Bending Moment 1

[sabrepoint]

Hi ... sorry this is so simple for you lot but I never did well at mechanics and it was sooo long ago.

1) I know if I plant a 5 meter high post in concrete and apply a 1 kN horizontal force at the pole tip, the pole moment is 5 kNm. That's easy enough, but what if I weld a right-angled fitting to the top and apply the load 1 meter down like so ...

_____A
| |
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| |<< 1 kN
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|
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------------ fixed in concrete

Assume the right-angled fitting is rigid. Please tell me how to calc the post bending moment.

2) And the second question I have (again using the 5 m high post fixed in conc) ... instead of a horizontal load (please disregard the 1 kN horz load shown in drawing), I apply a 1 kN VERTICAL load at 1 meter out from the post at point 'A' in drawing. How is the post moment calculated? Is it just 1 kNm?

Thanks!
Bill

 

[Neilmo]

Sabrepoint,

1)Bending moment at base = 1.0kN x (5.0m - 1.0m) = 4.0kNm

2)You are spot on, Bm(base) = 1.0kN x 1.0m = 1.0kNm

Regards,
Neilmo

 

[Bbird]

I go for Neilmo's solution.

It is quite easy to figure out for the cantilever. Point A is experiencing a load of the 1 kN horizontal load plus a moment of 1kNm in &quot;clockwise direction&quot;. Thus for the fixed end to reach equilibrium the original fixed end moment of (anticlockwise) 5kNm has to offset the 1kNm clockwise moment there.

If one sketch out the BM diagram then the short 1m member has 0 to 1 kNm, the horizontal bit has a constant 1 kNm and the original cantilever has 1kNm at the top to -4kNm at the base if clockwise moment is assumed positive. The positive and negative moments cross each other exactly at the level where the 1kN applies.

 

[Neilmo]

Bbird,

Nice explanation, better than mine.

Neilmo

 

[Bbird]

Neilmo,

Thanks for the complement. Yours more concise. I wasn't going to bother at all but I thought the young engineer could do with a tip here.

Nice thing about engineering is we can always agree on facts and physical laws.

Bbird

 

[sabrepoint]

They're both great ... thanks!

Actually I had the correct answers as it turned out, but couldn't really explain. Values used were hypothetical ... amongst other things I occasionally survey power lines. The first scenario roughly simulates the transverse wind applied to a wire on a suspension insulator; the second the dead load on the structure when considering overturning.

Thanks again.