SandorR
Student
- Dec 17, 2020
- 16
Hello,
I am reading the book SCI P358 Green book Simple connections.
On page 117, formula for the fin plate resistance for bolt bearing on beam web is given as:
V_Rd = n / SQRT( (1 + alpha * n) / F_b,ver ) ^ 2 + (beta * n / F_b,hor) ^ 2) )
where n is the number of bolts, and F_b,ver and F_b,hor the horizontal and vertical bearing resistances of the beam web or fin plate.
I was able to derive this formula from the assumption that the resultant bearing stress ( Vertical load / n + load from the moment due to eccentricity) is less than the square root of the sums of horizontal and vertical utility ratios squared. That is, the formula implies that following should be true:
SQRT( (V_Ed,hor / F_b,hor) ^ 2 + (V_Ed,ver / F_b,ver) ^ 2 ) < 1
Why are we checking the resistance this way? Could we not simply check that Vertical load / n < F_b,ver AND that the horizontal load occuring from the moment is less than the horizontal bearing resistance? Horizontal force can be calculated as:
V_Ed,hor = M * y_max / I
where M = z * V_Ed,ver (where z is the eccentricity of the connection) y_max the distance of the further bolt from the neutral axis and I the moment of inertia of the bolt group.
So, my intuition would say that we should verify these two checks:
V_Ed,ver < F_b,ver
M * y_max / I < F_b,hor
But instead the book seems to combine the two into one check.
Would anybody know more about this subject, namely why my method is not used instead of the one provided by the book?
I am reading the book SCI P358 Green book Simple connections.
On page 117, formula for the fin plate resistance for bolt bearing on beam web is given as:
V_Rd = n / SQRT( (1 + alpha * n) / F_b,ver ) ^ 2 + (beta * n / F_b,hor) ^ 2) )
where n is the number of bolts, and F_b,ver and F_b,hor the horizontal and vertical bearing resistances of the beam web or fin plate.
I was able to derive this formula from the assumption that the resultant bearing stress ( Vertical load / n + load from the moment due to eccentricity) is less than the square root of the sums of horizontal and vertical utility ratios squared. That is, the formula implies that following should be true:
SQRT( (V_Ed,hor / F_b,hor) ^ 2 + (V_Ed,ver / F_b,ver) ^ 2 ) < 1
Why are we checking the resistance this way? Could we not simply check that Vertical load / n < F_b,ver AND that the horizontal load occuring from the moment is less than the horizontal bearing resistance? Horizontal force can be calculated as:
V_Ed,hor = M * y_max / I
where M = z * V_Ed,ver (where z is the eccentricity of the connection) y_max the distance of the further bolt from the neutral axis and I the moment of inertia of the bolt group.
So, my intuition would say that we should verify these two checks:
V_Ed,ver < F_b,ver
M * y_max / I < F_b,hor
But instead the book seems to combine the two into one check.
Would anybody know more about this subject, namely why my method is not used instead of the one provided by the book?
