Page 307 - Civil Engineering Formulas

BUILDING AND STRUCTURES FORMULAS 241

Mn (Cr Mo V) (Ni Cu)
C eq C (9.112)
6 5 15
where C carbon content, %
Mn manganese content, %
Cr chromium content, %
Mo molybdenum, %
V vanadium, %
Ni nickel content, %
Cu copper, %

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: W load,
lb (kg); w unit load, lb/linear in (kg/cm); M is 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
4
4
of the beam, in (mm ).
With pinned supports, concentrated load on the horizontal member, Fig. 9.9:
1 L 1 L 2 b 2L 2 L 3 b 3L 2 b (b /L 3 )(L 1 L 2 )
3
2
H W (9.113)
2
3
2
3
2 L 1 L 2 L 3 L 1 L 3 L 2 L 3 L 1 (I 3 /I 1 ) L 2 (I 3 /I 2 )
wb H(L 2 L 1 )
V 1 (9.114)
L 3
With pinned supports, concentrated load on one vertical member, Fig. 9.10:
3 3 2 2
2L 1 2a 3ab 2L 1 L 3 2L 1 L 3 b L 1 L 2 L 3 L 2 L 3 b

I 1 I 1 I 1 I 3 I 3 I 3 I 3
H 2 W
3 2 3 2
2L 1 2L 2 L 3 2L 1 L 2 L 3 2L 1 2L 1 L 3

I 2 I 3 I 3 I 1 I 3
(9.115)
Wa H 2 (L 1 L 2 )
V (9.116)
L 3
*Roark—Formulas for Stress and Strain, McGraw-Hill.