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

Table 7.2 Basic Loads Represented by Discontinuity Functions
Case load on Beam Discontinuity Expressions
w
1
a
M 0
x
wx ( ) = M 〈 x − a〉
V( x)
= M 〈 x − a〉
Mx ( ) = M 〈 x − a〉
0
0
0
−2
−1
0
P 0
2
w
x
wx ( ) = P 〈 x − a〉
V( x)
= P 〈 x − a〉
Mx ( ) = P 〈 x − a〉
0
0
0
−1
0
1
a
3
w
w 0
x
wx ( ) = w 〈 x − a〉
V( x)
= w 〈 x − a〉
0
0
0
1
a
w
Mx ( ) = 〈 x − a 〉
2
0 2
4
w
a
b
w 0
x
w0 wx
b x a 1
( ) = 〈 − 〉
w0 V( x)
2b x a 2
= 〈 − 〉
w
Mx ( ) = 〈
6b x − a 〉
0 3
5
w
w 0
wx ( ) = w0〈 x − a1〉 0 − w0〈 x − a2〉
0
x
V( x)
= w0〈 x − a1〉 1 − w0〈 x − a2〉
1
a w0
w
1 Mx ( ) = 〈 x − a 〉 − 〈 x − a 〉
a 2 2
2
1 2 0 2 2
6
w
a 1
a 2
b
w 0
x
w0
wx
b x a w
( ) = 〈 − 1〉 1 − 0 〈
b x − a 2 〉 1 − w 0〈 x − a 2〉
0
0
V x
wb x a w
( ) = 〈 − 1〉 2 − 0 〈
2 2b x − a 2 〉 2 − w 0〈 x − a 2〉
1
0
Mx
wb x a w
b x a w
( ) = 〈 − 〉 − 〈 − 〉 − 〈 x − a 〉
6 6 2
1 3 0 2 3 0 2 2
7
w
b
w
wx w x a
w b x a w
( ) = 0〈 − 1〉 0 − 0 〈 − 1〉 1 + 0 〈
b x − a 2 〉
1
0
V x w x a
x
wb x a w
( ) = 0〈 − 1〉 1 − 0 〈 − 1〉 2 + 0 〈
2 2b x − a 2 〉
2
a 1
w0
Mx x a
a 2
wb x a w
( ) = 〈 − 1〉 2 − 0 〈 − 1〉 3 + 0 〈
2 6 6b x − a 2 〉
3
228