Incorrect Static Indeterminancy?

[StructureMan44]

While attempting to refamiliarize myself with the fundamentals I found this document online for understanding the conjugate beam method.

http://comp.uark.edu/~icjong/docu/Guiding.Rules.in.CBM.pdf

On the top of page two there is a beam with fixed end conditions and a hinge. The paper says the beam is statically indeterminate to the first degree. This didn't seem right. Pulling out my Hibbeler structural analysis book from way back in college, it states that a structure is statically indeterminate if r > 3n where r=(force or moment components) and n=(# of parts). Furthermore, it states the degree of indeterminacy is r-3n, or the number of additional equations needed to solve for the unknown reactions.

Comparing this equation to the beam on page 2 of the link above, I get r = 8 (3 reactions at each end point and 2 reactions (x & y direction) at the hinge) and n =2. So I have 8-3(2) = 2 or the beam is statically indeterminate to the second degree.

The paper says this is first degree while Hibbeler seems to suggest it is second degree. To the experts here, which is correct?

 

[BAretired]

If you disregard the possibility of a horizontal reaction at the hinge, it is indeterminate to the first degree. You have two cantilever beams, each of which is determinate if not joined together at point B. The only indeterminate force is the vertical reaction at point B, the hinge.

If the two beams are sloping or if you wish to consider the horizontal reaction due to the deflection of the two cantilevers, there are two unknown forces, the horizontal and vertical reaction at point B. In that case, the structure is indeterminate to the second degree.

BA

 

[MacGruber22]

Yeah, often zero force reactions are disregarded in the indeterminacy.

 

[IDS]

Or replace the left hand cantilever with a spring with the same stiffness to vertical loads as the tip of the cantilever. It is clear then that there is only one redundant force.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[StructureMan44]

Thanks a lot folks