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V. BS5950 2000 - Unrestrained Simply Supported Beam

Design of a 9 m, unrestrained beam with end moments.

Reference

Steelwork Design Guide to BS 5950-1:2000, Volume 2, Worked Examples, SCI publication P326, Example 3, The Steel Construction Institute.

Problem

Intermediate point loads are applied to the bottom flange. These do not provide restraint against lateral-torsional buckling. The beam is designed in S275 steel.

Dead Loads, γfd = 1.4:

  • Selfweight ws = 3 kN/m
  • Point Load W1d = 40 kN
  • Point Load W2d = 20 kN

Imposed Loads, γfi = 1.6:

  • Point Load W1i = 60 kN
  • Point Load W2i = 30 kN

Comparison

Table 1. Comparison of results
Result Type Theory STAAD.Pro Difference
Shear capacity, Pv (kN) 636 635.9 none
Moment capacity, Mcx (kN-m) 404 404.5 none
Lateral-torsional buckling capacity, Mb (kN-m) 150 150.26 none

STAAD Input

TRACK 2 ALL
Maximum detail output
MLT 0.46ALL
Specifies the mLT value to use in the lateral-torsional buckling calculations
UNI 6.3 ALL
Specifies the lateral-torsional buckling length to be used
Tip: You can copy and paste this content directly into a .std file to run in STAAD.Pro.

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\UK\BS5950 2000\BS5950 2000 - Unrestrained Simply Supported Beam.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
JOB NAME Example no. 3
JOB CLIENT The Steel Construction Institute
JOB COMMENT Unrestrained beam with end moments
ENGINEER DATE Jun-2003
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 3 0 0; 3 6 0 0; 4 9 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
*************************************
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY BRITISH
1 TO 3 TABLE ST UB457X191X67
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 4 FIXED
*************************************
LOAD 1 DEAD
JOINT LOAD
2 FY -40
MEMBER LOAD
1 TO 3 UNI GY -3
UNIT MMS KN
JOINT LOAD
3 FY -20
UNIT METER KN
LOAD 2 LIVE
JOINT LOAD
2 FY -60
UNIT MMS KN
JOINT LOAD
3 FY -30
UNIT METER KN
LOAD COMB 100 COMBINATION LOAD CASE 3
1 1.4 2 1.6 
PERFORM ANALYSIS PRINT STATICS CHECK
***************************************
PARAMETER 1
CODE BS5950
TRACK 2 ALL
MLT 0.46 ALL
UNL 6.3 ALL
CHECK CODE ALL
FINISH
***************************************

STAAD Output

                         STAAD.Pro CODE CHECKING - (BSI )
                         ***********************
  PROGRAM CODE REVISION V2.13_5950-1_2000
      STAAD SPACE                                              -- PAGE NO.    5
 ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       1 ST UB457X191X67  PASS     BS-4.3.6           0.861       100
                         0.00            0.00         280.96        0.00
 =======================================================================
   MATERIAL DATA                
      Grade of steel           =  S 275
      Modulus of elasticity    =  205 kN/mm2  
      Design Strength  (py)    =  275  N/mm2  
   SECTION PROPERTIES (units - cm)
      Member Length =    300.00
      Gross Area =   85.50  Net Area =   85.50  Eff. Area =   85.50
                                    z-z  axis       y-y  axis
      Moment of inertia        :    29400.002        1450.000
      Plastic modulus          :     1470.000         237.000
      Elastic modulus          :     1296.868         152.712
      Effective modulus        :     1470.000         237.000
      Shear Area               :       43.411          38.539
   DESIGN DATA (units - kN,m)   BS5950-1/2000
      Section Class            :   PLASTIC     
                                    z-z  axis       y-y  axis
      Moment Capacity          :        404.3           63.0
      Reduced Moment Capacity  :        404.3           63.0
      Shear Capacity           :        716.3          635.9
   BUCKLING CALCULATIONS (units - kN,m)
   (axis nomenclature as per design code)
      LTB Moment Capacity (kNm) and LTB Length (m):   150.11,    6.300
      LTB Coefficients & Associated Moments (kNm):
      mLT =   0.46  :   mx =   0.00   :  my =   0.00   :  myx =   0.00
      Mlt =  280.96 :   Mx =    0.00  :  My =   0.00   :   My =   0.00
   CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m):
    CLAUSE        RATIO  LOAD     FX       VY      VZ      MZ      MY   
   BS-4.2.3-(Y)   0.238   100      -     151.0      -       -       - 
   BS-4.3.6       0.861   100      -     151.0      -    281.0      - 
    Torsion and deflections have not been considered in the design.
                        _________________________
      STAAD SPACE                                              -- PAGE NO.    6
 ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       2 ST UB457X191X67  PASS     BS-4.3.6           0.470       100
                         0.00            0.00         153.25        0.00
 =======================================================================
   MATERIAL DATA                
      Grade of steel           =  S 275
      Modulus of elasticity    =  205 kN/mm2  
      Design Strength  (py)    =  275  N/mm2  
   SECTION PROPERTIES (units - cm)
      Member Length =    300.00
      Gross Area =   85.50  Net Area =   85.50  Eff. Area =   85.50
                                    z-z  axis       y-y  axis
      Moment of inertia        :    29400.002        1450.000
      Plastic modulus          :     1470.000         237.000
      Elastic modulus          :     1296.868         152.712
      Effective modulus        :     1470.000         237.000
      Shear Area               :       43.411          38.539
   DESIGN DATA (units - kN,m)   BS5950-1/2000
      Section Class            :   PLASTIC     
                                    z-z  axis       y-y  axis
      Moment Capacity          :        404.3           63.0
      Reduced Moment Capacity  :        404.3           63.0
      Shear Capacity           :        716.3          635.9
   BUCKLING CALCULATIONS (units - kN,m)
   (axis nomenclature as per design code)
      LTB Moment Capacity (kNm) and LTB Length (m):   150.11,    6.300
      LTB Coefficients & Associated Moments (kNm):
      mLT =   0.46  :   mx =   0.00   :  my =   0.00   :  myx =   0.00
      Mlt =  153.25 :   Mx =    0.00  :  My =   0.00   :   My =   0.00
   CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m):
    CLAUSE        RATIO  LOAD     FX       VY      VZ      MZ      MY   
   BS-4.2.3-(Y)   0.041   100      -      26.2      -       -       - 
   BS-4.3.6       0.470   100      -      13.6      -    153.2      - 
    Torsion and deflections have not been considered in the design.
                        _________________________
      STAAD SPACE                                              -- PAGE NO.    7
 ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       3 ST UB457X191X67  PASS     BS-4.3.6           0.710       100
                         0.00            0.00         231.74        0.00
 =======================================================================
   MATERIAL DATA                
      Grade of steel           =  S 275
      Modulus of elasticity    =  205 kN/mm2  
      Design Strength  (py)    =  275  N/mm2  
   SECTION PROPERTIES (units - cm)
      Member Length =    300.00
      Gross Area =   85.50  Net Area =   85.50  Eff. Area =   85.50
                                    z-z  axis       y-y  axis
      Moment of inertia        :    29400.002        1450.000
      Plastic modulus          :     1470.000         237.000
      Elastic modulus          :     1296.868         152.712
      Effective modulus        :     1470.000         237.000
      Shear Area               :       43.411          38.539
   DESIGN DATA (units - kN,m)   BS5950-1/2000
      Section Class            :   PLASTIC     
                                    z-z  axis       y-y  axis
      Moment Capacity          :        404.3           63.0
      Reduced Moment Capacity  :        404.3           63.0
      Shear Capacity           :        716.3          635.9
   BUCKLING CALCULATIONS (units - kN,m)
   (axis nomenclature as per design code)
      LTB Moment Capacity (kNm) and LTB Length (m):   150.11,    6.300
      LTB Coefficients & Associated Moments (kNm):
      mLT =   0.46  :   mx =   0.00   :  my =   0.00   :  myx =   0.00
      Mlt =  231.74 :   Mx =    0.00  :  My =   0.00   :   My =   0.00
   CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m):
    CLAUSE        RATIO  LOAD     FX       VY      VZ      MZ      MY   
   BS-4.2.3-(Y)   0.180   100      -     114.8      -       -       - 
   BS-4.3.6       0.710   100      -     102.2      -    231.7      - 
    Torsion and deflections have not been considered in the design.
                        _________________________