| Applies To | |||
| Product(s): | STAAD.Pro | ||
| Version(s): | All | ||
| Environment: | N/A | ||
| Area: | Steel Design | ||
| Subarea: | Verifications | ||
| Original Author: | Shayn Roy Bentley Technical Support Group | ||
Validation Problem on Reduced Moment Capacity as per CL6.2.8 of EN 1993-1-1:2005.
1. Introduction:
The following is a validation problem for the EN 1993-1-1:2005 implementation in STAAD.Pro which shows Staad calculating the Reduced Moment of Resistance as per clause 6.2.8(3). The reduction is applicable when the applied Shear Force exceeds half the plastic shear resistance as per clause 6.2.8(2)
2. EN 1993-1-1:2005 clause reference:
Clause 6.2.8(2) states that if shear force is less than half the plastic shear resistance , then its effect on the moment resistance may be neglected , otherwise Clause 6.2.8(3) has to followed .
Clause 6.2.8(3) states that reduced moment resistance should be taken as the design resistance of the cross section, calculated using reduced yield strength (1-ρ) fy for the shear area where
ρ = (2 V Ed / V pl, Rd -1) ²
3. Validation Problem:
A British I section beam (UB 406x178x74, S275 grade steel) , 4 m long fixed at both the ends has been subjected to a uniformly distributed load of 1 KN/m and a concentrated point load 900 KN at the midpoint.
Maximum Shear Force (VY) is 452KN and the maximum Bending Moment (Mz) is 451.33 KNm
If the developed Shear Force is greater than half the plastic Shear Resistance, then Moment Capacity Reduction will be done as per CL 6.2.8 (3).
3.1 . Text Input Information.
The following is the text input information of the Staad model:
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 01-Feb-10
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 BRITISH
1 TABLE ST UB406X178X74
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 -900 2 0
PERFORM ANALYSIS
PRINT MEMBER FORCES
LOAD LIST 1
PARAMETER 1
CODE EN 1993-1-1:2005
SGR 1 ALL
EFT 4 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
3.2 . Manual Calculation:
Section: UB 406x178x74
Sectional Properties as per Bluebook
A = 94.5 cm²
b = 179.5 cm
t f = 16 mm
t w = 9.5 mm
r = 10.2 mm
As per CL 6.2.6.3
Shear Area: A v = A – 2 .b. t f + (t w + 2r). t f
A v = (94.5 x 100) – (2 x 179.5 x 16) + (9.5 + 2 x 10.2) x 1
= 4184.4 mm² = 41.84 cm ²
Shear Resistance of the section (along Y axis) VplRd,y= [(41.84e2 x 275 /√3)/1.0/]1000 = 664.4KN
VY > 0.5x VplRd,y . Hence moment capacity reduction is applicable
Now, for calculating the reduced moment capacity:
Note: Section is a Class1 section. Hence will use the plastic section modulii for calculating the moment capacities.
Reduced Moment Capacity = [[Section Modulus of Non Shear Area (SM1) x fy] + [Section Modulus of
Shear Area (SM2) x (1-ρ) fy]] / ɣ M
Plastic Section Modulus = 1500000 mm³ (as reported by Staad)
SM = SM1 + SM2
And, Total Area = Non Shear Area + Shear Area
Non-Shear Area = 9450 – 4184.4 = 5265.6 mm ²
SM 1 = Non Shear Area x Centroidal distance (y 1) (Please refer figure for y1)
= 5265.6 x 198.4 = 1044695 mm³
SM 2 = SM – SM1 = 1500000-1044695 = 455305 mm ³
As per CL 6.2.8 .3,
ρ = (2 V Ed / V pl, Rd -1) ²
= (2 x 452 / 664.4 - 1) ² (For 452 and 664.4, kindly see the Staad Output file)
= 0.13
So Reduced Moment Capacity
= (SM 1 x fy + SM 2 x (1-ρ) fy) / ɣ M
= 1044695 x 275 + 455305 x (1-0.13) x 275 (fy = 275 N / mm ³, ɣ M = 1)
= 396.23 KNm (As reported by Staad)
Note: A similar capacity reduction is applicable for the bending moment capacity about the y-y axis
3.3. STAAD Output
You may download this validation example from: