Heavy Speaker added on to Railing Post

[rsbmusicguy]

I ran into something the other day and unfortunately don't have access to my physics book right now...

I am doing an analysis on a post where they installed a new speaker system to a railing post. The speaker is very high in the air (big lever arm) and therefore when you push against the post this engages the weight of the speaker above and causes the railing to deflect more than it should.

The additional deflection in the post is a function of the speaker's interia? When I push the post the force transfers to the speaker above which gains interia. This additional force to counteract the inertia is the extra force I need to calculate?

Again, wish I had my physics book handy!

RSB

 

[KootK]

If we're looking at a static analysis, this is probably a classic P-Delta moment amplification problem. If you're studying the dynamics, that will be a trickier.

 

[rb1957]

I didn't think it was PC to call someone (like an orator, or speaker) "heavy" ...

another day in paradise, or is paradise one day closer ?

 

[IRstuff]

gravity challenged?

TTFN (ta ta for now)
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[MegaStructures]

If we’re talking dynamics this is a classic lollipop problem.

The force could only be magnified if there is a forcing function applied to the speaker that could closely match the natural frequency.

If there is a single initial force there’s no way that the resulting force on the post would be any higher than initial, besides the runaway buckling P-D effect KootK mentioned

Edit: The more I read your initial post the more I think you’re talking about excess deflection from a static lateral force, which is explained by increased bending due to the lateral translation at the top AKA P-D

“Any idiot can build a bridge that stands, but it takes an engineer to build a bridge that barely stands.”

 

[HTURKAK]

let me explain what i understand and pls correct me if i am wrong : A speaker installed on a railing post ( say CHS 1.25 in.) having total height say 3,0 m and you push the post from say h=1.5 m. and you observed that the speaker experience additional deflection and this is due to inertia of the speaker is that true?

There are some options for pushing the rod.. If we make further assumptions ; the post material S 235 ,
the section is compact so plastic hinge develop at bottom, and Mp=0.97 kN-m and the force to develop plastic moment is Fp=0.97/1.5=0.65 kN.

- If you push the rod with a force less than 0.65 kN and and apply the force slowly ;
The rod will experience deflection δ= P*H^3 /(3 EI) H is the pushing ht say 1500 mm

The speaker will experience the tip deflection δtip= P*H^3 /(3 EI)+ H*P*H^2 /(2 EI) = 5 P*H^3 /(6 EI) assuming the speake ht is 2H and second order effects neglected..
When you release the rod, the rod will vibrate as simple inverted pendulum with simple harmonic motion .

- If you push the rod with a force around 0.65 kN and and apply the force slowly ; and with further simplification that the rod is rigid plastic , The plastic hinge moment Mp=0.97 kN-m will develop at bottom and the rod experience tip deflection
δtip = θ*2H θ is the plastic rotation of the rod and will be calculated Work = Mp*θ


- If you push the rod with a force around 1.0 kN suddenly, the rod will experience angular acceleration α which can be calculated with Mt= (1-0.65)*h = I*α I is the mass moment of inertia of the rod + speaker . I= mL**2/3+ ML**2 m and M are the masses of rod and speaker.

- If you push the rod with a force more than 2.0 kN suddenly, the plastic hinge will not develop at bottom but somewhere 2/3H.

- Other options ; impact and shock loadings are totally different stories..

PS there might be some typos..