HW7 Tips and Answers


HW7.1

We know that the horizontal force will result in a downward component on the tube because of the angle of the guy wire.  The horizontal force is balanced by an equal and opposite horizontal component of the tension in the guy wire.  Just by looking at the geometry, you can see that a 6 Lb horizontal force will result in a 15 lb vertical force on the tube.

At what load will the tube buckle?  Depends on its slenderness ratio.  From the Modulus and Yield Strength, the Transition Slenderness Ratio is 117.4.  The Radius of Gyration of the tube is 0.80 in.  The tube is pinned-pinned, so its slenderness ratio is 224.9.  So we use the Euler equation to get its buckling load as 10,346 Lb.

A 3000 Lb horizontal force will result in a FOS of 1.38 against buckling of the tube.



HW7.2

The Transition Slenderness Ratio for this column material is 116.7.  The Rg of the column is 12.5mm and the fixed-free slenderness ratio is 320, so we treat it as an Euler column and get a buckling load of 39.2kN.
For a FOS of 2 against buckling, the load would be just half of the buckling load.
If the column is fixed-fixed, its slenderness ratio becomes 80 which is below the Transition Ratio and we analyze it with the Johnson equation.  We calculate the Critical Stress and multiply it by the cross section area of the column to get a Critical Load of 450.6kN.