Page 42 - Mechanical Engineer's Data Handbook

STRENGTHS OF MATERIALS 31

CW 111: M,,= WR (A to B) Simply supported beam, beam mass only
Stresses as for case I.
157
f=+@qi
Deflection in direction of load L

Deflection in direction normal

to load &=p(Rf+RL+:) El 2
Built-in beam, mass of beam only

Concentrated mass: for all cases with a single mass
r=&a

where: y = static deflection at load, g = acceleration
due to gravity.
For cantilever mass at end f= 1J2nJ3EI/mL3

I A.6 Transverse vibration of beams
Formulae are given for the fundamental frequency of
transverse vibrations of beams due to the beam’s own Simply supported beam, central mass
mass and due to concentrated masses.
f = 1 J2nJzZ3z
Ungorm cantilever, beam mass only
Frequency of vibration f = - fi
0.56
L2
where: m=mass per unit length of beam, I=second
moment of area, L=length of beam.

Simply supported beam, non-central mass

f= 1/2nJz&m