CIVIL ENGINEERING FORMULAS

BUILDING AND STRUCTURES FORMULAS 241

(9.112)

where C carbon content, %
Mnmanganese content, %
Crchromium content, %
Momolybdenum, %
Vvanadium, %
Ninickel content, %
Cucopper, %

To prevent underbead cracking, the weld must be cooled at an acceptable rate.
A higher carbon equivalent requires a longer cooling rate. Refer to ASTM 6 for
further requirements.

STATICALLY INDETERMINATE FORCES AND MOMENTS
IN BUILDING STRUCTURES*

Shear, moment, and deflection formulas for statically indeterminate forces
in rigid frames as present by Roark have the following notation: Wload,
lb (kg); wunit load, lb/linear in (kg/cm); Mis positive when clockwise;
V is positive when upward; y is positive when upward. Constraining
moments, applied couples, loads, and reactions are positive when acting as
shown. All forces are in pounds; all moments are in inch-pounds; all deflec-
tions and dimensions are in inches. is in radians and tan.I
moment of inertia of the section of the beam with respect to the neutral axis
of the beam, in^4 (mm^4 ).
With pinned supports, concentrated load on the horizontal member, Fig. 9.9:

(9.113)

(9.114)

With pinned supports, concentrated load on one vertical member, Fig. 9.10:

(9.115)

V (9.116)

WaH 2 (L 1 L 2 )

L 3

H 2 W

2 L 13

I 1



2 a^3

I 1



3 ab^2

I 1



2 L 12 L 3

I 3



2 L 1 L 3 b

I 3



L 1 L 2 L 3

I 3



L 2 L 3 b

I 3

2 L 13

I 2



2 L 22 L 3

I 3



2 L 1 L 2 L 3

I 3



2 L 13

I 1



2 L 12 L 3

I 3

V 1 

wbH(L 2 L 1 )

L 3

H

1

2

W

L 1 L 2 b 2 L 2 L 3 b 3 L 2 b^2 (b^3 /L 3 )(L 1 L 2 )

L 1 L 2 L 3 L 12 L 3 L 22 L 3 L 13 (I 3 /I 1 )L 23 (I 3 /I 2 )

CeqC

Mn

6



(CrMoV)

5



(NiCu)

15

*Roark—Formulas for Stress and Strain, McGraw-Hill.