Slender Web I Section Design - Staad Verification Problem

 

International Design Codes

800:2007 :2007 Indian Codes - Steel Design per IS 800 11F.2.2 Section Classification

The IS 800: 800: 2007 specification allows inelastic deformation of section elements. Thus local  buckling becomes an important criterion. Steel sections are classified as Plastic, Compact, Semi-Compact, or Slender  element  element sections depending upon their local buckling characteristics. is a  a function of the geometric properties of the section as well as nature of This classification is the load applied to the member. The design procedures are different depending on the section class. STAAD is capable is capable of determining the section classification for the standard shapes and design the section for the critical load case accordingly. The Section Classification is done is done as  per section 3.7 of IS 800 800:2007 :2007 and Table B2, for Outstanding and Internal Elements of a section. For the criteria for being included in those classes, clas ses, refer to secti section on 3.7.2-(a) –  (d)  (d) of the code. Slender Sections  Sections Slender

is capable  capable of designing I-Sections with slender webs for webs for IS 800 800:2007. :2007. STAAD.Pro is This feature requires STAAD.Pro V8i (SELECTseries 3) (release 20.07.08) or higher. The IS: IS:800-2007 800-2007 code does not provide any clear guidelines about what method should be adopted for the design of slender  section.  section. The "Flange Only" methodology is used is used where it is  is  web will resist shear with adequate assumed that flexure is taken is taken by the flanges alone and the web will shear buckling resistance. This method requires that the flanges be non-slender  non- slender  elements  elements (i.e., on the web is a is a slender  element)  element) to qualify for a valid vali d section for design. If any of the flange elements become slender , the design will not be performed and a warning message is  is  displayed in the output. International Design Codes

Indian Codes - Steel Design per IS 800:2007 800: 2007 11F.6 Verification Example Calculate compressive strength, bending strength, and shear strength of laterally supported  plate girder 800-6-200-10 given given Fy = 250 MPa and Fu = 420 MPa. Check per p er the IS800: 2007 Limit State Design methodology. 11F.6.1 Solution

 

Material properties: E = 2.05(10)5 MPa This is the default value of the modulus of elasticity elas ticity for steel used b by y STAAD.Pro. IS 5 800:2007 specifies that a modulus of 2.0(10)  MPa should be used.

μ = 0.3  G = E/2.0(1 + μ) = 78,846 MPa  Cross sectional properties: Ag = 800·6 + 2·(200·10) = 8,800 mm2  Izz = 912.1(10)6 mm4  Iyy =13.35(10)6 mm4  R yy yy = √(Iyy ⁄Area) = 38.95 mm R zz = √(Izz ⁄Area) = 321.95 mm  Force: Fx = 19.644 kN (Compression) Fy = 1.2 kN Fz = 2.0 kN Mx = 0.0 kN·m My = 10.0 kN·m Mz = 51.659 kN·m Section Classification

Flange:  b = (bf  - tw)/2 = (200 - 6)/2 = 97 mm

εf  = √(250/f y) = √(250/250) = 1.0   b/tf  = 97/10 = 9.7 >

9.4·ε, < 13.6·ε 

Thus, the flange is considered semi-compact. Web: Web:

 

r 2 = (Fx/Area)/f y = (19,644 / 8,800)/250 = 0.0089

> 42·ε = 42(1.0) = 42  d/tw = 800/6 = 133.33 > 123.8 Thus, the web is web is considered slender . The overall section is classified as slender . Calculation of compressive strength

 Net area of section: Ae= Ag - (d/t w - 42.0·ε) · tw2 = 8,800 - [133.33 - 42.0(1.0)]·(6) 2 = 5,512. mm2  Slenderness Slenderness ratio:  ratio:

(k yL/R y) = 0.33·(5,000) / 38.95 = 42.36 (k zL/R z) = 1.0·(5,000) / 321.95 3 21.95 = 15.53 Euler buckling stress (per Cl.7.1.2.1 of IS 800:2007):

 Non-dimensional effective slenderness ratio: slenderness ratio:

Imperfection factor, is equal to 0.49 class is c as T f  < 40.0 mm and buckling is about YY axis (perα,Table 7 and Tableand 10 buckling in IS 800:2007). Partial factor of safety γmo = 1.10 Per Cl.7.1.2.1 of IS 800:2007:

ϕ = 0.5[1 + α(λ - 0.2) + λ2] = 0.5[1 + 0.49(0.471 - 0.2) + (0.471)2] = 0.677 Stress reduction factor, χ  

 

f cd cd = χ·(f y/γmo) = 0.86·(250 / 1.1) = 195.5 MPa Design compressive strength (per Cl.7.1.2 of IS 800:2007): Pd = Ae·f ccdd = 5,512.·(195.5) = 1,077 kN Calculation of bending strength

web is  is slender  and  and hence it is disregarded in bending strength calculation. The web

Zez = Iz/(820/2) =656.1(10)6/410 = 1.60(10)6 mm3  Iy =2(10)(200)3 ⁄12 = 13.33(10)6 mm4  Zey = Iy ⁄(0.5×Bf ) = 13.33(10)6/(0.5×200) = 133,333 mm 3  Ixx = 2(Bf  · Tf 3/3.0) = 2.0[(200)(10)3/3.0] = 133.333(10)3 mm4  For laterally supported beam: Mdz = Zez · Fy/γmo = 1.60(10)6(250)/1.10 = 364 kN·m Mdy = Zey · Fy/γmo =133,333(250)/1.1 = 30.3 kN·m For laterally unsupported beam: Warping constant: Iw = (d + Tf )2 · Bf 3 · Tf /24.0 = (800 + 10) 2 · 2003 · 10/24.0 = 2.187(10)12 mm6  Elastic lateral torsional buckling moment (per Cl.8.2.2.1 of IS 800:2007): LLT = 5,000 mm

αLT = 0.49 for welded steel section per Cl.8.2.2 of IS 800:2007 ϕLTZ = 0.5×[1 + αLT (λLTZ - 0.2) + λLTZ2 ] = 1.13

f  bdz = (χ LTZ LTZ· Fy) ⁄ γmo = 0.574(250)/1.1 = 130.4 MPa

 

Mdz = Zez· f  bdz = 1.6(10)6(130.4) = 208.6 kN·m MdY = (Zey· Fy) / γmo = 133,333(250)/1.1 = 30.30 kN·m Calculation of shear strength

c = spacing of stiffener = 1000 mm d = depth of web = web = 800 mm c/d = 1000/800 = 1.25 > 1.0 Hence, per Cl.8.4.2.2.(a): k v = 5.35 + 4.0/(c/d)2 = 7.91 d/Tw = 800/6 = 133.33

Since, d/Tw > 67√(k v ⁄5.35), shear strength is governed governed by shear buckling.  Elastic critical stress of the web  web 

 Non-dimensional web slenderness ratio slenderness ratio for shear buckling stress:

Hence

Shear force corresponding to shear buckling = Av · τ b 

11F.6.2 Comparison

Table 11F.2-IS 800:2007 Verification Problem 1 Item Compressive Compr essive

Reference Reference STAAD.Pro Difference 1,077 1,077 1.076(10) 1.076(10) Negligible Negligible

 

Table 11F.2-IS 800:2007 Verification Problem 1 Item Reference Reference STAAD.Pro Difference Strength, Pd (kN) Major Axis Bending Strength, Mdz  (kN·m) 208.6 208.681 Negligible (Laterally unsupported) Minor Axis Bending Strength, Mdy (kN·m) (Laterally unsupported) Major Axis Shear Strength, VcrY (kN) MInor Axis Shear Strength, VcrZ (kN)

30.30

30.303

Negligible

359.5

359.732

Negligible

300.0

299.776

Negligible

11F.6.3 STAAD Input File

STAAD SPACE START JOB INFORMATION ENGINEER DATE 22-Oct-08 END JOB INFORMATION INPUT WIDTH 79 UNIT METER KN JOINT COORDINATES 1 0 0 0; 2 0 5 0; 3 5 5 0; MEMBER INCIDENCES 1 1 2; 2 2 3; 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 START USER TABLE TABLE 1 UNIT METER KN WIDE FLANGE SLEND   SLEND 0.0088 0.82 0.006 0.2 0.01 0.000912133 1.33477e-005 1.90933e-00 1.90933e-007 7 0.00492 0.004 END MEMBER PROPERTY AMERICAN 1 UPTABLE 1 SLEND  SLEND  MEMBER PROPERTY INDIAN 2 TABLE ST ISMB500 CONSTANTS MATERIAL STEEL ALL SUPPORTS 1 FIXED LOAD 1 LOADTYPE None TITLE LOAD CASE 1 JOINT LOAD 3 FY -2 MEMBER LOAD 2 UNI GY -2 JOINT LOAD

 

2 FX 1.2 2 FZ -2 SELFWEIGHT Y -1 ALL PERFORM ANALYSIS PRINT SUPPORT REACTION PRINT MEMBER FORCES PARAMETER 1 CODE IS800 LSD CAN 0 MEMB 1 ky 0.33 all stp 2 all TST 1 MEMB 1 TSP 1 MEMB 1 ***Laterally Unsupported**** *LAT 1 all TRACK 2 MEMB 1 CHECK CODE MEMB 1 PARAMETER 2 CODE IS800 LSD CAN 0 MEMB 1 ky 0.33 all stp 2 all TST 1 MEMB 1 TSP 1 MEMB 1 ***Laterally supported****

 

LAT 1 all TRACK 2 MEMB 1 CHECK CODE MEMB 1 FINISH 11F.6.4 Output

TRACK 2.0 output for the Laterally Laterall y unsupported check STAAD.PRO CODE CHECKING - IS-800 2007 (V2.0) ************************************************ |---------------------------------------------------------------------------------| | Member Number: 1 | SLEND    (UPT) | Member Section: ST SLEND | | Status: PASS Ratio: 0.401 Critical Load Case: 1 Location: 0.00 | | Critical Condition: Sec. 9.3.1.1 |

|

Cr itical Design Forces: Critical

(Unit: KN

METE)

| | FX: 19.644E+00 C FY: -1.200E+00 FZ: 2.000E+00 | | MX: 0.000E+00 MY: -10.000E+00 MZ: 51.659E+00 | |---------------------------------------------------------------------------------| | Section Properties: (Unit: CM ) | | AXX: 88.000E+00 IZZ: 91.213E+03 RZZ: 32.195E+00| | AYY: 48.000E+00 IYY: 1.335E+03 RYY: 3.895E+00| | AZZ: 40.000E+00 IXX: 19.093E+00 CW: 2.187E+06| | ZEZ: 2.225E+03 ZPZ: 2.580E+03 | | ZEY: 133.477E+00 ZPY: 207.200E+00 | |---------------------------------------------------------------------------------| Slenderness   Check: (Unit: METE) | Slenderness | | Actual Length: 5.000E+00 | | Parameters: LZ: 5.000E+00 LY: 5.000E+00 | | KZ: 1.000 KY: 0.330 | | Actual Ratio: 42.37 Allowable Ratio: 180.00 LOAD: 1 FX: 19.644E+00 C | |---------------------------------------------------------------------------------|

 

Slender; ; Flange Class: Semi-Compact; Web Web Class:  Class:  | Section Class: Slender Slender Slender |  | |---------------------------------------------------------------------------------| STAAD.PRO CODE CHECKING - IS-800 2007 (V2.0) ************************************************ |---------------------------------------------------------------------------------| | Member Number: 1 ||

Member Section:

ST

SLEND    SLEND

(UPT)

| |---------------------------------------------------------------------------------| | Tension: (Unit:KN METE) | | Parameters: FYLD: 250.000E+03 FU: 420.000E+03 | | NSF: 1.000 ALPHA: 0.800 DBS: 0 | | Capacity: 2.000E+03 As per sec. No.:Cl. 6.2 | | Actual Design Force: 0.000E+00 LC: 0 | |---------------------------------------------------------------------------------| |

Compression:

(Unit:KN

|

Buckling Class:

|

Capacity:

|

Actual Design Force:

METE)

| Major: b

Minor: c

As per Sec. No.:Cl. 7.1.2.2

| 1.076E+03

As per sec. No.:Cl. 7.1.2

| 19.644E+00

LC:

1

| |---------------------------------------------------------------------------------| | Shear: (Unit:KN ) | | Major Axis: Actual Design Force: -1.200E+00 LC: 1 Loc: 0.000E+00| | Capacity: 359.732E+00 As per sec. No.:Cl. 8.4.2 | | Minor Axis: Actual Design Force: -2.000E+00 LC: 1 Loc: 0.000E+00| | Capacity: 299.776E+00 As per sec. No.:Cl. 8.4.2 | |---------------------------------------------------------------------------------| | Bending: (Unit:KN METE) | | Parameters: Laterally Unsupported KX: 1.00 LX: 5.000E+00 General | | Major Axis: Actual Design Force: 51.659E+00 LC: 1 Loc: 0.000E+00| | Capacity: 208.681E+00 As per sec. No.:Cl. 8.2.2 | | Minor Axis: Actual Design Force: -10.000E+00 LC: 1 Loc: 0.000E+00| | Capacity: 30.303E+00 As per sec. No.:Cl. 8.2.1.1 |

 

  |---------------------------------------------------------------------------------| | Combined Interaction: | | Parameters: PSI: 1.00 C CMX: MX: 0.900 CMY: 0.900 CMZ: 0.900 | | Interaction Ratio: 0.401 As per sec. No.:Sec. 9.3.1.1 | | LC: 1 Loc: 0.000E+00 ||---------------------------------------------------------------------------------| | Checks | | | | Tension | | Compression | | Shear Major | | Shear Minor | | Bend Major |

Ratio

Load Case No.

Location from Start

0.000

0

0.000E+00

0.018

1

0.000E+00

0.003

1

0.000E+00

0.007

1

0.000E+00

0.248

1

0.000E+00

|

Bend Minor

0.340

1

0.000E+00

|

Sec. 9.3.1.1

0.401

1

0.000E+00

|

Sec. 9.3.2.2 (Z)

0.210

1

5.000E+00

|

Sec. 9.3.2.2 (Y)

0.233

1

5.000E+00

| | | | |---------------------------------------------------------------------------------|

TRACK 2.0 output for the laterally supported check STAAD.PRO CODE CHECKING - IS-800 2007 (V2.0) ************************************************ |---------------------------------------------------------------------------------| | Member Number: 1 | SLEND    (UPT) | Member Section: ST SLEND | | Status: PASS Ratio: 0.360 Critical Load Case: 1 Location: 0.00 | | Critical Condition: Sec. 9.3.1.1 | | Critical Cr itical Design Forces: (Unit: KN METE) | | FX: 19.644E+00 C FY: -1.200E+00 FZ: 2.000E+00 | | MX: 0.000E+00 MY: -10.000E+00 MZ: 51.659E+00 | |---------------------------------------------------------------------------------|

 

 | Section Properties: | | AXX: 88.000E+00 32.195E+00| | AYY: 48.000E+00 3.895E+00| | AZZ: 40.000E+00 2.187E+06| | ZEZ: 2.225E+03 ||

ZEY:

133.477E+00

(Unit:

CM

)

IZZ:

91.213E+03

RZZ:

IYY:

1.335E+03

RYY:

IXX:

19.093E+00

CW:

ZPZ:

2.580E+03

ZPY:

207.200E+00

| |---------------------------------------------------------------------------------| Slenderness   Check: (Unit: METE) | Slenderness | | Actual Length: 5.000E+00 | | Parameters: LZ: 5.000E+00 LY: 5.000E+00 | | KZ: 1.000 KY: 0.330 | | Actual Ratio: 42.37 Allowable Ratio: 180.00 LOAD: 1 FX: 19.644E+00 C | |---------------------------------------------------------------------------------| Slender; ; Flange Class: Semi-Compact; Web Web Class:  Class: | Section Class: Slender Slender Slender |  | |---------------------------------------------------------------------------------| STAAD.PRO CODE CHECKING - IS-800 2007 (V2.0) ************************************************ |---------------------------------------------------------------------------------| | Member Number: 1 | SLEND    (UPT) | Member Section: ST SLEND | |---------------------------------------------------------------------------------| | Tension: (Unit:KN METE) | |

|

Parameters:

FYLD:

250.000E+03

FU:

420.000E+03

| NSF: 1.000 ALPHA: 0.800 DBS: 0 | | Capacity: 2.000E+03 As per sec. No.:Cl. 6.2 | | Actual Design Force: 0.000E+00 LC: 0 | |---------------------------------------------------------------------------------| | Compression: (Unit:KN METE) | | Buckling Class: Major: b Minor: c As per Sec. No.:Cl. 7.1.2.2 | | Capacity: 1.076E+03 As per sec. No.:Cl. 7.1.2 | | Actual Design Force: 19.644E+00 LC: 1 |

 

  |---------------------------------------------------------------------------------| | Shear: (Unit:KN ) | | Major Axis: Actual Design Force: -1.200E+00 LC: 1 Loc: 0.000E+00| | Capacity: 359.732E+00 As per sec. No.:Cl. 8.4.2 | | Minor Axis: Actual Design Force: -2.000E+00 LC: 1 Loc: 0.000E+00| | Capacity: 299.776E+00 As per sec. No.:Cl. 8.4.2 | |---------------------------------------------------------------------------------| | Bending: (Unit:KN METE) | | Parameters: Laterally Supported KX: 1.0 1.00 0 LX: 5. 5.000E+00 000E+00 General | | Major Axis: Actual Design Force: 51.659E+00 LC: 1 Loc: 0.000E+00| | Capacity: 363.710E+00 As per sec. No.:Cl. 8.2.1.1 | | Minor Axis: Actual Design Force: -10.000E+00 LC: 1 Loc: 0.000E+00| | Capacity: 30.303E+00 As per sec. No.:Cl. 8.2.1.1 | |---------------------------------------------------------------------------------| | Combined Interaction: | | Parameters: PSI: 1.00 C CMX: MX: 0.900 CMY: 0.900 CMZ: 0.900 | | Interaction Ratio: 0.360 As per sec. No.:Sec. 9.3.1.1 | | LC: 1 Loc: 0.000E+00 | |---------------------------------------------------------------------------------| | Checks Ratio Load Case No. Location from Start | | | |

|

Tension

0.000

0

0.000E+00

|

Compression

0.018

1

0.000E+00

|

Shear Major

0.003

1

0.000E+00

|

Shear Minor

0.007

1

0.000E+00

|

Bend Major

0.142

1

0.000E+00

|

Bend Minor

0.340

1

0.000E+00

|

Sec. 9.3.1.1

0.360

1

0.000E+00

|

Sec. 9.3.2.2 (Z)

0.126

1

5.000E+00

|

Sec. 9.3.2.2 (Y)

0.141

1

5.000E+00

| | | | | | | |

 

  |---------------------------------------------------------------------------------|