Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

Table 8.1 Selecting Standard Steel Shapes for Beams
Step 1: Calculate the minimum section modulus required for the specific span and loading.
Step 2: In the tables of section properties (such as those presented in Appendix B), locate the section modulus values. Typically, the
beam will be oriented so that bending occurs about the strong axis; therefore, find the column that gives S for the strong axis
(which is typically designated as the X–X axis).
Step 3: Start your search at the bottom of the table. Shapes are typically sorted from heaviest to lightest; therefore, the shapes at the
bottom of the table are usually the lightest-weight members. Scan up the column until a section modulus equal to or slightly
greater than S min is found. This shape is acceptable, and its designation should be noted.
Step 4: Continue scanning upwards until several acceptable shapes have been determined.
Step 5: After several acceptable shapes have been identified, select one shape for use as the beam cross section. The lightest-weight
cross section is usually chosen, because the cost of the beam is directly related to the weight of the beam. However, other
considerations could affect the choice. For example, a limited height might be available for the beam, thus necessitating a
shorter and heavier cross section instead of a taller, but lighter, shape.
ExAmpLE 8.5
A
1,200 lb 1,200 lb 1,200 lb
B C D
6 ft 6 ft 6 ft 6 ft
Beam and loading.
E
b
h
Cross section.
A 24 ft long simply supported wooden beam
supports three 1,200 lb concentrated loads that
are located at the quarter points of the span. The
allowable bending stress of the wood is 1,800 psi.
If the aspect ratio of the solid rectangular
wooden beam is specified as h/b = 2.0, determine
the minimum width b that can be used for
the beam.
A
1,200 lb 1,200 lb 1,200 lb
B
6 ft 6 ft 6 ft 6 ft
1,800 lb 1,800 lb
V
1,800 lb
10,800 lb·ft
600 lb
C
14,400 lb·ft
−600 lb
D
−1,800 lb
10,800 lb·ft
E
Plan the Solution
By the graphical method presented in Section 7.3, the shearforce
and bending-moment diagrams for the beam and loading
will be constructed at the outset. With the use of the
maximum internal bending moment and the specified allowable
bending stress, the required section modulus can be determined
from the flexure formula [Equation (8.10)]. The
beam cross section can then be proportioned so that its
height is twice as large as its width.
SolutioN
Construct the Shear-Force and
Bending-Moment Diagrams
The shear-force and bending-moment diagrams for the
beam and loading are shown. The maximum internal bending
moment occurs at C.
Required Section Modulus
The flexure formula can be solved for the minimum
section modulus required to support a maximum internal
bending moment of M = 14,400 lb · ft without exceeding
the 1,800 psi allowable bending stress:
M
266
σ
max
M
= ≤ σ
S
allow