Prefaces, Ch. 1: Fundamental Principles

Problems: 1.22, 1.23, 1.30, 1.31, 1.42, 1.47, 1.48

Read other problems. Discuss where needed.

The assigned problems deal with equilibrium equations and vector operations.  Attempt the problems before reading the chapter to see if you already possess the required techniques.

Malvern's Statics:  Read part of  chapter "Structures and machines" up to and including Trusses: Method of Joints and Method of Sections.

Week 2

Ch. 2: Introduction to Mechanics of Deformable Bodies

Problems: 2.3, 2.4, 2.6, 2.8, 2.11, 2.12, 2.18, 2.20, 2.24, 2.28, 2.31, 2.33, 2.41, 2.42, 2.52. Read 2.55

Cee220/Class Notes/Axially Loaded Members

Mechanics of Solids/Notes and Solutions/Method of Joints, Problems 1.30, 1.31

Ch. 3: Forces and Moments Transmitted by Slender Members

Problems: 3.1-3.8, 3.9, 3.10, 3.12, 3.13, 3.14, 3.15, 3.20, 3.22, 3.25, 3.28, 3.29, 3.31

Read 3.16, 3.21

Week 4

Ch. 4: Stress and Strain, Secs. 4.1 to 4.7, 4.15.

WebNotes-Part1

WebNotes-Part2

Problems: 4.2, 4.3, 4.6, 4.7, 4.9, 4.10, 4.11, 4.13, 4.14, 4.15, 4.25, 4.30, 4.32?, 4.33

Read problems 4.1, 4.2, 4.4, 4.26, 4.30, 4.31, 4.34

Notes:

Problems 4.10 and 4.14 are usually treated as part of the text. They can be done using arguments of symmetry and simple free-body diagrams.  See CEE220 notes on combined states of stress or Hibbeler's book.

Do not forget that the absolute maximum shear stress is half the algebraic difference  between the maximum and minimum principal stresses.  Thus in a pressure vessel where the in-plane principal stresses are tensile, the third principal stress is the minimum one.  It varies from 0 on the outer face to -p at the inner face subjected to pressure p.  p is small compared with the in-plane stresses, so the minimum principal stress can be taken as zero.

In Problem 4.25, you need to relate the inclination angle of the seam to the width of the strip. The seam is a helix, which makes a constant angle a with the circumferential direction.  Thus tana = Dz/rDq = pitch/2pr.  Note that the pitch is axial, whereas w as defined in the figure is perpendicular to the seam.

Problem 4.32:  I don't understand the statement of the problem.

Week 6

Ch. 4: Stress and Strain, Secs. 4.8 to 4.14

Problems: 4.17, 4.18, 4.20, 4.21, 4.22, 4.23, 4.24, 4.29

Read problems  4.16, 4.19

Weeks 7, 8

Ch. 5: Stress-Strain-Temperature Relations

Secs. 5.1 to 5.8, (5.9, 5.10 lightly), 5.11 to 5.15, (5.16 - 5.18 lightly)

Problems: 5.1 to 5.4, 5.7, 5.8, 5.9, 5.10, 5.12, 5.13, 5.14, 5.16, 5.20, 5.24, 5.25, 5.27, 5.31, 5.32, 5.41, 5.48, 5.52

Read 5.5, 5.6, 5.21, 5.22, 5.28, 5.42, 5.43, 5.49, 5.50, 5.51

Week 9

Ch. 6: Torsion

Notes:

a) In Sec. 6.2, a discussion, based on symmetries, shows that a radial line in a cross-section of a circular shaft in torsion must remain straight.  The discussion is interesting in that it illustrates how arguments of symmetry can be used to draw significant conclusions. However, one can present the topic in a different manner:  The simplest model for the deformation of a shaft in torsion is to assume that a cross-section rotates as a rigid figure about an axis of twist.  One can then show that this assumption satisfies all the governing equations and boundary conditions for the case of pure torsion of a shaft of circular cross-section.  For a non-circular cross-section, the assumption turns out to be wrong.  In that case, in addition to the twisting rotation, the deformation model requires an axial displacement that warps the cross-section.

You may want to read the CEE 220 web notes on torsion.

b) Try to do Example 2 using the general solution for springs in parallel.  In the present case the springs are torsional, having stiffness GI_z/L. 

c) The last paragraph of Sec. 6.14 indicates that deformation remains to be studied.  See the web notes for CEE 459 on torsion and Problem 6.42.

Problems: 6.1, 6.2, 6.3(try the springs-in-parallel approach), 6.5, 6.6, 6.7, 6.8, 6.14, 6.15, 6.19, 6.27, 6.35, 6.40, 6.43

Weeks 10, 11

Ch. 7: Stresses due to Bending

Secs. 7.1 to 7.5.  See also CEE 220 notes.

Comment:  CDL call the centroidal axis the neutral axis.  My notes call neutral axis the intersection of the neutral plane with the cross-section, which is the z axis. The axial strain and stress are zero on what is called neutral.

Problems: 7.1, 7.2, 7.6, 7.8, 7.14, 7.15, 7.16, 7.17, 7.19, 7.20, 7.25, 7.29, 7.30

Secs. 7.6 to 7.8

Problems: 7.36, 7.37, 7.38, 7.39, 7.41, 7.42, 7.43, 7.44, 7.46 (theory of composite beams), 7.49, 7.51 (theory of reinforced concrete beams in elastic behavior), 7.52, 7.62

Secs. 7.9, 7.10, See material of 7.11 in CEE 549, 7.12 (see also CEE 459)

Problems: 7.65, 7.70, 7.75, 7.76, 7.77, 7.79, 7.81

Weeks 12, 13

Ch. 8: Deflections due to Bending

Secs. 8.1 to 8.3

Problems to be done by integration of the bending moment-curvature relation:

8.15, 8.2(without use of singularity functions), 8.2(with use of singularity functions)

Sec. 8.4

Problems to be done by superposition of available solutions:

8.3, 8.5, 8.6, 8.7, 8.8, 8.10, 8.16(1,2), 8.67, 8.22, 8.48, 8.47

Sec. 8.5

Problems to be done by integration of the Load-Deflection differential equation:

8.2, 8.3

Sec. 8.6

Problems to be done by Castigliano's Theorem (II):

8.22, 8.23, 8.24, 8.65(b)

Sec. 8.7: Limit Analysis

Problems 8.50, 8.51, 8.53, 8.54

Week 14

Ch. 9: Stability of Equilibrium: Buckling

Secs. 9.1 to 9.4

Problems: 9.1 to 9.6, 9.18, 9.7

Notes:

Prob. 9.5: Recall that, for infinitesimal displacements, the change in length of a straight line depends only on the axial end-displacements, i.e. the displacement components along that line.

Prob. 9.6: Draw a general buckled shape, assuming some x₁ and x₂.  Write two equilibrium equations not involving the reactions at the support.  Recognize an eigenvalue problem.

Problems: 9.8 to 9.10, (9.10 - modified: Let F = 0, and find buckling load):  all by EIv'' = M.

Secs. 9.5 to 9.8

Problems: 9.11, 9.13, 9.14, 9.15

Note: In Prob. 9.15 (g), the snap-through should be from q₁ to 2p - q₁.