Rock bolt analysis, cantilever calculation

[dockfoxes]

Hi,

I am new here and I am looking for some help with my university project. I am trying to (simply) analyse a rock bolt as a simple cantilever at an angle.
The idea is that there is a rock that needs securing, to make things easier the rock is perpendicular to the rock face, the bolt passes through the rock and into the mountain. The length of the bolt is 2.4m in total, 1m of this is into the mountain, essentially a 1m fixed support, meaning the remaining 1.4m is inside the rock and functioning as a cantilever.

I am having real trouble getting my head around the sums as all examples of cantilevers are horizontal. Any online examples of inclined members are always beams with fixed ends.

If i take the 22.5 degree example, with a UDL acting vertically on the bolt at 67.9kN m. I have calculated the distance horizontally as 1.29m and vertically as 0.53m, with a hypot of 1.4m This means a load of 1.29 x 67.9 = 87.8kN

Which i assume means Ay (if A is the fixed support) is also 87.8 kN as there are no other forces in the y direction.

Does this then mean that the moment acting on this is 87.8kN x 1.29m = 113 kN?

Do i then convert the UDL into a point load and multiply by L/2 which would mean 87.8kN x 1.29m/2 = 57 kN or do i use trig to convert the UDL into a perpendicular load and multiply this by L/2. Plus the same at the fixed support? Then calculate a horizontal loads in the same manner at both points.

Sorry this reads so badly, i am going around in circles in my head and confusing myself even as i write. If anyone can follow this or point me in the direction of a webpage/video that talks about inclined cantilevers and not inclined members of beams i would be most grateful.


Rob

[Cragyon]

See "Theoretical Calculation and Analysis on the Composite Rock-Bolt Bearing Structure in Burst-Prone Ground
"

rock-bolt.pdf

[samantha_tores]

Interesting paper.