Civil Engineering Reference
In-Depth Information
Fig. 9.10
Numeric integration assumptions
τ
1
2
1
2
τ
()
(
)
()
(
)
(
)
∫
d
r
τ
=
r
+
r
⇒
r
τ
=+
r
r
+
r
τ
=+
r
r
+
r
(9.182)
kk
+
1
k
k
k
+
1
k
k
k
+
1
2
0
and thus
Δ
t
⎫
1
2
t
Δ
(
)
(
)
r
r
∫
r
r
d
τ
r
r
r
=+
+
=+
+
⎪
⎪
⎬
k
1
k
k
k
1
k
k
k
1
+
+
+
2
0
(9.183)
t
Δ
2
τ
Δ
t
⎡
⎤
⎪
(
)
(
)
∫
d
t
r
=+
r
r
+
r
+
r
τ
=+Δ⋅
r
r
+
r
+
r
⎪
⎢
⎥
k
+
1
k
k
k
k
+
1
k
k
k
k
+
1
2
4
⎣
⎦
⎭
0
