Answers to the Problems

Chapter 1

  1. 1.1   upper P Subscript italic c r Baseline equals StartFraction c Over upper L EndFraction
  2. 1.2   upper P Subscript italic c r Baseline equals StartFraction c Over upper L EndFraction
  3. 1.3   (a) upper P Subscript italic c r Baseline equals StartFraction italic k upper L Over 2 EndFraction

             (b) upper P Subscript italic c r Baseline equals StartFraction k 1 k 2 Over k 1 plus k 2 EndFraction upper L

  4. 1.4   (a) upper P Subscript italic c r Baseline equals StartFraction italic k upper L Over 2 EndFraction

             (b) upper P Subscript italic c r Baseline equals StartFraction k 1 k 2 Over k 1 plus k 2 EndFraction upper L

  5. 1.5   upper P Subscript italic c r Baseline equals Baseline StartFraction c 1 plus 4 c 2 Over 2 upper L EndFraction

  6. 1.6   StartFraction upper P Over upper P Subscript italic c r Baseline EndFraction equals StartFraction 2 Over sine theta EndFraction left-bracket one half cosine 2 theta minus cosine left-parenthesis 45 Superscript o Baseline minus alpha right-parenthesis sine left-parenthesis 45 Superscript o Baseline minus theta right-parenthesis right-bracket

Chapter 2

  1. 2.1   upper P Subscript italic c r Baseline equals StartFraction pi squared italic upper E upper I Over upper L squared EndFraction

           Mode 1: y equals StartFraction normal upper Delta Over 2 EndFraction left-parenthesis 1 minus cosine StartFraction pi x Over upper L EndFraction right-parenthesis

           Mode 2: y equals StartFraction normal upper Delta Over 2 EndFraction left-parenthesis 1 minus cosine StartFraction 3 pi x Over upper L EndFraction right-parenthesis

  2. 2.2   StartLayout 1st Row 1st Column tangent italic k upper L Subscript c 2nd Column equals StartFraction 4 italic k upper L Subscript c Baseline upper I Subscript b Baseline Over 4 upper I Subscript b Baseline plus k squared upper L Subscript c Baseline upper L Subscript b Baseline upper I Subscript c Baseline EndFraction 2nd Row 1st Column upper L Subscript b 2nd Column equals 2 upper L Subscript c Baseline comma upper I Subscript b Baseline equals upper I Subscript c Baseline 3rd Row 1st Column upper P Subscript italic c r 2nd Column equals StartFraction 1.14 pi squared italic upper E upper I Subscript c Baseline Over upper L Subscript c Superscript 2 Baseline EndFraction EndLayout
  3. 2.3   Pcr = 32.69 kips (145.26 kN)
  4. 2.4   
  5. 2.5   
  6. 2.6   
  7. 2.7   
  8. 2.8   

Chapter 3

  1. 3.3   Allowable strength, Pa = 254.74 kips (1143.23 kN) ...

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