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

Table 8.2 Area and Radial Distance to Neutral Axis for Selected cross Sections
309
bENdINg OF CuRVEd bARS
Shape Cross Section Radius of Neutral Surface
b
A. Rectangle
r o
d
A
rn
=
ro
b ln
ri
A = bd
r i
O
c
B. Circle
r c
r
n
A
=
2π ( rc − rc 2 − c
2 )
A = πc 2
O
2b
C. Ellipse
r c
2a
A
rn
=
2π
b
r − r − a
a
A = π ab
( c c 2 2
)
O
D. Triangle
r o
b
d
ri
A
rn
=
br ⎛ r ⎞
o o
⎜ln
⎟ − b
d ⎝ ri
⎠
1
A = bd
2
O
b 2
E. Trapezoid
r o
b 1
d
r i
r
n
A
=
1 ⎡
d br br r
⎤
( )ln
o
⎢ 1 o − 2 i − db ( 1 − b2
) ⎥
⎣
r
⎦
1
A = b b d
2 ( 1 + 2 )
i
O