V. IS456 2000-Doubly Reinforced Rectangular Beam
Verify the design of a rectangular beam per IS 456:2000.
Details
- Length of beam, L = 3,000 mm (clear span)
- Width of beam, B = 250 mm
- Depth of beam, D = 300 mm
- Clear cover = 30 mm
- Diameter of main reinforcement = 16 mm
- Diameter of stirrups = 8 mm
- Characteristic strength of concrete, fck = 20 N/mm2
- Yield strength of steel, fy = 415 N/mm2
Loads: total uniform force = 50 kN/m
Validation
Effective Depth, d = 300 – 30 – 8 – (16/2) = 254 mm
Depth of Compression Reinforcement, d’ = 30 + (16/2) + 8 = 46 mm
Design for Flexure
Limiting moment value, Mz,limit = 0.138×fck×B×d2 = 44.52 kN·m
From the STAAD.Pro analysis, Mz = 55.44 kN·m > Mz,limit at the start of the member (x = 0).
So, the actual moment is greater than limiting moment then the section will be design as doubly reinforced section.
- Percentage of tension reinforcement ρt = 1.212
- Percentage of compression reinforcement ρc = 0.288
Reinforcement at Start of Member (x = 0): top bars
Ast,top_a = 1.212×B×d/100 = 769.6 mm2
Provide 4 - 16 mm diameter bars. Actual Ast, top = 4×(π/4)×(16)2 = 804.2 mm2
Reinforcement at Start of Member (x = 0): bottom bars
Ast,bot_a = 0.288×B×d/100 = 182.9 mm2
Provide 2 - 16 mm diameter bars. Actual Ast, bot = 2×(π/4)×(16)2 = 402.1 mm2
From the STAAD.Pro analysis, Mz = 54.11 kN·m > Mz,limit at the end of the member (x = 3 m).
- Percentage of tension reinforcement ρt = 1.183
- Percentage of compression reinforcement ρc = 0.256
Reinforcement at End of Member (x = 3 m): top bars
Ast,top_b = 1.183×B×d/100 = 751.2 mm2
Provide 4 - 16 mm diameter bars. Actual Ast, top = 3×(π/4)×(16)2 = 804.2 mm2
Reinforcement at End of Member (x = 3 m): bottom bars
Ast,bot_b = 0.256×B×d/100 = 162.6 mm2
Provide 2 - 16 mm diameter bars. Actual Ast, bot = 2×(π/4)×(16)2 = 402.1 mm2
Design for Shear
Provide percentage of tension steel, ρt = 1.266.From Table 19 of IS 456:2000, for M20 grade concrete, shear stress: Tc = 0.673 N/mm2.
Factored shear force as per linear structural analysis in STAAD.Pro, Fy = 117.9 kN.The nominal shear stress, Tv = 117.9 / (B×d) = 117.9×103 / (250 × 254) = 1.86 N/mm2.
The maximum shear stress from Table 20 of IS 456:2000 for M20 grade concrete, Tc,max = 2.8 N/mm2.
Shear strength of the reinforcement: Vus = Fy - Tc×B×d = 117.9 - 0.673×250×254×103 = 75.16 kN.
Provide 2 legged 8 mm diameter bar. So, the area of shear reinforcement, Asv = π/4 × 82×2 = 100.5 mm2.
Using formula of IS 456:2000 spacing for vertical stirrups: sv = 0.87×(fy ×Asv × d) / Vus = 122.8 mm.
So, provide 2 legged 8 mm diameter bar stirrups at 100 mm center to center.
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Required area of steel at top of start section (mm2) | 769.4 | 772.79 | negligible | |
| Required area of steel at bottom of start section (mm2) | 182.6 | 186.11 | negligible | |
| Required area of steel at top of end section (mm2) | 751.2 | 754.73 | negligible | |
| Required area of steel at bottom of end section (mm2) | 162.3 | 166.44 | negligible | |
| Spacing of shear reinforcement at ends (mm) | 100 | 100 | none |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\10 Concrete Design\India\IS456 2000-Doubly Reinforced Rectangular Beam.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 25-Jul-18
END JOB INFORMATION
INPUT WIDTH 79
*******************************************************************************
*This Problem is created to verify the design results produced by the program *
*with hand calculated design results for a rectangular(300 mm * 250 mm) Doubly*
*reinforced beam section as per IS456:2000 *
* *
*******************************************************************************
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 3 0; 3 0 6 0; 4 0 9 0; 5 3 9 0; 6 6 9 0; 7 6 6 0; 8 6 3 0;
9 6 0 0; 10 3 6 0; 11 3 3 0; 12 3 0 0; 13 0 0 3; 14 0 3 3; 15 0 6 3; 16 0 9 3;
17 3 9 3; 18 6 9 3; 19 6 6 3; 20 6 3 3; 21 6 0 3; 22 3 6 3; 23 3 3 3; 24 3 0 3;
25 0 0 6; 26 0 3 6; 27 0 6 6; 28 0 9 6; 29 3 9 6; 30 6 9 6; 31 6 6 6; 32 6 3 6;
33 6 0 6; 34 3 6 6; 35 3 3 6; 36 3 0 6;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 4 5; 5 5 6; 6 6 7; 7 7 8; 8 8 9; 9 3 10; 10 10 7;
11 2 11; 12 11 8; 13 5 10; 14 10 11; 17 11 12; 18 2 14; 19 3 15; 20 4 16;
21 5 17; 22 6 18; 23 7 19; 24 8 20; 25 10 22; 26 11 23; 27 13 14; 28 14 15;
29 15 16; 30 16 17; 31 17 18; 32 18 19; 33 19 20; 34 20 21; 35 15 22; 36 22 19;
37 14 23; 38 23 20; 39 17 22; 40 22 23; 41 23 24; 42 14 26; 43 15 27; 44 16 28;
45 17 29; 46 18 30; 47 19 31; 48 20 32; 49 22 34; 50 23 35; 51 25 26; 52 26 27;
53 27 28; 54 28 29; 55 29 30; 56 30 31; 57 31 32; 58 32 33; 59 27 34; 60 34 31;
61 26 35; 62 35 32; 63 29 34; 64 34 35; 65 35 36;
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 2.17185e+07
POISSON 0.17
DENSITY 23.5616
ALPHA 1e-05
DAMP 0.05
TYPE CONCRETE
STRENGTH FCU 27579
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
4 5 9 TO 12 18 TO 26 30 31 35 TO 38 42 TO 50 54 55 59 TO 62 PRIS YD 0.3 ZD 0.25
1 TO 3 6 TO 8 13 14 17 27 TO 29 32 TO 34 39 TO 41 51 TO 53 56 TO 58 -
63 TO 65 PRIS YD 0.4 ZD 0.4
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 9 12 13 21 24 25 33 36 FIXED
LOAD 1 LOADTYPE Dead TITLE DL
MEMBER LOAD
4 5 9 TO 12 18 TO 26 30 31 35 TO 38 42 TO 50 54 55 59 TO 62 UNI GY -3.125
4 5 9 TO 12 18 TO 26 30 31 35 TO 38 42 TO 50 54 55 59 TO 62 UNI GY -1.875
LOAD 2 LOADTYPE Live TITLE LL
MEMBER LOAD
4 5 20 22 44 46 54 55 UNI GY -7.875
21 30 31 45 UNI GY -15.75
9 TO 12 18 19 23 24 42 43 47 48 59 TO 62 UNI GY -45
25 26 35 TO 38 49 50 UNI GY -90
LOAD COMB 3 GENERATED IS:456/IS:800 GENRAL_STRUCTURES 1
1 1.5 2 1.5
LOAD COMB 4 GENERATED IS:456/IS:800 GENRAL_STRUCTURES 2
1 1.2 2 1.2
LOAD COMB 5 GENERATED IS:456/IS:800 GENRAL_STRUCTURES 3
1 1.5
LOAD COMB 6 GENERATED IS:456/IS:800 GENRAL_STRUCTURES 4
1 0.9
LOAD COMB 7 COMBINATION LOAD CASE 7
1 1.0 2 1.0
PERFORM ANALYSIS PRINT ALL
START CONCRETE DESIGN
CODE INDIAN
CLB 0.03 ALL
CLT 0.03 ALL
FC 20000 MEMB 59
FYMAIN 413688 MEMB 59
FYSEC 413688 MEMB 59
MAXMAIN 16 MEMB 59
MAXSEC 8 MEMB 59
MINMAIN 16 MEMB 59
MINSEC 8 MEMB 59
TRACK 2 MEMB 59
DESIGN BEAM 59
END CONCRETE DESIGN
FINISH
STAAD.Pro Output
==================================================== IS 456 - 2000 B E A M D E S I G N R E S U L T S ==================================================== ============================================================================ IS-456 L I M I T S T A T E D E S I G N B E A M N O. 59 D E S I G N R E S U L T S M20 Fe415 (Main) Fe415 (Sec.) LENGTH: 3000.0 mm SIZE: 250.0 mm X 300.0 mm COVER: 40.0 mm DESIGN LOAD SUMMARY (KN MET) ---------------------------------------------------------------------------------- SECTION |FLEXURE (Maxm. Sagg./Hogg./Eqv. moments) | SHEAR (in mm) | P MZ MX ME Load # | VY MX VE Load # ---------------------------------------------------------------------------------- 0.0 | 0.00 0.00 0.00 0.00 1 | 112.94 0.77 117.85 3 | 0.00 -55.44 0.77 -56.44 3 | 250.0 | 0.00 0.00 0.00 0.00 1 | 94.19 0.77 99.10 3 | 0.00 -29.55 0.77 -30.54 3 | 500.0 | 0.00 0.00 0.00 0.00 1 | 75.44 0.77 80.35 3 | 0.00 -8.35 0.77 -9.34 3 | 750.0 | 0.00 8.17 0.77 9.16 3 | 56.69 0.77 61.60 3 | 0.00 0.00 0.00 0.00 1 | 1000.0 | 0.00 20.00 0.77 20.99 3 | 37.94 0.77 42.85 3 | 0.00 0.00 0.00 0.00 1 | 1250.0 | 0.00 27.14 0.77 28.13 3 | 19.19 0.77 24.10 3 | 0.00 0.00 0.00 0.00 1 | 1500.0 | 0.00 29.60 0.77 30.59 3 | 0.44 0.77 5.35 3 | 0.00 0.00 0.00 0.00 1 | 1750.0 | 0.00 27.36 0.77 28.36 3 | -18.31 0.77 23.21 3 | 0.00 0.00 0.00 0.00 1 | 2000.0 | 0.00 20.44 0.77 21.44 3 | -37.06 0.77 41.96 3 | 0.00 0.00 0.00 0.00 1 | 2250.0 | 0.00 8.84 0.77 9.83 3 | -55.81 0.77 60.71 3 | 0.00 0.00 0.00 0.00 1 | 2500.0 | 0.00 0.00 0.00 0.00 1 | -74.56 0.77 79.46 3 | 0.00 -7.46 0.77 -8.45 3 | 2750.0 | 0.00 0.00 0.00 0.00 1 | -93.31 0.77 98.21 3 | 0.00 -28.44 0.77 -29.43 3 | 3000.0 | 0.00 0.00 0.00 0.00 1 | -112.06 0.77 116.96 3 | 0.00 -54.11 0.77 -55.11 3 | ---------------------------------------------------------------------------- STAAD SPACE -- PAGE NO. 11 SUMMARY OF REINF. AREA (Sq.mm) ---------------------------------------------------------------------------- SECTION | TOP | BOTTOM | STIRRUPS (in mm) | Reqd./Provided reinf. | Reqd./Provided reinf. | (2 legged) ---------------------------------------------------------------------------- 0.0 | 772.79/ 804.25( 4-16d )| 186.11/ 402.12( 2-16d )| 8d @ 100 mm 250.0 | 384.93/ 402.12( 2-16d )| 0.00/ 402.12( 2-16d )| 8d @ 100 mm 500.0 | 153.61/ 402.12( 2-16d )| 0.00/ 402.12( 2-16d )| 8d @ 100 mm 750.0 | 0.00/ 402.12( 2-16d )| 129.04/ 402.12( 2-16d )| 8d @ 100 mm 1000.0 | 0.00/ 402.12( 2-16d )| 251.83/ 402.12( 2-16d )| 8d @ 100 mm 1250.0 | 0.00/ 402.12( 2-16d )| 349.91/ 402.12( 2-16d )| 8d @ 100 mm 1500.0 | 0.00/ 402.12( 2-16d )| 385.60/ 402.12( 2-16d )| 8d @ 100 mm 1750.0 | 0.00/ 402.12( 2-16d )| 353.09/ 402.12( 2-16d )| 8d @ 100 mm 2000.0 | 0.00/ 402.12( 2-16d )| 257.70/ 402.12( 2-16d )| 8d @ 100 mm 2250.0 | 0.00/ 402.12( 2-16d )| 129.04/ 402.12( 2-16d )| 8d @ 100 mm 2500.0 | 153.61/ 402.12( 2-16d )| 0.00/ 402.12( 2-16d )| 8d @ 100 mm 2750.0 | 368.69/ 402.12( 2-16d )| 0.00/ 402.12( 2-16d )| 8d @ 100 mm 3000.0 | 754.73/ 804.25( 4-16d )| 166.44/ 402.12( 2-16d )| 8d @ 100 mm ---------------------------------------------------------------------------- SHEAR DESIGN RESULTS AT DISTANCE d (EFFECTIVE DEPTH) FROM FACE OF THE SUPPORT ----------------------------------------------------------------------------- SHEAR DESIGN RESULTS AT 452.0 mm AWAY FROM START SUPPORT VY = 79.04 MX = 0.77 LD= 3 Provide 2 Legged 8d @ 100 mm c/c SHEAR DESIGN RESULTS AT 452.0 mm AWAY FROM END SUPPORT VY = -78.16 MX = 0.77 LD= 3 Provide 2 Legged 8d @ 100 mm c/c ============================================================================