Title: Lecture 17 DesignTBeams
1Lecture 17 Design(T-Beams)
2Lecture Goals
- Design of T-Beams
- Known section dimensions
3Design Procedure for section dimensions are
unknown (T- Reinforced Beams)
Assume that the material properties, loads, and
span length are all known. Estimate the
dimensions of self-weight using the following
rules of thumb a. The depth, h, may be taken as
approximate 8 to 10 of the span (1in deep per
foot of span) and estimate the width, b, as
about one-half of h. b. The weight of a
rectangular beam will be about 15 of the
superimposed loads (dead, live, etc.). Assume
b is about one-half of h. Immediate values of h
and b from these two procedures should be
selected. Calculate self-weight and Mu.
4Design Procedure for Singly Reinforced Flange
Beams when flange is in compressionKnown
dimensions
- Calculate controlling value for the design
moment, Mu. - Assume that resulting section will be tension
controlled, et 0.005 so that can take f 0.9.
5Design Procedure for Singly Reinforced Flange
Beams when flange is in compressionKnown
dimensions
- Calculate d, since h is known
For one layer of reinforcement. For two layers of
reinforcement.
6Design Procedure for Singly Reinforced Flange
Beams when flange is in compressionKnown
dimensions
- Determine the effective width of the flange, beff
- Check whether the required nominal moment
capacity can be provided with compression in the
flange alone. - and
7Design Procedure for Singly Reinforced Flange
Beams when flange is in compressionKnown
dimensions
- If Need
to utilize web below flanges. Go to step
4. - If Use
design procedure for rectangular beams
with b beff , (d -a/2) 0.95d - Note f 0.9 for flexure without axial load
(ACI 318-02 Sec. 9.3)
8Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known
- Find nominal moment capacity provided by
overhanging flanges alone (not including web
width) - For a T shaped section
-
- and
9Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known
- Find nominal moment capacity that must be
provided by the web.
10Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known
- Calculate depth of the compression block, by
solving the following equation for a.
11Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known
- Find required reinforcement area, As (reqd)
12Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known
- Select reinforcing bars so As (provided) As
(reqd). Confirm that the bars will fit within
the cross-section. It may be necessary to change
bar sizes to fit the steel in one layer or even
to go to two layers of steel.
10
13Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known
- Calculate the actual Mn for the section
dimensions and reinforcement selected. Check
strength f Mn Mu (keep over-design
within 10 )
11
14Singly Reinforced Beams where flange is in
compression Design Procedure when section
dimensions are known
- Check whether As provided is within allowable
limits. - As (provided) As (min)
12
15Minimum Area
Calculate the minimum amount of steel
16Additional Requirements for flanged sections when
flange is in tension
ACI 318 Section 10.6.6
Must distribute flexural tension steel over
effective flange width, be (tension)
17Additional Requirements for flanged sections when
flange is in tension
ACI 318 Section 10.6.6
When be (comp) gt l/10 some
longitudinal reinforcement shall be
provided in outer portions
of flange.
18Additional Requirements for flanged sections when
flange is in tension
ACI 318 Section 10.6.6
For l use centerline dimensions when adjacent
spans for - M _at_ support are not equal, use
average l to calculate be (tension) One scenario
when be (tension) lt be (compression)
19Design Procedure for SR Beam Unknown Dimension
Do a preliminary geometric size based on the
following
20Design Procedure for SR Beam Unknown Dimension
Assume
A reasonable value for k in terms rkbal and As r
Abal Effective flange width based on ACI
guidelines. Desired ration of b and d. b 0.5
0.65 d Depth of the flange based on design of the
slab.
1 2 3 4
21Example Problem
T-Beam with unknown dimensions, hf 6
in.(slab) fc 4500 psi fy 60 ksi. Three
spans continuous beam, simply supported on walls.
Spans are (25ft, 30 ft. and 25 ft.) The beam
spacing is 14 ft center to center Using
estimated values h 26 in. , b 16 in. Max
Mu 300 k-ft Max - Mu 435 k-ft
22Example Problem-Tension
Determine the kbal of the beam Determine the b1
term for the concrete
23Example Problem
Calculate a desired k 0.4 0.6
kbal Determine the Ru term for the concrete
24Example Problem
From the design of the Determine the Ru term
for the concrete
25Example Problem
The nominal moment is defined as The bd2
value will for design is
26Example Problem
Assume that the b 0.65d so that Determine
the value for b
27Example Problem
Determine h assuming a single layer of
reinforcement Check to see if the estimate
will work
Over-designed by 10.9 so it will work but we
would need to go back an recalculate the weight
28Example Problem
Calculate the actual value for k
Use the quadratic formula
29Example Problem
Calculate the actual value for k
30Example Problem
Calculate the actual value for k Calculate the
As required for the beam
31Example Problem
Calculate the actual value for As
32Example Problem
The flange is in tension so the reinforcement,
the beff in tension must be computed according to
ACI 10.6.6
33Example Problem
The size of the flange in compression is from
8.10.2 of the ACI code, the beff in compression
34Example Problem
The size of the flange in compression is from
8.10.2 of the ACI code, the beff in compression
Use 82 in. for the compression flange.
35Example Problem
The flange is in tension so the reinforcement,
the beff in tension must be computed according to
ACI 10.6.6
Use 33 in.