V. ACI 318-14 Rectangular Beam without Torsion
Design of a doubly reinforced rectangular beam.
Details
Determine the required area of tension and compression reinforcement.
The beam cross-section is limited to size 14in X 23 in. The factored moment Mu= 516 ft-kips.
f'c= 4000psi, fy=60,000 psi.
Validation
dcover = 2.5 in
Check if Compression Reinforcement is Required
Use Ζ = 0.9.
Refer to table 6-1 of PCA Notes (ref. 2).
b = 14 in
d = 20.5 in
Mn = Mu/Ζ = 573.33 ft-kip
Rn = Mn / (b*d2) = 1.169(10)3 psi
Rnt = 911 psi
Rn > Rnt
Hence, both compression and tension reinforcement is required.
Max. Moment with Compression Reinforcement
Mnt
This condition corresponds to tension controlled limit (Ζ = 0.9).
Depth of neutral axis, c = 0.375dt = 0.375d = 7.687 in
β1 = 0.85 (from table 6.1 (ref. 2)
a = β1*c = 6.534 in
Compressive force, C = 0.85·fc·a·b = 311.036 kips
Tension force, T = C = 311.036 kips
Nominal moment strength resisted by the concrete section, without compression reinforcement, Mnt = T(d - a/2) = 446.669 ft-kips
Nominal moment strength resisted by the concrete section, with compression reinforcement, Mnc = Mn - Mnt = 126.664 ft-kips
Area of Tension Steel
Area of tension steel required, As,nt , to develop Mnt
As,nt = T / fy = 5.184 in2
Additional Area of Tension Steel
Area of tension steel required, As,additional , required to counteract additional moment due to T-C couple.
As,additional = (Mn - Mnt) / [ fy· (d - dcover)] = 1.407 in2
Total tension steel required:
As = As + As,nt = 6.591 in2
Comparison
| Parameter | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Area Required (compression) (in2) | 1.441 | 1.61 | 11.0 | The required steel calculation assumes a single layer of bottom bars and the effective depth = 0.375×dt based on the single bar layer. The reference (ref. 2) calculations only considers a strength design and does not check for the minimum spacing requirements. STAAD.Pro however considers two layers of bars in the design to account for the minimum criteria and hence uses a neutral axis position based on the two bar layers. Thus the minor difference in the steel areas calculated. |
| Area Required (tension) (in2) | 6.591 | 6.355 | 3.6% |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\10 Concrete Design\US\ACI 318-14 Rectangular Beam Without Torsion.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
***********************************************************************
* This example is a replica of example no 6.2 of PCA Notes 318-11.
***********************************************************************
ENGINEER DATE 29-Aug-18
JOB NAME PCA Example 6.2
JOB CLIENT Bentley Systems Inc.
ENGINEER NAME TK
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 8 0 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 1.91667 ZD 1.16667
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
JOINT LOAD
2 MZ 464.417
PERFORM ANALYSIS
PRINT SUPPORT REACTION ALL
START CONCRETE DESIGN
CODE ACI
UNIT INCHES KIP
MAXMAIN 8 ALL
MINMAIN 8 ALL
*MIMB 6 ALL
*MXMB 6 ALL
CLT 2 ALL
CLB 2 ALL
TRACK 2 ALL
DESIGN BEAM ALL
END CONCRETE DESIGN
FINISH
STAAD Output
STAAD.PRO CONCRETE DESIGN - (ACI-318-14) v2.0 *********************************************** Units: KIP , INCHES (Unless Noted Otherwise) Member : 1 DESIGN SUMMARY ----------------------------------------------------------------------------- | Status : Pass Type : Beam Length: 96.000 | | Critical Ratio : 0.910 Criteria: Flexure | | Critical Clause: 9.5.2 | ----------------------------------------------------------------------------- CROSS SECTION ------------------------------------------------------- | Shape: Rectangular | Width: 14.00 | Depth: 23.00 | ------------------------------------------------------- DESIGN INPUTS ------------------------------------------------------------------------- | Concrete | Fc 4.000 | | Ec 0.360E+04 | | Steel | Fy(main) 60.000 | Fy(trans) 60.000 | Es 0.290E+05 | | Cover | Top 2.000 | Bottom 2.000 | Sides 1.500 | ------------------------------------------------------------------------- CRITICAL STRENGTH RESULTS ----------------------------------------------------------------------- | Category | Demand | Min Capacity | Max Capacity | Ratio | ----------------------------------------------------------------------- | Axial | 0.000| -871.565 | 554.580 | 0.000 | | Flexure | 5573.004| -2586.136 | 6122.188 | 0.910 | | Shear Y | 0.000| -24.729 | 24.729 | 0.000 | | Shear Z | 0.000| -26.729 | 26.729 | 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 | Top | 1.610 | 2.370 | 3 | # 8 | 1 | | | Bottom | 6.355 | 7.900 | 10 | # 8 | 2 | | 24.000 | Top | 1.610 | 2.370 | 3 | # 8 | 1 | | | Bottom | 6.355 | 7.900 | 10 | # 8 | 2 | | 48.000 | Top | 1.610 | 2.370 | 3 | # 8 | 1 | | | Bottom | 6.355 | 7.900 | 10 | # 8 | 2 | | 72.000 | Top | 1.610 | 2.370 | 3 | # 8 | 1 | | | Bottom | 6.355 | 7.900 | 10 | # 8 | 2 | | 96.000 | Top | 1.610 | 2.370 | 3 | # 8 | 1 | | | Bottom | 6.355 | 7.900 | 10 | # 8 | 2 | --------------------------------------------------------------------------------- STAAD SPACE -- PAGE NO. 6 LONGITUDINAL BAR LAYOUT --------------------------------------------------------------------------- | | Bars | Location | Distance | Anchor | | Position | Nums | Size | Start | End | From Face | Start End | --------------------------------------------------------------------------- | Top | 3 | # 8 | 0.00| 96.00 | 2.50 | Yes Yes | | Bottom | 5 | # 8 | 0.00| 96.00 | 2.50 | Yes Yes | | Bottom | 5 | # 8 | 0.00| 96.00 | 4.50 | Yes Yes | --------------------------------------------------------------------------- TRANSVERSE BAR LAYOUT ------------------------------------------------------------------------------------ | | Asv | Rebar Specification | | Zone | Dir.| From | To | Reqd. | Prov. | Nums | Size | Spacing | Legs | ------------------------------------------------------------------------------------ | 1 | Y | 0.00 | 96.00 | 0.0286 | 0.0292 | 8 | # 4 | 13.71 | 2 | | 1 | Z | 0.00 | 96.00 | 0.0286 | 0.0292 | 8 | # 4 | 13.71 | 2 | ------------------------------------------------------------------------------------ ------------------------ Member: 1 Design Ends ------------------------