V. IS456 2000-Singly Reinforced Rectangular Beam
Verify the designed results produced by the program with hand calculated design results for a rectangular beam section as per IS456:2000.
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 = 12 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 = 25 kN/m
Validation
Effective Depth, d = 300 – 30 – 8 – (12/2) = 256 mm
Design for Flexure
Limiting moment value, Mz,limit = 0.138×fck×B×d2 = 0.138 × 20 × 250 × 2562 × 106 = 45.22 kN·m
From the STAAD.Pro analysis, Mz = 30.26 kN·m < Mz,limit at the start of the member (x = 0).
So, the actual moment is less than limiting moment then the section will be design as singly reinforced section.
- Percentage of tension reinforcement ρt = 0.583
Reinforcement at Start of Member (x = 0): top bars
Ast = 0.583×B×d/100 = 0.583 × 250 × 256 / 100 = 373.0 mm2
Provide 4 - 12 mm diameter bars. Actual Ast, top = 4×(π/4)×(12)2 = 452.4 mm2
From the STAAD.Pro analysis, Mz = 24.57 kN·m < Mz,limit at the end of the member (x = 3 m).
The actual moment is less than the limiting moment. Thus, the section is designed as a singly reinforced section.
- Percentage of tension reinforcement ρt = 0.46
Reinforcement at End of Member (x = 3 m): top bars
Ast = 0.46×B×d/100 = 0.46 × 250 × 256 / 100 = 294.4 mm2
Provide 3 - 12 mm diameter bars. Actual Ast, top = 3×(π/4)×(12)2 = 393.3 mm2
Shear Strength of Concrete
Provide percentage of tension steel, ρt = 0.707.
From Table 19 of IS 456:2000, for M20 grade concrete, shear stress: Tc = 0.546 N/mm2 .
Factored shear force as per linear structural analysis in STAAD.Pro, Fy = 58.15 kN.
The nominal shear stress, Tv = Fy / (B×d) = 58.15 / (250 × 256) = 0.909 N/mm2 .
The maximum shear stress from Table 20 of IS 456:2000 for M20 grade concrete, Tc,max = 2.8 N/mm2 .
Tc < Tv < Tc,max , so provide shear reinforcement.
Shear strength of the reinforcement: Vus = Fy - Tc × B × d = 58.15 - 0.546 × 250 × 256 × 103 = 23.19 kN.
Provide 2 legged 8 mm diameter bar. So, the area of shear reinforcement, Asv = π/4 × 82×2 = 100.5 mm2 .
Using the formula of IS 456:200, the spacing for vertical stirrups:
- 0.75 × d = 0.75 × 256 = 192 mm
- 300 mm
- ( 0.87× fy × Asv ) / (0.4 × B) = 393 mm
- Sv = 401 mm
So, provide 2 legged 8 mm diameter bar stirrups at 190 mm center to center.
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Reqd. area of steel at start section (mm2) | 373 | 376.80 | negligible | |
| Reqd. area of steel at end section (mm2) | 294.4 | 297.10 | negligible | |
| Spacing of shear reinforcement (mm) | 192 | 190 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\10 Concrete Design\India\IS456 2000-Singly 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
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
MEMBER RELEASE
59 START MX
59 END MX
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 -20
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
PRINT SUPPORT REACTION
PRINT MEMBER FORCES
LOAD LIST 3 TO 6
START CONCRETE DESIGN
CODE INDIAN
CLB 0.03 ALL
CLT 0.03 ALL
FC 20000 MEMB 59
FYMAIN 415000 MEMB 59
FYSEC 415000 MEMB 59
MAXMAIN 12 MEMB 59
MAXSEC 8 MEMB 59
MINMAIN 12 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 3 | 58.15 0.00 58.15 3 | 0.00 -30.26 0.00 -30.26 3 | 250.0 | 0.00 0.00 0.00 0.00 3 | 48.77 0.00 48.77 3 | 0.00 -16.90 0.00 -16.90 3 | 500.0 | 0.00 0.00 0.00 0.00 3 | 39.40 0.00 39.40 3 | 0.00 -5.88 0.00 -5.88 3 | 750.0 | 0.00 2.80 0.00 2.80 3 | 30.02 0.00 30.02 3 | 0.00 0.00 0.00 0.00 3 | 1000.0 | 0.00 9.13 0.00 9.13 3 | 20.65 0.00 20.65 3 | 0.00 0.00 0.00 0.00 3 | 1250.0 | 0.00 13.12 0.00 13.12 3 | 11.27 0.00 11.27 3 | 0.00 0.00 0.00 0.00 3 | 1500.0 | 0.00 14.77 0.00 14.77 3 | 1.90 0.00 1.90 3 | 0.00 0.00 0.00 0.00 3 | 1750.0 | 0.00 14.07 0.00 14.07 3 | -7.48 0.00 7.48 3 | 0.00 0.00 0.00 0.00 3 | 2000.0 | 0.00 11.03 0.00 11.03 3 | -16.85 0.00 16.85 3 | 0.00 0.00 0.00 0.00 3 | 2250.0 | 0.00 5.64 0.00 5.64 3 | -26.23 0.00 26.23 3 | 0.00 0.00 0.00 0.00 3 | 2500.0 | 0.00 0.00 0.00 0.00 3 | -35.60 0.00 35.60 3 | 0.00 -2.09 0.00 -2.09 3 | 2750.0 | 0.00 0.00 0.00 0.00 3 | -44.98 0.00 44.98 3 | 0.00 -12.16 0.00 -12.16 3 | 3000.0 | 0.00 0.00 0.00 0.00 3 | -54.35 0.00 54.35 3 | 0.00 -24.57 0.00 -24.57 3 | ---------------------------------------------------------------------------- STAAD SPACE -- PAGE NO. 35 SUMMARY OF REINF. AREA (Sq.mm) ---------------------------------------------------------------------------- SECTION | TOP | BOTTOM | STIRRUPS (in mm) | Reqd./Provided reinf. | Reqd./Provided reinf. | (2 legged) ---------------------------------------------------------------------------- 0.0 | 376.80/ 452.39( 4-12d )| 0.00/ 226.19( 2-12d )| 8d @ 190 mm 250.0 | 197.12/ 226.19( 2-12d )| 0.00/ 226.19( 2-12d )| 8d @ 190 mm 500.0 | 153.61/ 226.19( 2-12d )| 0.00/ 226.19( 2-12d )| 8d @ 190 mm 750.0 | 0.00/ 226.19( 2-12d )| 130.06/ 226.19( 2-12d )| 8d @ 190 mm 1000.0 | 0.00/ 226.19( 2-12d )| 130.06/ 226.19( 2-12d )| 8d @ 190 mm 1250.0 | 0.00/ 226.19( 2-12d )| 150.62/ 226.19( 2-12d )| 8d @ 190 mm 1500.0 | 0.00/ 226.19( 2-12d )| 170.70/ 226.19( 2-12d )| 8d @ 190 mm 1750.0 | 0.00/ 226.19( 2-12d )| 162.15/ 226.19( 2-12d )| 8d @ 190 mm 2000.0 | 0.00/ 226.19( 2-12d )| 130.06/ 226.19( 2-12d )| 8d @ 190 mm 2250.0 | 0.00/ 226.19( 2-12d )| 130.06/ 226.19( 2-12d )| 8d @ 190 mm 2500.0 | 153.61/ 226.19( 2-12d )| 0.00/ 226.19( 2-12d )| 8d @ 190 mm 2750.0 | 153.61/ 226.19( 2-12d )| 0.00/ 226.19( 2-12d )| 8d @ 190 mm 3000.0 | 297.10/ 339.29( 3-12d )| 0.00/ 226.19( 2-12d )| 8d @ 190 mm ---------------------------------------------------------------------------- SHEAR DESIGN RESULTS AT DISTANCE d (EFFECTIVE DEPTH) FROM FACE OF THE SUPPORT ----------------------------------------------------------------------------- SHEAR DESIGN RESULTS AT 454.0 mm AWAY FROM START SUPPORT VY = 41.20 MX = 0.00 LD= 3 Provide 2 Legged 8d @ 190 mm c/c SHEAR DESIGN RESULTS AT 454.0 mm AWAY FROM END SUPPORT VY = -37.40 MX = 0.00 LD= 3 Provide 2 Legged 8d @ 190 mm c/c ============================================================================ ********************END OF BEAM DESIGN RESULTS********************