Strength of materials (Euler Theory)

1. Jul 26, 2011

defdek

A bar of length 4m when used as simply supported beam and subjected to a uniform distribution load of 30kN/m over whole span, deflects 15 mm at the center. Determine the crippling loads when it is used as a column with following end conditions.
a)both ends pin-jointed
b)One end fixed and other hinged
c)Both ends fixed

E=(5wl^4)/(348 x inertia x change in length)

So the formula i can use for all the questions is:
P=[ (pi^2)[(5wL^4)/(348 x change in length x inertia)](inertia) ]/L^2

?

2. Jul 26, 2011

the_red_jeste

you are right in your equation for E for a simply supported beam with u.d.l. What is your section profile? rectangular? circular? since you will need a value for the stiffness I

You also need to calculate your radius of gyration about each principle axis of stress (x-x & y-y)
R=SQRT(Section Inertia/Section Area)
this will give you an indication of the column classification and thus failure type as to whether it is slender/intermeditate/short. Short columns tend to kneel -inelastic buckling c.f slender which elastically buckle.

you have different boundary conditions/end conditions for the column so your second equation for P is invalid for cases b & c.

3 types
a - simple supported
b - propped cantilever
c - fully built in

you are talking about crippling loads so this would imply the max. load possible without complete failure of the bar (ie. the bar has buckled but can still carry the load)
the hinge point for failure will be different in each 3 cases given the different boundary conditions.

(Have you covered Euler's Theory of Column Buckling?) if not then I suggest you treat each of the three cases as a beam/column and apply standard beam fomulae to the three cases with a lateral load u.d.l on the column/beam

I hope this helps get you started