Circular Ring (11, 5)

Equations:

A = π ⋅ (ro

2

– ri

2

)

I =

π

4

– ri

4

)

 

 

-- ⋅ (ro

 

 

 

 

 

 

 

 

4

 

 

 

 

J =

π

⋅ (ro

4

– ri

4

)

Id = I + A ⋅ d

2

--

 

 

 

 

2

 

 

 

 

 

 

 

Example:

Given: ro=4_∝, ri=25.0Å, d=.1_mil.

Solution: A=3.0631E–7_cm^2, I=1.7038E–10_mm^4, J=3.4076E–10_mm^4, Id=3.0648E–10_mm^4.

Triangle (11, 6)

Equations:

b ⋅ h A = ----------

2

b ⋅ h3 Ix = ------------

36

P = b + v2 + h2 + (b – v)2 + h2

b ⋅ h ⋅ ( 2 ⋅ 2) Iy = ---------- b – b v + v

36

J =

b----------⋅ h ⋅ (h2

+ b2

– b ⋅ v + v2)

Id = Ix + A ⋅ d2

 

36

 

 

 

Example:

Given: h=4.33012781892_in, v=2.5_in, P=15_in, d=2_in.

Solution: b=5.0000_in, Ix=11.2764_in^4, Iy=11.2764_in^4, J=22.5527_in^4, A=10.8253_in^2,

Id=54.5776_in^4.

5-46 Equation Reference