CIVIL ENGINEERING FORMULAS

78 CHAPTER TWO

Pab^2

L^2 a

P

P

wk/t wk/t

wk/t

wk/t

aL

aL

wk/t

PP PP PP

L–2a

L/4 L/4 L/4 L/5L/5L/5

L/3

P

P

P

L/3

L/2 L/2

L/3

L/4 L/5L/5

L/2

aa

P

P

b

Pa^2 b

L^2

PL

8

PL

8

2 PL

9

2 PL

5

wL^2

12

5 wL^2

192

11 wL^2

192

wk/t

wk/t

wk/t

L/2

L/2

L/2 L/2

L/2

L/2

L/2 L/2

L/4 L/4

L/2

3 wL^2

160

wL^2

30

7 wL^2

960

wk/t

wk/t wk/t

5 wL^2

96

wL^2

32

5 wL^2

192

23 wL^2

960

wL^2

30

wL^2

20

wa^2 (6 – 8a+ 3a^2 )L^2

12

wa^3 (4 – 3a)L^2

12

wa^2 (10 – 15a+ 6a^2 )L^2

30

wa^3 (5 – 4a)L^2

20

wL^2

15

wL^2

60

wk/t

wk/t

wk/t

wk/t wk/t

aL

aL

aL

aL

M

wa^2 (10 – 10a+ 3a^2 )L^2

60

Parabola

Parabola

wa^3 (5 – 3a)L^2

60

wa^2 (3 – 2a)L^2

6

M

4

M

M

4

M(1 – a) (3a – 1) Ma(1 – 3a)

Pa(L – a)

L

5 PL

16

• 
  

FIGURE 2.27 Fixed-end moments in beams. (Brockenbrongh and Merritt-Structural
Designer’s Handbook, McGraw-Hill.)