Anderson, T. L.
“Mechanics of Materials”
The Engineering Handbook.
Ed. Richard C. Dorf
Boca Raton: CRC Press LLC, 2000
© 1998 by CRC PRESS LLC
During hydrostatic testing, brittle failure of a high pressure, thick-walled chemical reactor vessel occurred
in the manufacturer's test shop. Brittle failure can occur without any prior noticeable deformation; it is
characterized by a very rapid crack propagation of up to 6 thousand feet per second. Brittle fracture is the
most dangerous type of failure. (Source: Harvey, J. 1974. Theory and Design of Modern Pressure
Vessels, 2nd ed. Van Nostrand Reinhold. With permission.)
© 1998 by CRC PRESS LLC
II
Mechanics of Materials
Ted L. Anderson
Structural Reliability Technology
4 Reactions T. Anagnos
Types of Supports • Actual versus Idealized Support Conditions • Static Determinacy and Indeterminacy •
Computation of Reactions
5 Bending Stresses in Beams J. M. Gere
Longitudinal Strains in Beams • Normal Stresses in Beams (Linearly Elastic Materials)
6 Shear Stresses in Beams J. M. Gere
Shear Stresses in Rectangular Beams • Shear Stresses in Circular Beams • Shear Stresses in the Webs of
Beams with Flanges
7 Shear and Moment Diagrams G. R. Buchanan
Sign Convention • Shear and Moment Diagrams • Shear and Moment Equations
8 Columns L. W. Zachary and J. B. Ligon
Fundamentals • Examples • Other Forms of Instability
9 Pressure Vessels E. Livingston and R. J. Scavuzzo
Design Criteria • Design Formulas • Opening Reinforcement
10 Axial Loads and Torsion N. R. Bauld, Jr.
Axially Loaded Bars • Torsion
11 Fracture Mechanics T. L. Anderson
Fundamental Concepts • The Energy Criterion • The Stress Intensity Approach • Time-Dependent Crack
Growth and Damage Tolerance • Effect of Material Properties on Fracture
THE RESPONSE OF MATERIALS TO STRESS is an important topic in engineering. Excessive
stress can lead to failure by plastic deformation, buckling, or brittle fracture. Thus it is essential for
the design engineer to estimate stresses correctly and to determine the limit state for the material
and structure of interest.
Stress is defined as force per unit cross-sectional area. In general, the stress state in a body can
be three-dimensional and can vary from point to point. This section, however, focuses primarily on
simple loading cases such as bending and axial loading of beams, columns, and shafts. Readers
who are concerned with more complicated situations are encouraged to consult a textbook on solid
mechanics or theory of elasticity. Forces and moments that induce stresses in a structure can be
considered as either loads or reactions. Wind loading, gravitational forces, and hydrostatic pressure
are examples of loads, while reactions are forces that arise from supports thatresist movement of a
structure that is subject to loads. Chapter 4 discusses reactions in more detail. Beams and
columns are the primary load-bearing members in a range of structures, including bridges and
buildings. Chapters 5and 6 address bending stresses and shear stresses in beams, respectively,
while Chapter 7 introduces shear and moment diagrams for beams. Chapter 8 considers buckling
© 1998 by CRC PRESS LLC
instability in columns subject to compressive axial loads. Vessels that are subject to hydrostatic
pressure, such as pressure vessels, pipes, and storage tanks, are another important class of
structure. Chapter 9 lists the basic equations that relate stress to hydrostatic pressure in these
configurations. Chapter 10 covers the analysis of axial and torsion loading in bars and shafts.
This chapter addresses both statically determinate and statically indeterminate loading cases.
Structures can fail by brittle fracture when the material contains cracks or other flaws. Traditional
strength-of-materials approaches do not address brittle fracture or cracks in materials. Fracture
mechanics is a relatively new engineering discipline that relates critical combinations of stress,
crack size, and a property called toughness that quantifies material resistance to fracture. Chapter
11 gives a brief introduction to this field.
© 1998 by CRC PRESS LLC
