##### 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.

## 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 nd 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/cm3

## 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.

 Calculator Usage Column Buckling and Compression Member Design To calculate column factor of safety for given parameters. In this example, column is classified as strut or short column with eccentric loading and stress equations have been used. Sectional Properties Calculator To calculate sectional properties of standard profiles. In this example, I-beam has been calculated.