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V. ACI 318-11 Rectangular Singly Reinforced Beam

Design of a singly reinforced concrete beam per the ACI 318-2011 code.

References

  1. ACI 318-11
  2. PCA Notes 2011: Example 7.1

Details

Determine the Required Area of Tension Reinforcement for given Concrete and Steel Properties with Given Factored Moment.

Select a rectangular beam size and required reinforcement to carry service load moments MDL = 56 ft-kips and MLL= 35 ft-kips. Select reinforcement to control flexural cracking.

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
  • cover = 2 in

Validation

This is a complete design procedure for rectangular sections with tension reinforcement only, a minimum beam depth will be computed using the maximum reinforcement permitted for tension-controlled flexural members, ρt..

dcover = dist. from bottom of beam up to center of bottom bar = Cc + 1/2(bar diameter) = 2.5 in = 63.5 mm

Determine the maximum tension-controlled reinforcement ratio fro material strengths from Table 6-1 of PCA Notes on ACI 318-11.

ρt. = 0.01806

Compute bd2 required:

Mu = 1.2·MDL + 1.6·MLL = 123 ft·kips

R n = ρ t f y ( 1 0.5 ρ t f y 0.85 f' c ) = 910.9   psi
b d 2 r e q d = M u ϕ R n = 1 , 803 in 3

Size members so that bd2(prov) ≥ bd2(req'd).

b = 10 in (column width)

d = 1 , 803 10 = 13.43 in

Total beam depth, D > d + dcover = 15.93 in; use a D = 16 in; d = 13.5 in.

ρ p r o v = 0.85 f' c f y 1 - 1 - 2 R n , p r o v 085 f' c = 0.018
A s = ρ prov · b · d prov = 2.406  in 2

Verify the design.

T = Asfy = 2.406×60 = 144.36 kips

Design moment strength, ϕMn = Dm

Strength reduction factor, ϕ = 0.9
D m = ϕ [ A s f y ( d prov - a 2 ) ] = 123.2  ft·kip

Dm > Mu, hence design OK.

Compute minimum reinforcement

A s , min = | 200 f y b d = 0.45  in 2 3 f c f y b d = 0.427  in 2 max

Since As > As,min, the design satisfies the minimum reinforcement criteria.

Compute the reinforcement provided

Use 2-#10 bars: As = 2.53 in2

Check Bar Spacing

End bar diameter, ⌀ = 1.27 in, two bars in a layer

f s = 2 3 f y = 40 ( 10 ) 3  psi

Maximum spacing allowed:

s max = | 15 40,000 f s - 2.5 C c 12 40,000 f s min = 10  in

Spacing provided:

s p r o v = b - ( 2 C c + 2 × 0.5 ) N - 1 = 4.73  in

Results

Table 1. Comparison of results
Parameter Hand Calculation STAAD.Pro Difference Comments
Area of steel required (in2) 2.406 2.423 0.7
Bar spacing (in) 4.73 4.73 0  

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\10 Concrete Design\US\ACI\318-2011\ACI-318-11 Singly Reinforced Rectangular Beam.std is typically installed with the program.

STAAD PLANE RECTANGULAR CONCRETE BEAM DESIGN PER ACI 318 2011
START JOB INFORMATION
ENGINEER DATE 18-December-19
JOB NAME PCA Example 7.1
JOB CLIENT Bentley Systems Inc.
ENGINEER NAME TK
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 10 0 0;
MEMBER INCIDENCES
1 1 2;
UNIT INCHES KIP
MEMBER PROPERTY AMERICAN
1 PRIS YD 16 ZD 10
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 3150
POISSON 0.17
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 2 PINNED
UNIT FEET KIP
LOAD 1 DEAD LOAD
MEMBER LOAD
1 UNI GY -4.48
LOAD 2 LIVE LOAD
MEMBER LOAD
1 UNI GY -2.8
LOAD COMB 3 ACI 318R-02
1 1.2 2 1.6 
PERFORM ANALYSIS
UNIT INCHES KIP
START CONCRETE DESIGN
CODE ACI 2011
*MINMAIN 8 ALL
*MAXMAIN 9 ALL
TRACK 2 ALL
DESIGN BEAM 1
END CONCRETE DESIGN
FINISH

STAAD Output

          ACI 318-11   BEAM  NO.     1   DESIGN RESULTS 
          =============================================
   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=    123.20 KIP-FT  AT  5.00 FT, LOAD    3|
   |   REQD STEEL=  2.44 IN2, RHO=0.0183, RHOMX=0.0214 RHOMN=0.0033 |
   |   MAX/MIN/ACTUAL BAR SPACING= 10.00/ 2.54/ 4.73 INCH           |
   |   REQD. DEVELOPMENT LENGTH = 48.52 INCH                        |
   |----------------------------------------------------------------|
     Cracked Moment of Inertia Iz at above location =    1817.34 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        3/    1
     0.83        0.650/    0.000        37.64/      0.00        3/    0
     1.67        1.231/    0.000        68.44/      0.00        3/    0
     2.50        1.723/    0.000        92.40/      0.00        3/    0
     3.33        2.101/    0.000       109.51/      0.00        3/    0
     4.17        2.341/    0.000       119.78/      0.00        3/    0
     5.00        2.423/    0.000       123.20/      0.00        3/    0
     5.83        2.340/    0.000       119.78/      0.00        3/    0
     6.67        2.101/    0.000       109.51/      0.00        3/    0
     7.50        1.723/    0.000        92.40/      0.00        3/    0
     8.33        1.231/    0.000        68.44/      0.00        3/    0
     9.17        0.650/    0.000        37.64/      0.00        3/    0
    10.00        0.000/    0.000         0.00/      0.00        3/    1
          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=   38.19 KIP  Vc=   21.42 KIP  Vs=   29.50 KIP
    Tu=    0.00 KIP-FT  Tc=   1.95 KIP-FT  Ts=   0.00 KIP-FT  LOAD     3
    NO STIRRUPS ARE REQUIRED FOR TORSION.
    REINFORCEMENT IS REQUIRED FOR SHEAR.
    PROVIDE NUM. 4 2-LEGGED STIRRUPS AT  6.7 IN. C/C FOR   46. IN.
      RECTANGULAR CONCRETE BEAM DESIGN PER ACI 318 2011        -- PAGE NO.    4
    AT END   SUPPORT - Vu=   38.19 KIP  Vc=   21.42 KIP  Vs=   29.50 KIP
    Tu=    0.00 KIP-FT  Tc=   1.95 KIP-FT  Ts=   0.00 KIP-FT  LOAD     3
    NO STIRRUPS ARE REQUIRED FOR TORSION.
    REINFORCEMENT IS REQUIRED FOR SHEAR.
    PROVIDE NUM. 4 2-LEGGED STIRRUPS AT  6.7 IN. C/C FOR   46. IN.
  ___   1J____________________  120.X  10.X  16_____________________   2J____ 
 |                                                                           |
 |                                                                           |
 |                                                                           |
 |  8#4 C/C  7                                                 8#4 C/C  7    |
 | 2#10H   3.   0.TO  120.                                                   |
 ||=========================================================================||
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 |___________________________________________________________________________|
  _________    _________    _________    _________    _________     _________ 
 |         |  |         |  |         |  |         |  |         |   |         |
 |         |  |         |  |         |  |         |  |         |   |         |
 |         |  |         |  |         |  |         |  |         |   |         |
 |         |  |         |  |         |  |         |  |         |   |         |
 | 2#10    |  | 2#10    |  | 2#10    |  | 2#10    |  | 2#10    |   | 2#10    |
 |   OO    |  |   OO    |  |   OO    |  |   OO    |  |   OO    |   |   OO    |
 |         |  |         |  |         |  |         |  |         |   |         |
 |_________|  |_________|  |_________|  |_________|  |_________|   |_________|
   ********************END OF BEAM DESIGN**************************