ARCH 461/561 Lecture 41 Beam Sizing #3 Example Problem

Lecture 41
Example Problem

Beam Sizing # 3

Given:
the uniformly loaded beam shown below.
Determine:
the most efficient W section for this loading based on bending, shear, and deflection. (Fb=24 ksi, Fv=14.5 ksi) (ignore the self-weight of the beam)(max D= l/360)

Lecture 41

Solution:
First size the beam according to bending. The moment that the applied loads create is used and thus,
S= M/F = (256,000 #ft)(12 in/ft)/24,000psi = 128 in^3
this is the required Section Modulus. The steel tables are consulted and a section is chosen (W21x68 which has an S = 140 in^3). The required section must now be modified to reflect the fact that we have added the weight of the beam to the loads that th e beam must carry.
(actual load / assumed load)(S) equals
(2068 #/ft / 2000 #/ft )(128 in^3) = 132.5 in^3 < 140 in^3 so the beam is still OK.

Now check the shear (including the beam weight)

And now check the deflection of the beam.

Lecture 41 Example Problem

Lecture 41
Example Problem