Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

Table A.1 properties of plane Figures
1. Rectangle 6. Circle
h
y′ y
x–
C
b
y–
x
x′
I
A = bh
h
y = I
2
b
x = I
2
bh
=
3
3
x′ I
3
bh
=
12
2. Right triangle 7. Hollow Circle
h
y′ y
x−
C
b
x
y−
x′
A =
bh
2
3. triangle 8. Parabola
y′
x−
a
C
b
y
y−
x
h
x′ I
4. trapezoid 9. Parabolic Spandrel
h
C
b
a
−y
x
x
y
y ′ =
h
y = I
3
b
x = I
3
I
A =
3
bh
=
12
x′ I y′
bh
2
h
y = I
3
( a + b)
x =
3
x′
3
bh
=
12
I
x
y
( a + b)
h
A =
2
3
hb
=
12
x
y
3
bh
=
36
1 ⎛ 2a
+ b⎞
y =
h
3 ⎝
⎜
a + b ⎠
⎟
I
x
3
hb
3
3
bh
=
36
3
hb
=
36
3
hb
=
12
bh a ab b
36 ( 2 2
= − + )
3
h
36( a b) ( a 2 4 ab b 2
=
+ +
+
)
h
y′
r
C
C
d
d
D
y′
−x
C
y
y
y
r
R
b
Zero slope
−x
Zero
slope
b
C
y
x
x
x
−y
y−
h
x
x′
x′
2
π d
A = πr
=
4
I
x
πr
πd
= Iy
= =
4 64
2
4 4
2 2
π
A ( R r ) D d
4 ( 2 2
= π − = − )
π
Ix
Iy
R r
4 ( 4 4
= = − )
h
y′ =
b
x ′ 2
2
A =
x
2bh
3
3b
= y
8
h
y′ =
b
x ′ 2
2
A =
x
bh
3
π
= D d
64 ( 4 −
4)
=
3h
5
3b 3h
= y =
4 10
5. Semicircle 10. General Spandrel
r
y, y′
C
−y
x
x′
2
πr
A =
2
4r ⎛ π 8 ⎞
y = Ix
= − r
3π ⎝
⎜
8 9π
⎠
⎟
4
πr
Ix′ = Iy′
=
8
4
y′
−x
Zero
slope
b
C
y
−y
x
h
x′
h
y′ =
b
x ′ n
n
bh
A =
n + 1
x =
n
n
+
+
1
b
2
y =
n + 1
h
4n
+ 2
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