CIVIL ENGINEERING FORMULAS

TABLE 2.1 Uniformly Loaded Continuous Beams over Equal Spans

(Uniform load per unit lengthw;length of each spanl)

Shear on each side Distance to point

Notation of support. Lleft, of max moment, Distance to

Number of Rright. reaction at Moment Max. measured to point of inflection,

of support any support is LR over each moment in right from measured to right

supports of span LRsupport each span support from support

2 1 or 2 0 0 0.125 0.500 None

3 1 0 0 0.0703 0.375 0.750

2 0.0703 0.625 0.250

4 1 0 0 0.080 0.400 0.800

2 0.025 0.500 0.276, 0.724

1 0 0 0.0772 0.393 0.786

5 2 0.0364 0.536 0.266, 0.806

3 0.0364 0.464 0.194, 0.734

1 0 0 0.0779 0.395 0.789

6 2 0.0332 0.526 0.268, 0.783

3 0.0461 0.500 0.196, 0.804

1 0 0 0.0777 0.394 0.788

2 0.0340 0.533 0.268, 0.790

7 3 0.0433 0.490 0.196, 0.785

4 0.0433 0.510 0.215, 0.804

1 0 0 0.0778 0.394 0.789

8 2 0.0338 0.528 0.268, 0.788

3 0.0440 0.493 0.196, 0.790

4 0.0405 0.500 0.215, 0.785

Values apply to wl wl wl^2 wl^2 ll

The numerical values given are coefficients of the expressions at the foot of each column.

(^12) 
142
(^71) 
142
(^72) 
142
(^11) 
142
(^70) 
142
(^67) 
142
(^15) 
142
(^75) 
142
(^86) 
142
(^56) 
142
(^9) 
104
(^53) 
104
(^53) 
104
(^8) 
104
(^51) 
104
(^49) 
104
(^11) 
104
(^55) 
104
(^63) 
104
(^41) 
104
(^3) 
38
(^19) 
38
(^18) 
38
(^4) 
38
(^20) 
38
(^23) 
38
(^15) 
38
(^2) 
28
(^13) 
28
(^13) 
28
(^3) 
28
(^15) 
28
(^17) 
28
(^11) 
28
(^1) 
10
(^5) 
10
(^6) 
10
(^4) 
10
(^1) 
8
(^5) 
8
(^5) 
8
(^3) 
8
(^1) 
2
50