V. ACI 318-14 Tee Beam
Calculate the flexural capacity of a T-beam subjected to major axis moment, given Ast
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
From Table 7.1 of PCA (ref. 2):
, hence beam acts as a T
Compression strength of the flange:
Asf = Cf/fy = 2.267 in2
this is the required area to equilibrate Cf.
Flexural strength of the flange:
To check whether this section is tension controlled, refer to PCA Table 7.1 (ref. 2):
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
ϕMn = 8,332 in·k = 694.4 ft·k
STAAD Input
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
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
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 Output
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 | ------------------------------------------------------------------------------ DESIGN INPUTS ------------------------------------------------------------------------- | 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 ------------------------