Mechanics of Materials

Citation

Beer, F. P., Johnston, E. R., Jr., DeWolf, J. T., & Mazurek, D. F. (2026). Mechanics of Materials (2026 release). McGraw Hill.

Chapter Summary

The book has eleven chapters, followed by appendices on units, centroids and moments of areas, material properties, rolled-steel shapes, beam deflections and slopes, and the Fundamentals of Engineering examination. McGraw Hill's current listing for the 2026 release gives the same eleven chapters as the seventh edition (2015), whose published contents and preface supply the section-level details below. The preface calls the text a first course in mechanics of materials (or strength of materials) for sophomore or junior engineering students and expects a prior course in statics. Sections marked as optional in that edition cover advanced or specialty topics.

Chapter 1: Introduction—Concept of Stress

Chapter 1 begins with a review of statics and then introduces stress in the members of a structure, stress on an oblique plane, components of stress under general loading, and design considerations, including the factor of safety. The preface notes that it presents both allowable stress design and load and resistance factor design, and that an axial load can produce shearing as well as normal stresses depending on the section considered.

Chapter 2: Stress and Strain—Axial Loading

Stress and strain under axial load, statically indeterminate problems, temperature changes, Poisson's ratio, the generalized Hooke's law, shearing strain, Saint-Venant's principle, stress concentrations and plastic deformations. Optional sections cover dilatation and bulk modulus, stress–strain relationships for fiber-reinforced composites and residual stresses.

Chapter 3: Torsion

Circular shafts in torsion, angle of twist, statically indeterminate shafts, the design of transmission shafts and stress concentrations. Plastic deformation, elastoplastic shafts, residual stresses, noncircular members and thin-walled hollow shafts are optional.

Chapter 4: Pure Bending

Stresses and deformations of symmetric members in the elastic range, composite members, stress concentrations, eccentric axial loading, unsymmetric bending and the general case of eccentric axial loading. Plastic deformations and curved members are optional.

Chapter 5: Analysis and Design of Beams for Bending

Shear and bending-moment diagrams, the relationships among load, shear and bending moment, and the design of prismatic beams for bending, based on allowable normal stress. Singularity functions and nonprismatic beams are optional sections.

Chapter 6: Shearing Stresses in Beams and Thin-Walled Members

Horizontal shearing stress in beams, longitudinal shear on an element of arbitrary shape and shearing stresses in thin-walled members, with the shear flow formula derived in the traditional way. Optional sections cover the stress distribution in a narrow rectangular beam, plastic deformations, and unsymmetric loading with the shear center. (The 2026 listing titles this chapter "Stresses in Beams and Thin-Walled Members".)

Chapter 7: Transformations of Stress and Strain

Transformation of plane stress, Mohr's circle, the general state of stress, three-dimensional stress analysis and stresses in thin-walled pressure vessels. Theories of failure, plane strain transformation, three-dimensional strain and strain rosettes are optional. The preface explains that this material is delayed until students have solved problems with combined loadings.

Chapter 8: Principal Stresses Under a Given Loading

An optional chapter, to be read after Chapter 7. It covers principal stresses in a beam, the design of transmission shafts and stresses under combined loads, including principal stresses and the maximum shearing stress at a point.

Chapter 9: Deflection of Beams

Deformation under transverse loading, statically indeterminate beams and the method of superposition, with integration as the first method. Optional sections cover singularity functions (to be used only if they were covered in Chapter 5) and the moment-area theorems, which the preface says are presented in two lessons.

Chapter 10: Columns

Stability of structures, eccentric loading and the secant formula, and centric and eccentric load design. According to the preface, the chapter includes material on the design of steel, aluminum and wood columns.

Chapter 11: Energy Methods

Strain energy, elastic strain energy, strain energy for a general state of stress, impact loads, and single loads. Multiple loads, Castigliano's theorem, deflections by Castigliano's theorem and statically indeterminate structures are optional.

Key Concepts

Chapters 1–4: Loading, Stress and Strain

• Stress at a point: introduced in Chapter 1 and revisited for torsion and bending, where stresses depend on the orientation of the surface.
• Statically indeterminate problems: first treated in Chapter 2 by combining deformation analysis with equilibrium, then used throughout.
• Plastic deformation and residual stress: introduced for axial loading in Chapter 2, with optional sections for shafts and beams.

Chapters 5–8: Beams, Shear and Combined Stress

• Shear and bending-moment diagrams: Sections 5.1 and 5.2.
• Shear flow: derived in Chapter 6 for beams and thin-walled members.
• Mohr's circle and principal stresses: Chapter 7, applied to combined loading in Chapter 8.

Chapters 9–11: Deflection, Stability and Energy

• Integration and superposition: the main methods for beam deflection in Chapter 9.
• Columns: the stability of structures and the secant formula in Chapter 10.
• Castigliano's theorem: an optional energy method for deflections and indeterminate structures.

Critical Analysis

Strengths

• A clear, stated method. The preface states that the book builds on a few basic concepts and simplified models, uses free-body diagrams and "picture equations" throughout, and (in the seventh edition) uses a four-step SMART approach (Strategy, Modeling, Analysis, Reflect & Think) in all sample problems.
• Optional material is marked. Advanced topics such as residual stresses, noncircular torsion, curved beams, the shear center and failure criteria sit in asterisked sections in the places where they belong, so instructors can omit them without breaking the sequence.
• Pacing of the core topics. Mohr's circle and stress transformation wait until Chapter 7, after axial, torsional and bending loads have been treated, so students meet the need for them through combined loading. Statically indeterminate problems appear from Chapter 2 on.
• Problem sets in both unit systems. The preface says half the concept applications, sample problems and assigned problems use SI units and half use U.S. customary units, and McGraw Hill says the authors have prepared detailed solutions to all problems for the instructor's manual.

Limitations

• Scope. The eleven chapters cover the standard first course. There is no chapter on thick-walled cylinders, fracture or fatigue, and the failure theories appear only as an optional section of Chapter 7.
• Statics is assumed. Chapter 1 reviews statics, but the preface expects a prior statics course, and every chapter relies on free-body diagrams.
• Heavy optional content. Many sections carry asterisks (for example in Chapters 2, 3, 4, 6, 7, 9 and 11), and Chapter 8 is optional, so the book has more material than a typical course uses.
• Edition differences. McGraw Hill's listing does not describe what changed in the 2026 release, and its Chapter 6 title and appendix list differ slightly from the seventh edition, so section-level details may not match exactly.

Where It Fits in the Course

Among the mechanics-of-materials books on the list, Beer and Johnston is one of two standard first courses; the other is Hibbeler's Mechanics of Materials. They cover broadly similar ground, and either can be the main text, with the other as a source of extra worked problems and a different explanation.

Ugural and Fenster's Advanced Mechanics of Materials and Applied Elasticity is the next step, taking students from elementary strength of materials into elasticity, plates, shells and contact stresses, and Sadd's Elasticity: Theory, Applications, and Numerics is a graduate treatment of elasticity. J. E. Gordon's The New Science of Strong Materials and Blockley's Structural Engineering: A Very Short Introduction are non-technical accounts that can be read before or alongside a first course for intuition about stress, strength and failure.

How to Use This Book

The book is for second- or third-year engineering students (mechanical, civil, aerospace and related fields) after a statics course. A practical plan:

• Core: Chapters 1 to 7 and 9 to 11 without the asterisked sections, in order.
• Add as the course needs: the optional sections on plastic behaviour, composite materials, curved members, the shear center, failure theories and Castigliano's theorem; Chapter 8 once Chapter 7 is done.
• Statics refresher: Chapter 1's review, plus Sections 5.1 and 5.2 on shear and bending-moment diagrams, and the appendix on centroids and moments of areas.
• Practice: use the sample problems as models for the solution method, then work the assigned problems in the unit system you need, and use the review and summary at the end of each chapter before an examination.