Page 137 - Civil Engineering Formulas

78 CHAPTER TWO

P P
2
2
Pab Pa b PL PL
2 2 8 8
L a b L L/2 L/2
P P P P
Pa(L – a) 2PL
a L–2a a L L/3 L/3 L/3 9
P P P P P P P
2PL
5PL
L/4 L/4 L/4 L/4 16 L/5 L/5 L/5 L/5 L/5 5
w k/t w k/t
wL 2 wL 2 wL 2
20 30 12
w k/t w k/t
2
3
2
wa (6 – 8a + 3a )L 2 wa (4 – 3a)L 2 11wL 2 5wL 2
12 aL 12 192 L/2 192
w k/t w k/t
2 2 2 3 2 2 2
wa (10 – 15a + 6a )L wa (5 – 4a)L wL 3wL
30 aL 20 30 L/2 160
w k/t w k/t
2 2 2 3 2 2 2
wa (10 – 10a + 3a )L wa (5 – 3a)L 23wL 7wL
60 aL 60 960 L/2 960
k/t
w w k/t
Parabola
2 2
wL 5wL
15 L/2 L/2 96
w k/t
w k/t
Parabola
wL 2 wL 2
60 32
L/2 L/2
w k/t w k/t w k/t w k/t
2 2 2
wa (3 – 2a)L 5wL
6 192
aL aL L/4 L/2 L/4
M M
M(1 – a) (3a – 1) Ma(1 – 3a) – M M
4 4
aL L/2 L/2
FIGURE 2.27 Fixed-end moments in beams. (Brockenbrongh and Merritt-Structural
Designer’s Handbook, McGraw-Hill.)