Eccentric axial loading away from the centroid

1
Eccentric axial loadingaway from the centroid

• SFx0
• SMCz0

2
When we create a surface, we consider the forces
and moments with respect to the centroid of the
surface.
These are equivalent, but the bottom one
is useful for determining stresses.
3
Any time, the line of action an external
force doesnt pass through the centroid!!!!!
4
?
Neutral AxisCentroidal Axis Neutral
Axis??x0 Neutral AxisCentroidal Axis If P0
and either Mz0 or My0
5
y
z
193.75mm
6
y
z
Z -.19375m
Z .08125m
Assume P100kN
7
Note- If the equation contains two variables,
pick a value for one of them, solve for the
other! Pick a second value, solve for the
other?2 points on the line
8
Z-20mm


z
-z


9
4.108

• P at A, B, and C
• P at A and B
• Need to use statics to determine
• equivalent Ptotal, Mx and Mz
• Ptotal -3P Mx? Mz?
• Ptotal -2P Mx? Mz?
• Need to consider different x,z locations
• to determine maximum.

• Answers in book
• All four forces
• 3 forces
• 2 forces

10
What is your strategy for finding the stresses at
point A and D, if P400N?
1. ? 2. ? 3. ? 4. ?
11
4.114
You need to compute this centroid location
11.846 mm

• Need to find centroid
• Need to locate and orient x,y,z axes
• Need to do statics to get P, My, Mz
• Need to compute Iy and Iz
• Need to determine y,z for points A and D
• Need to locate neutral axis--If combined ?x 0
  then combined ?x 0

12
4.117
40mm
50mm
A
Need to find centroid Need to locate and orient
x,y,z axes Need to do statics to get P, My, Mz in
terms of P Need to compute Iy and Iz Need to
determine y,z for points maximum stress Need to
locate neutral axis--If combined ?x 0 then
combined ?x 0