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| | Applies To | | |
| | | | |
| | Product(s): | STAAD.Pro V8i | |
| | Version(s): | All | |
| | Environment: | N/A | |
| | Area: | STAAD.Pro Wiki | |
| | Subarea: | EC3 Torsion Design | |
| | Original Author: | Anisurya Ghosh | |
| | | | |
INTRODUCTION:
Torsion design in EC3 is given in Cl. 6.2.7 of EN 1993-1-1:2005.
Note: Cl. 6.2.7 only deals with members subject to torsion and those that are subject to torsion and shear force. This clause does not deal with members subject to combined bending and torsion. This implementation will however use this clause (6.2.7) to report the output for all torsion checks. Also any distortion deformations and any amplification in the torsional or shear stresses due to distortions will be neglected for this implementation.
The program allows for two types of checks for members subject to torsion:
Basic Stress Check: This method is intended to be a simplified stress check for torsional effects. This method will produce the output corresponding to Cl. 6.2.7(5) of EN 1993-1-1.
Detailed Check: This method will perform a full torsional analysis of the member. All the four clause checks [Cl. 6.2.7(9), Cl. 6.2.7(1), Cl. 6.2.7(5) & EC-3-6 App A] will be performed.
STAAD INPUT:
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 06-Jun-17
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 4 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+008
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-005
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY EUROPEAN
1 TABLE ST HD320x127
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 FIXED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -1
1 CON GY -100 2 0.075
PERFORM ANALYSIS
LOAD LIST 1
PARAMETER 1
CODE EN 1993-1-1:2005
SGR 1 ALL
*ALH 0.5 ALL
CMT 5 ALL
TORSION 2 ALL
TRACK 2 ALL
CHECK CODE ALL
PRINT MEMBER PROPERTIES ALL
FINISH
CALCULATION:
Problem:
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BMD:
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Load: w= 100 KN, UDL= 1 KN/m, Span: 4m
Grade of Steel: S275
Outputs:
MA= 51.33 KN-M, MB= 51.33 KN-m, SFA= 52 KN, SFB= 52 KN
Torsion: T = 3.75 KN-M.
Try with European HD320X127
We get: D= 320 mm, B= 300 mm, Tf= 20.5 mm, Tw= 11.5 mm, Iz= 30820 cm4, Iy= 9239 cm4,
Zz= 1926.5 cm3, Zy= 615.93 cm3, J= 225.1 cm4, H= 2.069*10^12 mm6
CMT = 5 -> END1: Torsion Fixed, Warping Fixed END2: Torsion Fixed, Warping Fixed
Basic Torsion Check [TOR=1]
The stress check will be performed using equation 6.1 of EN 1993-1-1:2005 as given below:
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The stress check as per equation 6.1 is performed at various stress points of a cross section as shown in figures below:
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Stress calculation at different points [Unit-N-mm]:
Point No. | σx | σbz | σby | T*t/J | (Vy*Q)/(Iz*t) | (Vz*Q)/(Iy*t) |
1 | 0 | 26.64 | 0 | 34.15 | 0 | 0 |
2 | 0 | 26.64 | 0 | 34.15 | 3.73 | 0 |
3 | 0 | 23.23 | 0 | 34.15 | 14.41 | 0 |
4 | 0 | 0 | 0 | 19.157 | 15.154 | 0 |
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Therefore, the Ratio acc. To Cl. EC-6.2.7(5) is 0.100.
STAAD.Pro value is 0.100, henceOK.
STAAD OUTPUT (TOR=1):
ADDITIONAL CLAUSE CHECKS FOR TORSION (units- kN,m):
CLAUSE RATIO LOAD DIST FX VY VZ MZ MY MX
EC-6.2.7(5) 0.100 1 0.0 0.0 52.0 0.0 51.3 0.0 -3.8
Detail Torsion Check [TOR=2]
Normalized Warping function:
Wns = WB/4 = (320-20.5)*300/4 = 22462.5 mm2
Warping Statical Moment: Sw1 = h*B^2*Tf/6 = (299.5*300^2*20.5)/6 = 92096250 mm4
Qfmax = 300/2*20.5*299.5/2 = 460481.25 mm3
Let us take, z=0
For this case, CMT=5.0. So, we will use Case 6 from Appendix B of P057.
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Now, TEd = Tt, Ed + Tw, Ed= GJφ’ – EHφ’’’
Torsion Component: GJφ’ = 0
Warping component: EH φ’’’ = 205000*2.069*10^12*(-8.841*10^-12) = -3.749 KN-M
Therefore, TEd = 3.749 KN-M
Torsional Resistance TRd = Tt, Rd+ Tw, Rd
Now, Tt, Rd = (fy/√3)/ Γm0*J/t = (275/√3)*225.1*10^4/20.5 = 17.43 KN-M
And Tw, Rd = (fy/ Γm0)* t * b2 / 6 = 275*20.5*300^2/6 = 84.56 KN-M
TRd = 101.99 KN-M
Now, Tt, Ed / Tt, Rd = 0/17.43 = 0 <1 OK
Tw, Ed / Tw, Rd= 3.749/84.56 =0.044<1 OK
Check for Cl. 6.2.7(1):
Ratio = 0.044 OK.
Check for Cl. 6.2.7(9):
The current version of EC-3 in STAAD.pro checks for shear resistance of a section based on Cl. 6.2.6 and the plastic shear resistance (in the absence of torsion) is worked out as:
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Where Av = Shear Area = 51.728*100 mm2 here.
For I or H Sections:
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Now, Ratio = VEd/Vpl, T, Rd= 52/821.29 =0.063<1
STAAD.Pro value is 0.063, hence OK.
Check for Cl. 6.2.7(5):
The stress check will be performed using equation 6.1 of EN 1993-1-1:2005 as given below:
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Therefore, the Ratio acc. To Cl. EC-6.2.7(5) is 0.035
STAAD.Pro value is 0.035, hence OK.
Check for Cl. EC: 6 - A.1:
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STAAD.Pro value is 0.128[OK]
STAAD OUTPUT (TOR=2):
TORSION CALCULATIONS (units - kN,m)
Total Torsional Load T = -7.5
Effective Length for Torsion = 4.000
END1: Torsion Fixed, Warping Fixed END2: Torsion Fixed, Warping Fixed
Max. section forces & capacities: [@ x = 0.000](units - kN,m)
Torsion at section = 3.8
Pure Torsion Component = 0.0
Warping Torsion Component = -3.8
Pure Torsion Capacity = 17.4
Warping Torsion Capacity = 84.6
Total Torsion Capacity = 102.0
ADDITIONAL CLAUSE CHECKS FOR TORSION (units- kN,m):
CLAUSE RATIO LOAD DIST FX VY VZ MZ MY MX
EC-6.2.7(1) 0.044 1 0.0 0.0 52.0 0.0 51.3 0.0 3.8
EC-6.2.7(9) 0.063 1 0.0 0.0 52.0 0.0 51.3 0.0 3.8
EC-6.2.7(5) 0.035 1 0.0 0.0 52.0 0.0 51.3 0.0 3.8
EC:6 - A.1 0.128 1 0.0 0.0 52.0 0.0 51.3 0.0 3.8
COMPARISON REPORT:
| Clause | Ratio |
| STAAD.Pro | Hand Calculation | % Deviation |
| EC-6.2.7(1) | 0.044 | 0.044 | 0 |
| EC-6.2.7(9) | 0.063 | 0.063 | 0 |
| EC-6.2.7(5) | 0.035 | 0.035 | 0 |
| EC:6 - A.1 | 0.128 | 0.1282 | 0 |
