# V. IS456 2000-Singly Reinforced Square Beam

Verify the designed results produced by the program with hand calculated design results for a square beam section as per IS456:2000.

## Details

A three story, concrete structure is subject to gravity loads only. Beam 59 is to be designed:
Section properties:
• Length of beam, L = 3,000 mm (clear span)
• Width of beam, B = 300 mm
• Depth of beam, D = 300 mm
• Clear cover = 30 mm
• Diameter of main reinforcement = 16 mm
• Diameter of stirrups = 8 mm
Material properties:
• Characteristic strength of concrete, fck = 20 N/mm2
• Yield strength of steel, fy = 415 N/mm2

Loads: total uniform force = 35 kN/m

## Validation

Effective Depth, d = 300 – 30 – 8 – (16/2) = 254 mm

Design for Flexure

Limiting moment value, Mz,limit = 0.138×fck×B×d2 = 0.138 × 20 × 300 × 2542 × 106 = 53.42 kN·m

From the STAAD.Pro analysis, Mz = 40.46 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.

From SP16 table 2 flexure, reinforcement percentage for singly reinforced section:
• Percentage of tension reinforcement ρt = 0.674

Reinforcement at Start of Member (x = 0): top bars

Ast = 0.674 × B × d / 100 = 0.674 × 300 × 254 / 100 = 513.6 mm2

Provide 3 - 16 mm diameter bars. Actual Ast, top = 3×(π/4)×(16)2 = 603.2 mm2

From the STAAD.Pro analysis, Mz = 35.84 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.

From SP16 table 2 flexure, reinforcement percentage for singly reinforced section:
• Percentage of tension reinforcement ρt = 0.585

Reinforcement at Start of Member (x = 3): top bars

Ast = 0.585 × B × d / 100 = 0.585 × 300 × 254 / 100 = 445.6 mm2

Provide 3 - 16 mm diameter bars. Actual Ast, top = 3×(π/4)×(16)2 = 603.2 mm2

Shear Strength of Concrete

Provide percentage of tension steel, ρt = 0.792.

From Table 19 of IS 456:2000, for M20 grade concrete, shear stress: Tc = 0.57 N/mm2 .

Factored shear force as per linear structural analysis in STAAD.Pro, Fy = 80.29 kN.

The nominal shear stress, Tv = Fy / (B×d) = 80.29 / (300 × 254) = 1.054 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 = 80.29 - 0.57 × 300 × 254 × 103 = 36.85 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:
Per Cl. 26.5.1.5 of IS 456:2000, the maximum spacing for of shear reinforcement is the least of:
• 0.75 × d = 0.75 × 256 = 191 mm
• 300 mm
• ( 0.87× fy × Asv ) / (0.4 × B) = 302.5 mm
• Sv = 250.2 mm

So, provide 2 legged 8 mm diameter bar stirrups at 190 mm center to center.

## Results

Reqd. area of steel at start section (mm2) 513.6 519.32 negligible
Reqd. area of steel at end section (mm2) 445.6 449.98 negligible
Spacing of shear reinforcement (mm) 190 185 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\10 Concrete Design\India\IS456 2000-Singly Reinforced Square Beam.STD is typically installed with the program.

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 0.3
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
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
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 -30
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
1 1.0 2 1.0
PERFORM ANALYSIS PRINT ALL
PRINT SUPPORT REACTION
PRINT MEMBER FORCES
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 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

====================================================
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:   300.0 mm X  300.0 mm   COVER: 40.0 mm
----------------------------------------------------------------------------------
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 |   80.29     0.00    80.29     3
|    0.00   -40.46     0.00   -40.46     3 |
250.0 |    0.00     0.00     0.00     0.00     3 |   67.16     0.00    67.16     3
|    0.00   -22.03     0.00   -22.03     3 |
500.0 |    0.00     0.00     0.00     0.00     3 |   54.04     0.00    54.04     3
|    0.00    -6.88     0.00    -6.88     3 |
750.0 |    0.00     4.99     0.00     4.99     3 |   40.91     0.00    40.91     3
|    0.00     0.00     0.00     0.00     3 |
1000.0 |    0.00    13.58     0.00    13.58     3 |   27.79     0.00    27.79     3
|    0.00     0.00     0.00     0.00     3 |
1250.0 |    0.00    18.89     0.00    18.89     3 |   14.66     0.00    14.66     3
|    0.00     0.00     0.00     0.00     3 |
1500.0 |    0.00    20.91     0.00    20.91     3 |    1.54     0.00     1.54     3
|    0.00     0.00     0.00     0.00     3 |
1750.0 |    0.00    19.66     0.00    19.66     3 |  -11.59     0.00    11.59     3
|    0.00     0.00     0.00     0.00     3 |
2000.0 |    0.00    15.12     0.00    15.12     3 |  -24.71     0.00    24.71     3
|    0.00     0.00     0.00     0.00     3 |
2250.0 |    0.00     7.30     0.00     7.30     3 |  -37.84     0.00    37.84     3
|    0.00     0.00     0.00     0.00     3 |
2500.0 |    0.00     0.00     0.00     0.00     3 |  -50.96     0.00    50.96     3
|    0.00    -3.80     0.00    -3.80     3 |
2750.0 |    0.00     0.00     0.00     0.00     3 |  -64.09     0.00    64.09     3
|    0.00   -18.18     0.00   -18.18     3 |
3000.0 |    0.00     0.00     0.00     0.00     3 |  -77.21     0.00    77.21     3
|    0.00   -35.84     0.00   -35.84     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 |  519.32/ 603.19( 3-16d )|    0.00/ 402.12( 2-16d )|  8d  @ 185 mm
250.0 |  261.02/ 603.19( 3-16d )|    0.00/ 402.12( 2-16d )|  8d  @ 185 mm
500.0 |  184.34/ 603.19( 3-16d )|    0.00/ 402.12( 2-16d )|  8d  @ 185 mm
750.0 |    0.00/ 402.12( 2-16d )|  154.84/ 603.19( 3-16d )|  8d  @ 185 mm
1000.0 |    0.00/ 402.12( 2-16d )|  156.06/ 603.19( 3-16d )|  8d  @ 185 mm
1250.0 |    0.00/ 402.12( 2-16d )|  221.19/ 603.19( 3-16d )|  8d  @ 185 mm
1500.0 |    0.00/ 402.12( 2-16d )|  246.77/ 603.19( 3-16d )|  8d  @ 185 mm
1750.0 |    0.00/ 402.12( 2-16d )|  230.86/ 603.19( 3-16d )|  8d  @ 185 mm
2000.0 |    0.00/ 402.12( 2-16d )|  174.69/ 603.19( 3-16d )|  8d  @ 185 mm
2250.0 |    0.00/ 402.12( 2-16d )|  154.84/ 603.19( 3-16d )|  8d  @ 185 mm
2500.0 |  184.34/ 603.19( 3-16d )|    0.00/ 402.12( 2-16d )|  8d  @ 185 mm
2750.0 |  212.33/ 603.19( 3-16d )|    0.00/ 402.12( 2-16d )|  8d  @ 185 mm
3000.0 |  449.98/ 603.19( 3-16d )|    0.00/ 402.12( 2-16d )|  8d  @ 185 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 =    56.56 MX =     0.00 LD=    3
Provide 2 Legged  8d  @ 185 mm c/c
SHEAR DESIGN RESULTS AT   452.0 mm AWAY FROM END SUPPORT
VY =   -53.48 MX =     0.00 LD=    3
Provide 2 Legged  8d  @ 185 mm c/c
============================================================================
********************END OF BEAM DESIGN RESULTS********************