V. ACI 318-11 Rectangular Singly Reinforced Beam
Design of a singly reinforced concrete beam per the ACI 318-2011 code.
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
Size members so that bd2(prov) ≥ bd2(req'd).
b = 10 in (column width)
Total beam depth, D > d + dcover = 15.93 in; use a D = 16 in; d = 13.5 in.
Verify the design.
T = Asfy = 2.406×60 = 144.36 kips
Design moment strength, ϕMn = Dm
Strength reduction factor, ϕ = 0.9Dm > Mu, hence design OK.
Compute minimum reinforcement
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
Maximum spacing allowed:
Spacing provided:
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\10 Concrete Design\US\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 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**************************