CIVIL ENGINEERING FORMULAS

40 CHAPTER TWO

R 1

d 1

y 11

d 1 =y 11 R 1 +y 12 R 2 +y 13 R 3

d 2 =y 21 R 1 +y 22 R 2 +y 23 R 3

d 3 =y 31 R 1 +y 32 R 2 +y 33 R 3

y 21

y 31

d 2

d 3

R 0

L 1 L 2

W

L 3 L 4

R 2 R 3 R 4

(a)

(b)

(c)

y 13

1

1

1

y 23 y 33

y 12

y 22

y 32

(e)

(d)

FIGURE 2.5 Reactions of continuous beam (a) found by making

the beam statically determinate. (b) Deflections computed with inte-

rior supports removed. (c), (d), and (e) Deflections calculated for

unit load over each removed support, to obtain equations for each

redundant.