Initially Straight Column with an Eccentric Load


This applet uses the secant formula to calculate the maximum displacement and stress in an eccentrically loaded column.

Values should be typed into the top 9 input fields using the units shown. Large numnbers can be entered using engineering notation, ie: 5461300 can be entered as 5.4613e6.
The input field yMax is for the maximum distance to the surface on the compression side of the column from the neutral surface of the column in the plane of bending.
Recommendations for end factors for structural steel columns can be found in specialist publications by civil engineering bodies. The 4 fields adjacent to and lower than the 'Calculate' button are for results, in the units shown. The maximum displacement is with respect to the original straight centre line of the column.

The field by the 'Calculate' button will normally remain empty unless the maximum displacement is negative or the maximum displacement is more than half of the column length. If either of these occur then the word 'Fail' appears in this field indicating that the specified column is not suitable for the conditions.
NB. The instruction to display the 'Fail' message takes no account of the maximum stress calculated and the yield strength of the column material. The user must check the maximum compressive stress shown with the capabilities of the material of the column.

NB The results shown in the three fields below the 'Calculate' button should be checked by running the cursor to the end of the figures to check for an 'E' with further digits!

Each time the applet is run the input values and the results (with the exception of the 'Fail' message) are added to the 'History' areas on the right. This is to facilitate keeping track of making changes and running the applet again several times.

When large numbers containing a lot of digits need to be displayed in the 'History' text area columns for 'Load', 'Second moment of area' and 'Area', scroll bars appear at the foot of these columns to enable the full numbers to be seen.

The 'Design Factor' or 'Factor of Safety', (fos) is applied to the load when calculating the maximum displacement and the maximum compressive stress. It should be noted that the nature of the secant formula means that the effect of the design factor on the results is non linear and can be very strongly non linear near the load that gives instability and negative displacements.
Dr David J Grieve, 28th April 2011.