V. ACI 318-14 Rectangular Beam without Torsion
Design of a doubly reinforced rectangular beam.
Details
To determine the Required Area of Tension and Compression Reinforcement for given Concrete and Steel Properties with Given Factored Moment.
Design of Rectangular Beam with Compression Reinforcement-Doubly Reinforced
A beam cross-section is limited to size 14in X 23 in . Determine the required area of reinforcement for a factored moment Mu= 516 ft-kips. fc= 4000psi, fy=60,000 psi.,
Design Properties, available:
Validation
dcover = 2.5 in
Step 1: Check if compression reinforcement is required, using Ζ = 0.9.
See 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.
Step 2: Determine maximum 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
Step 3: Determine area of tension steel
Area of tension steel required, As,nt , to develop Mnt
As,nt = T / fy = 5.184 in2
Step 4: Determine additional area of tension steel required
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 | STAAD.Pro | Reference | Difference | Comments |
|---|---|---|---|---|
| Area Required (compression) (in2) | 1.441 | 1.61 | 11.0 | See note (*) below. |
| Area Required (tension) (in2) | 6.591 | 6.355 | 3.6% | See note (*) below. |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\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| -21.019 | 21.019 | 0.000 | | Shear Z | 0.000| -22.720 | 22.720 | 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 ------------------------