More Eccentric Loading

1
More Eccentric Loading
2
Strategystresses at A and Band neutral axis?
3
4.142
What is P? What is Iz? What is Iy?
x
y
E H G
Does 150lb force contribute to Mz?, to My? Same
questions for 500lb and 250lb?
.9 .9
.9
2 2
z
Intersection of neutral axis with AB (y0.9) or
BD (z -2)?
4
Strategy to find a so P50kN will cause max
stress to be lt or 90MPa (compression)

• ?
• ?
• ?
• ?

5
x
z
4.145
y
-50kN
W150x24 look up in Appendix ? A, Iy, Iz and
dimensions
(P)(75mm)?My or Mz (P)(a)?My or Mz
a36.8mm
6
What is the moment arm for Force 1? Force
2? Force 3?
7
4.186
If all loads act then the moments cause by loads
at 1 and 3 cancel
x
y
If load at point 3 is removed, the load at point
1 causes a moment about the centroid the load
at point 2 does not.
z
A(0,120,45) B(0,-120,45)
8
Equation and diagram for formula sheet
9
Shear Force (V) and Bending Moment (M) Diagrams

• Getting a head start

10
The plot tells us what the shear force V, and
bending moment M are for a cross-section.
When oriented this way, these quantities are
plotted positive.
Right end Left end
11

• Before next class
• Study Sample Problem 5.1
• x10, x22.49999, x32.50001
• x45.49994, x55.50001,x67.49999
• and Sample Problem 5.2
• Notice the length of each FBD is x
• 0ltxlt8ft, 8ftltxlt11ft, 11ftltxlt16ft

12
Designing Beams

• Need to know the state of stress at all the
  different points in the beam.
• If the beam has a uniform cross-section the
  section modulus is useful for design purposes.

Section modulus