V. ACI 318-08 Rectangular Singly Reinforced Beam
Flexural and shear reinforcement design of a singly reinforced concrete beam per the ACI 318-2008 code.
Details
A 10' simply supported beam is subjected to an ultimate uniform load of 9.736 k/ft.
- f'c = 4,000 psi
- fy = 60,000 psi
- fyt = 60,000 psi
- cover = 2.5 in
- D = 16 in
- bw = 10 in
Calculations
Validation
Bending Reinforcement
ϕ = 0.9Minimum reinforcement of flexural members [Cl 10.5]
The ultimate moment:
The depth of the compression block is:
Hence, a < amax .
The area of the tensile steel reinforcement required is:
Use 2-#10 bars: As = 2.53 in2
Shear Reinforcement
ϕ = 0.75Limit of concrete strength: , hence OK. [Cl 11.1.2]
Shear and moment at a distance, d, from the support:
Per Cl 11.2.2.1 equation 11.5, the unfactored shear capacity of concrete is:
The maximum shear capacity of the reinforcement is:
The minimum shear reinforcement , Av/s, for any load combination is:
Use 2-legged #4 stirrups (Av = 0.39 in2 per stirrup).
Use maximum spacing of 6.75 in: Avs/s = 0.39 / 6 = 0.058 in2/in
Results
| Parameter | Hand Calculation | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Design moment, Mu (ft·k) | 121.7 | 121.7 | none | |
| Tension reinforcement required, As,re'd (in2) | 2.371 | 2.41 | 1.6% | OK |
| Design shear, Vu1 (kip) | 37.73 | 37.73 | none | |
| Shear reinforcement, Av/s (in2/in) | 0.058 | 0.058* | none | |
| Vc (kip) | 21.48 | 21.34 | negligible | |
| Vs (kip) | 28.83 | 28.97 | negligible |
*Shear reinforcement provided by STAAD: Avs/s = 0.39 / 6.7 = 0.058 in2/in
Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \Verification Models\10 Concrete Design\US\ACI 318-08 Rectangular Singly Reinforced Beam.STD is typically installed with the program.
STAAD
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 06-May-19
JOB CLIENT Bentley Systems Inc.
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 10 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 1.333 ZD 0.8333
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -9.736
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES
PRINT SUPPORT REACTION ALL
START CONCRETE DESIGN
CODE ACI 2008
UNIT INCHES KIP
TRACK 2 ALL
DESIGN BEAM ALL
END CONCRETE DESIGN
FINISH
Output
=====================================================================
BEAM NO. 1 DESIGN RESULTS - FLEXURE PER CODE ACI 318-08
LEN - 10.00FT. FY - 60000. FC - 4000. SIZE - 10.00 X 16.00 INCHES
LEVEL HEIGHT BAR INFO FROM TO ANCHOR
FT. IN. FT. IN. FT. IN. STA END
_____________________________________________________________________
1 0 + 2-3/4 2-NUM.10 0 + 0-0/0 10 + 0-0/0 YES YES
|----------------------------------------------------------------|
| CRITICAL POS MOMENT= 121.70 KIP-FT AT 5.00 FT, LOAD 1|
| REQD STEEL= 2.41 IN2, RHO=0.0180, RHOMX=0.0214 RHOMN=0.0033 |
| MAX/MIN/ACTUAL BAR SPACING= 10.00/ 2.54/ 4.73 INCH |
| REQD. DEVELOPMENT LENGTH = 48.53 INCH |
|----------------------------------------------------------------|
Cracked Moment of Inertia Iz at above location = 1816.05 inch^4
REQUIRED REINF. STEEL SUMMARY :
-------------------------------
SECTION REINF STEEL(+VE/-VE) MOMENTS(+VE/-VE) LOAD(+VE/-VE)
(FEET) (SQ. INCH) (KIP-FEET)
0.00 0.000/ 0.000 0.00/ 0.00 1/ 0
0.83 0.642/ 0.000 37.19/ 0.00 1/ 0
1.67 1.215/ 0.000 67.61/ 0.00 1/ 0
2.50 1.700/ 0.000 91.28/ 0.00 1/ 0
3.33 2.071/ 0.000 108.18/ 0.00 1/ 0
4.17 2.307/ 0.000 118.32/ 0.00 1/ 0
5.00 2.388/ 0.000 121.70/ 0.00 1/ 0
5.83 2.307/ 0.000 118.32/ 0.00 1/ 0
6.67 2.071/ 0.000 108.18/ 0.00 1/ 0
7.50 1.700/ 0.000 91.28/ 0.00 1/ 0
8.33 1.215/ 0.000 67.61/ 0.00 1/ 0
9.17 0.642/ 0.000 37.19/ 0.00 1/ 0
10.00 0.000/ 0.000 0.00/ 0.00 1/ 0
B E A M N O. 1 D E S I G N R E S U L T S - SHEAR
AT START SUPPORT - Vu= 37.73 KIP Vc= 21.34 KIP Vs= 28.97 KIP
Tu= 0.00 KIP-FT Tc= 1.95 KIP-FT Ts= 0.00 KIP-FT LOAD 1
NO STIRRUPS ARE REQUIRED FOR TORSION.
REINFORCEMENT IS REQUIRED FOR SHEAR.
PROVIDE NUM. 4 2-LEGGED STIRRUPS AT 6.7 IN. C/C FOR 47. IN.
STAAD SPACE -- PAGE NO. 6
AT END SUPPORT - Vu= 37.73 KIP Vc= 21.34 KIP Vs= 28.97 KIP
Tu= 0.00 KIP-FT Tc= 1.95 KIP-FT Ts= 0.00 KIP-FT LOAD 1
NO STIRRUPS ARE REQUIRED FOR TORSION.
REINFORCEMENT IS REQUIRED FOR SHEAR.
PROVIDE NUM. 4 2-LEGGED STIRRUPS AT 6.7 IN. C/C FOR 47. IN.
___ 1J____________________ 120.X 10.X 16_____________________ 2J____
| |
| |
| |
| 8#4 C/C 7 8#4 C/C 7 |
| 2#10H 2.63 0.TO 120. |
||=========================================================================||
| |
|___________________________________________________________________________|
_________ _________ _________ _________ _________ _________
| | | | | | | | | | | |
| | | | | | | | | | | |
| | | | | | | | | | | |
| | | | | | | | | | | |
| 2#10 | | 2#10 | | 2#10 | | 2#10 | | 2#10 | | 2#10 |
| OO | | OO | | OO | | OO | | OO | | OO |
| | | | | | | | | | | |
|_________| |_________| |_________| |_________| |_________| |_________|
********************END OF BEAM DESIGN**************************