# 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

## Validation

Ag = D×bw = 16 × 10 = 160 in2

d = D - cover = 16 - 2.5 = 13.5 in

Bending Reinforcement

ϕ = 0.9

Minimum reinforcement of flexural members [Cl 10.5]

 $β1=0.85−0.05(f′c−4,0001,000)=0.85$ [Cl 10.2.7]

The ultimate moment:

$Mu=wul28=9.736(12)28=121.7⁢ ft⋅k$

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 = 0.75

Limit of concrete strength: $f′c=63.2<100$, hence OK. [Cl 11.1.2]

$ρw=Asbwd=0.018$

λ = 1

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:

ϕVc = 0.75×21.48 = 16.11 kip

The maximum shear capacity of the reinforcement is:

 [Cl 11.4.7.9]

The minimum shear reinforcement , Av/s, for any load combination is:

 [Cl 11.4.6.3 and R11.4.7]

Use 2-legged #4 stirrups (Av = 0.39 in2 per stirrup).

smax = d/2 = 13.5 /2 = 6.75 in

Use maximum spacing of 6.75 in: Avs/s = 0.39 / 6 = 0.058 in2/in

## Results

Table 1. Comparison of results
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

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\10 Concrete Design\US\ACI 318-08 Rectangular Singly Reinforced Beam.STD is typically installed with the program.

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
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


   =====================================================================
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 :
-------------------------------
(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**************************