Baseplate check using yield line - for a 2 bolt connection

[MasterrrrBlasterrrr]

thread507-434905

My calculation for the baseplate capacity in the thread I have referenced:


(1) Calculate the bolt tension. I would use the lever arm from web of the 50SHS to the line of bolts.
e = 25 - 2.5 = 22.5mm (assuming 5mm wall)

M* = 3.2 x 0.4 = 1.28 kNm

T*b = 1.28/(0.0225x2) = 28.4 kN
(Check the nominated chemset anchor has this capacity)


(2) Check bending of the plate.
I'm assuming the bolt is 50mm from the face of SHS

For simplicity, will first assume the plate cantilevers from the SHS.
M*plate = 28.4*0.05 = 1.42 kNm

There is 100mm width of plate to act as a cantilever.
Sx = 100x10^2/4 = 2500 mm^3

Fb = M/S = 1.42E6/2500 = 568 MPa.
FAILS.

Using Yield Lines, the effective length of plate that yields = 2x100 + 85.
The bending stress over a yield line length of 285mm = 199 MPa.
This is acceptable, but highly stressed.

I would make the dropper larger, and the plate wider and thicker.
Would prefer a design solution where the plate is OK in one-way bending as a cantilever.

The yield line pattern that accompanies the 285mm length probably involves prying action on the bolt?
So, the bolt tension may be 30% or so greater than 28.4 kN.

I suggest a 75SHS dropper, with 150x12 plate.

T*b = 1.28/(0.035*2) = 18.3 kN
M*plate = 18.3 x 0.05 = 0.91 kNm (assuming one way bending in cantilever action)

Sx =150x12^2/4= 5400 mm^3
Fb = 0.91e6/5400 = 168 MPa

Works fine


Yield line pattern for 2 way bending in plate is attached.


In a late correction:

The portion of the yield line that has effective length 85mm undergoes rotation of "2 theta".
If doing calcs by virtual work, the M*theta for this component will be 2 x 85 = 170mm
So, total effective length of yield line that unrgoes "1xtheta" rotation = 370mm

 

[KootK]

(1) Calculate the bolt tension. I would use the lever arm from web of the 50SHS to the line of bolts.
e = 25 - 2.5 = 22.5mm (assuming 5mm wall)

This implies that your bolt is 25 mm from the the wall but, further on, you mention that it is 50 mm from the wall. I'm also not clear why you've divided by two since you only have one bolt in tension.

T*b = 1.28/(0.0225x2) = 28.4 kN
(Check the nominated chemset anchor has this capacity)

I feel that your lever arm for this should be at least the distance from the bolt to the far side HSS wall. So about 100 mm + assuming that your bolts are indeed 50 mm off of your wall. This may well get you back to being able to use a one way bending calc.

The yield line pattern that accompanies the 285mm length probably involves prying action on the bolt?

I get 276 mm and yes, I would consider prying.

 

[MasterrrrBlasterrrr]

See below for Virtual work calcs.
Bending occurs about the axis which the bolts are on, as described in the original post I referenced.

The plate works OK.

 

[txeng91]

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https://www.hilti.com/content/hilti...ral-engineering/profis-engineering-suite.html