
(c) Limit State of collapse: Torsion.
(d) Limit state of collapse: Compression.
Limit State of Serviceability: This limit state corresponds
to the serviceability requirements i.e., deformation,
cracking etc. It is categorized into following types:
(a)Limit state of deflection.
(b) Limit state of cracking
(c) Limit state of vibration.
(d) Limit state of corrosion.

9. IS Code for LSM -IS 456:2000
●This method is based upon the probabilities variation in the loads and
material properties.
●Limit state method takes into account the uncertainties associated with loads
and material properties, thus uses partial factors of safety to obtain design
loads and design stresses.
●The limit state method is based on predictions unlike working stress method
which is deterministic in nature, assumes that the loads, factors of safety and
material stresses are known accurately.
●In the limit state method, the partial safety factors are derived using
probability and statistics and are different for different load combinations,
hence giving a more rational and scientific design procedure.

10. Assumptions of the Limit state method:
1.Plane section normal to the axis remains plane after bending
2. The max. Strain in concrete at the outermost compression fiberis taken as
0.0035 in bending.
3. The compressive strength of the concrete in the structure shall be assumed to
be 0.67times the characteristic strength & partial safety factor of material may be
1.50.
4. The tensile strength of concrete is ignored.
5. The stresses in the reinforcement are divided depending on the stress strain
curve for the types of steel used.
6. The max. Strain in the tension reinforcement at the time of failure shall not be
less than
(fy/1.15 Es)+0.002

11. Design Procedure
1.Calculate applied moment (M
u
) using beam span and
imposed loads.
2. Determine Effective Flange Width (b
e)
3. Choose the web dimensions (b
w) and (h) based on
either negative bending requirements at the supports,
or shear requirements.
4. Assume, a=h
f, then calculate (As) using the following
expression:
5. Check the assumed value of (a):In Equation 2, plug
the value of (b
e
) found in Step 2.
If a< hf, design the beam as a rectangular section and
follow the design procedure of the rectangular beam.
If a> hf, design the beam a T-section and go to
Step 6
6. Compute the reinforcement area required to balance
the moment of the flange use Equation 3, and then
flange moment employ Equation 4
7. Calculate moment of the web:
8. Assume a rectangular stress block depth (such as a= 100
mm), then estimate the amount of reinforcement area (A
sw
)
required to balance the web moment:
The value of (d) should be computed using the following
formula:
d= beam height-concrete cover-stirrup diameter-
0.5*longitudinal steel diameter Equation 7
Then check assumed rectangular stress block depth (a) using
(A
sw
):
Use the new (a) and plug it into Equation 6, then compute
new (A
sw
). Repeat this process till correct (A
sw
) is reached.
Commonly three trials are enough.
9. Compute total As which is equal to (A
sf
+A
sw
), then
determine the number of reinforcement:
No. of Bars= As/ area of single bar Equation 9
10. sketch the final design on which all necessary data are
represented.

12. SHEAR REINFORCEMENT
IN BEAMS

13. TYPES OF SHEAR REINFORCEMENT
The following three types of shear reinforcement are used :
●Vertical stirrups.
●Bent up bars along with stirrups.
●Inclined stirrups.

14. Vertical Stirrups
●These are the steel bars vertically placed around the tensile reinforcement at
suitable spacing along the length of the beam.
●Their diameter varies from 6 mm to 16 mm.
●The free ends of the stirrups are anchored in the compression zone of the beam to
the anchor bars (hanger bar) or the compressive reinforcement.
●Depending upon the magnitude of the shear force to be resisted the vertical stirrups
may be one legged, two legged, four legged
●It is desirable to use closely spaced stirrups for better prevention of the diagonal
cracks.
●The spacing of stirrups near the supports is less as compared to spacing near the
mid-span since shear force is maximum at the supports.

16. Bent up Bars along with Vertical Stirrups
●Some of the longitudinal bars in a beam can be bent up near the supports where they are
not required to resist bending moment (Bending Moment is very less near the supports).
●These bent up bars resist diagonal tension. Equal number of bars are to be bent on both
sides to maintain symmetry.
●The bars can be bent up at more than one point uniformly along the length of the beam.
These bars are usually bent at 45 degrees.
●This system is used for heavier shear forces.
●The total shear resistance of the beam is calculated by adding the contribution of bent up
bars and vertical stirrups.
●The contribution of bent up bars is not greater than half of the total shear reinforcement.

18. Inclined Stirrups
●Inclined stirrups are also provided generally at 45º for resisting diagonal tension
●They are provided throughout the length of the beam.

19. CRANKED BAR
●It is a type of bar that can resist both positive and negative moments.
●It is used more particularly to resist negative bending moment.
●It in the most of the cases bent bar.
●It is used to avoid cutting of the reinforcement bar at different locations.

21. CUTTING BAR
●This is a method of cutting the long steel bars in the beam where it is not required.
●Cutting bar is used to make the structure economical and safe.
●Through this method we are usually trimming off the steel bar at positions where
load bearing is not needed.

22. Limit state method
A limit state belongs to a state of prospective failure apart from which the structure stops
implementing its proposed function suitably, by way of either safety or serviceability;
There are 2 types of limit states:
1. Ultimate limit states / Limit state of collapse, which treat strength, overturning, sliding, buckling,
fatigue, fracture, etc
2. Serviceability limit states, which treat trouble to occupancy and/or malfunction because of extreme
deflection, crack-width, vibration, leakage, etc.
LSM provides a wide-ranging and logical solution to a design issue by taking into consideration
numerous safety factor format which intends to offer sufficient safety at ultimate loads and sufficient
serviceability at working/service loads by taking into account all possible 'limit states'.