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Sample Problem : I Beam Buckling Calculations

A structure
with mass of 110 kg will be carried by two I-beams as shown in the figure. I-beams are so located that center of mass of structure
remain just at the center between two beams. The height of the I-beam is 1 meter and cross sectional dimensions
of I-beam are also given in the figure.
If the design factor of the I beam is taken as 3, what is the factor of safety
of I- beams ?
(Assume that all the mass of structure is concentrated at Cog). The material of
the I-beam is ASTM A572 steel with yield strength of 290 MPa and elastic modulus
of 140 GPa. I beams are fixed to ground and structure so end conditions are
fixed-fixed.

##### Solution:

## Step 1 : Write down input parameters (including material properties) which are
defined in the sample example.

The force due to the mass of the structure can be calculated by F=m*a. So
F=110*9.81=1079.1 N. Since there are two columns, the force per column is
1079.1/2=539.55 N

INPUT PROPERTIES SUMMARY |

Parameter |
Symbol |
Value |
Unit |

Width of Column |
B |
76 |
mm |

Flange Thickness |
h |
7.6 |
mm |

Web Thickness |
b |
4 |
mm |

Flange-flange inner face height |
H |
119 |
mm |

Length of Column |
L |
1 |
m |

Design factor |
n_{d} |
3 |
--- |

Eccentricity |
e |
2 |
m |

Applied Force |
P |
539.55 |
N |

End Condition |
Fixed-Fixed |

Yield Strength (A572 Steel) |
Sy |
290 |
MPa |

Elastic modulus(A588 Steel) |
E |
140 |
GPa |

Density(A204 Steel) |
ρ |
7.85 |
g/cm^{3} |

## Step 3 : Cross sectional properties of round column are needed for compression
calculations. To calculate cross sectional properties, go to "Sectional
Properties Calculator" page and select "I Beam".

## Step 4 : Calculate cross-sectional area and second moment of area by using
the values summarized in step 1.

## Step 5 : Go back to "Compression Member Design" page and calculate
factor of safeties for x-x and y-y direction by using parameters given in step 1 and step 4.

According to calculations, factor of safety is calculated as 3.92
(minimum value) and this value
is larger than design factor(3). According to input parameters, the columns can
carry the structure.

#####
Summary

The problem is completely solved with calculators which are summarized as
follows.