# V. ACI 318-14 Tee Beam

Calculate the flexural capacity of a T-beam subjected to major axis moment, given Ast

## References

1. ACI 318-14: Sections 19.2.1, 20.2.2, 22.3, and 22.4; Tables 22.2.2.4.3, 22.4.2.1, 27.3.2.1
2. PCA Notes 2011: Tables 6.1, 7.1

## Details

A T-beam of length 5ft is subjected to a major axis moment has the following concrete and steel properties.
• Width of T flange, Bf = 30 in
• Depth of T, D = 26 in
• Thickness of flange, Tf = 4 in
• Thickness of web, Tw = 10 in
• Steel modulus of elasticity, Es = 29,000 ksi
• Ultimate strain, εu = 0.003
• Yield strength of reinforcing steel, fy = 60 ksi
• Compressive strength of concrete (normal weight concrete), fc = 4,000 psi
• Clear spacing for outermost bottom reinforcement to bottom face, Cc = 1.5 in
• Strength reduction factor, ϕ = 0.9
• Rebar diameter for #10 bar, Ød = 1.27 in

## Validation

$d ⁢ = D − C c − Ø d 2 = 23.865$
$d ′ ⁢ = C c + Ø d 2 = 2.135$
$R n = 6 , 400 ϕ × 0.85 × f c × B f × d 2 = 0.122$

From Table 7.1 of PCA (ref. 2):

$w = ( 0.1726 − 0.1648 ) ( 0.19 − 0.18 ) × ( R n − 0.1648 ) + 0.18 = 0.147$

$a = 1.18 × w × d = 4.138 > T f$, hence beam acts as a T

Compression strength of the flange:

$C f = 0.85 × f c × ( B f + T w ) × T f = 136$

Asf = Cf/fy = 2.267 in2

this is the required area to equilibrate Cf.

Flexural strength of the flange:

$M n w = 6 , 400 ϕ − M n f = 4.001 × 10 − 3 in⋅k$

To check whether this section is tension controlled, refer to PCA Table 7.1 (ref. 2):

$R n = M n w f c × T w × d 2 = 0.176$
$w = ( 0.1802 − 0.1726 ) ( 0.2 − 0.19 ) × ( R n − 0.1726 ) + 0.19 = 0.192$
$ρ = w n f c f y = 0.013 < 0.01806$

based on PCA Table 6.1 (ref. 2), thus the section is tension controlled.

Asw = ρ×Tw×d = 3.06 in2

Assume 6- #10 bars, divided between top and bottom: Ast, tot = 6 × 1.27 in2 = 7.62 in2

$a w = ( A s t , t o t − A s f ) f y 0.85 × f c × T w = 9.447 in$
$M n = ( A s t , t o t − A s f ) × f y ( d − a w 2 ) + A s f × f y × ( d − T f 2 ) = 9 , 258 in⋅k$

ϕMn = 8,332 in·k = 694.4 ft·k

## Results

Table 1. Comparison of results
Flexural capacity (ft·k) 694.4 698.938 <1% OK

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\10 Concrete Design\US\ACI 318-14 Tee Beam.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 23-Feb-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 4 0; 2 5 4 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 453600
POISSON 0.17
DENSITY 0.14999
ALPHA 5.5e-06
DAMP 0.05
TYPE CONCRETE
STRENGTH FCU 576
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 PRIS YD 2.16667 ZD 2.5 YB 1.83333 ZB 0.833333
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 FIXED
2 MZ 533.33333
PERFORM ANALYSIS
START CONCRETE DESIGN
CODE ACI
MAXMAIN 10 ALL
MINMAIN 9 ALL
MXMS 5 ALL
MIMS 4 ALL
TRACK 2 ALL
DESIGN BEAM ALL
END CONCRETE DESIGN
FINISH


                       STAAD.PRO CONCRETE DESIGN - (ACI-318-14)   v2.0
***********************************************
Units: KIP   , FEET   (Unless Noted Otherwise)
Member :      1
DESIGN SUMMARY
-----------------------------------------------------------------------------
| Status         :   Pass         Type    : Beam            Length:    5.000 |
| Critical Ratio :   0.763        Criteria: Flexure                          |
| Critical Clause:   9.5.2                                                   |
-----------------------------------------------------------------------------
CROSS SECTION
------------------------------------------------------------------------------
| Shape: Tee-Shape   | YD:    2.17 | ZD:    2.50 | ZB:    0.83 | YB:    1.83 |
------------------------------------------------------------------------------
-------------------------------------------------------------------------
| Concrete | Fc         576.000 |                     | Ec     0.519E+06 |
| Steel    | Fy(main)  8639.999 | Fy(trans)  8639.999 | Es     0.418E+07 |
| Cover    | Top          0.125 | Bottom        0.125 | Sides      0.125 |
-------------------------------------------------------------------------
CRITICAL STRENGTH RESULTS
-----------------------------------------------------------------------
| Category |    Demand     |  Min Capacity  |  Max Capacity  |  Ratio  |
-----------------------------------------------------------------------
| Axial    |          0.000|       -825.395 |        411.480 |   0.000 |
| Flexure  |        533.333|        -23.984 |        698.938 |   0.763 |
| Shear Y  |          0.000|        -17.485 |         17.485 |   0.000 |
| Shear Z  |          0.000|         -8.467 |          8.467 |   0.000 |
| Torsion  |          0.000|          0.000 |          0.000 |   0.000 |
-----------------------------------------------------------------------
LONGITUDINAL BAR DETAILS AT CROSS SECTIONS
---------------------------------------------------------------------------------
| Distance | Position |  Ast-reqd  |  Ast-prov  | No(s)bars| Size | No of Layers |
---------------------------------------------------------------------------------
|    0.000 |  Bottom  |      0.039 |      0.053 |     6    |  #10 |       2      |
|    1.250 |  Bottom  |      0.039 |      0.053 |     6    |  #10 |       2      |
|    2.500 |  Bottom  |      0.039 |      0.053 |     6    |  #10 |       2      |
|    3.750 |  Bottom  |      0.039 |      0.053 |     6    |  #10 |       2      |
|    5.000 |  Bottom  |      0.039 |      0.053 |     6    |  #10 |       2      |
---------------------------------------------------------------------------------
LONGITUDINAL BAR LAYOUT
---------------------------------------------------------------------------
|                |    Bars     |      Location     | Distance  |   Anchor  |
|       Position | Nums | Size | Start  |   End    | From Face | Start End |
---------------------------------------------------------------------------
|         Bottom |    3 | #10  |    0.00|     5.00 |     0.18  |  Yes  Yes |
|         Bottom |    3 | #10  |    0.00|     5.00 |     0.37  |  Yes  Yes |
---------------------------------------------------------------------------
STAAD SPACE                                              -- PAGE NO.    5
TRANSVERSE BAR LAYOUT
----------------------------------------------------------------------------
|                            |  Asv Density  |     Rebar Specification      |
| Zone | Dir.|  From |  To   | Reqd. | Prov. | Nums | Size | Spacing | Legs |
----------------------------------------------------------------------------
Minimum transverse reinforcement is not required as per Cl.9.6.3.1
------------------------ Member:     1 Design Ends ------------------------