Structural Analysis Book
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Introductory Structural Analysis Problems
Nielsen
Introduction:
This book is intended as a study aid for students studying Introductory Structural Analysis. The Author has strived to present problems that would be found in a typical engineering class, in a hand drawn style that will be familiar to any student who has put pencil to engineering paper.
If any errors or omissions are discovered, please report them to NieKo Technical Publishing for correction in future editions.
1
Introductory Structural Analysis Problems
Nielsen
2
Introductory Structural Analysis Problems
Nielsen
Problems: Determinate Structures:
Page
1) Equations of Equilibrium a) Beams b) Frames c) Trusses
9
2) Shear and Moment Diagrams a) Beams b) Frames
21
3) Virtual Work – Deflections a) Beams b) Frames c) Trusses
33
4) Visual Integration –Deflections a) Beams b) Frames c) Trusses
51
Indeterminate Structures – Support Reactions Page 1) Force Method with Virtual Work a) Beams b) Frames
65
2) Force Method with Visual Integration a) Beams b) Frames
81
3) Moment Distribution Method a) Beams b) Frames
93
3
Introductory Structural Analysis Problems
Nielsen
4
Introductory Structural Analysis Problems
Nielsen
Notation: A - Area (sq. in.) L – Length (feet or inches) E – Modulus of Elasticity (K/in2) or (ksi) I – Moment of Inertia (in4) k – kips = 1000 lbs. mv – Virtual Moment (kft) M – Real Moment (kft) n – Virtual Axial Force (k) N – Real Axial Force (k) FEM – Fixed End Moment (kft) DF – Distribution Factors FBD – Free Body Diagram ƒ aa – Flexibility Coefficient Δ - Deflection (in)
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Introductory Structural Analysis Problems
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Introductory Structural Analysis Problems
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7
Introductory Structural Analysis Problems
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8
Introductory Structural Analysis Problems
Nielsen
Equations of Equilibrium Statically Determinate Structures Beams Frames Trusses
Since the problems shown deal with 2 dimensional structures, the following equations of equilibrium are used throughout this book. Sum of the forces in the X direction are zero.
∑Fx = 0 Sum of the forces in the Y direction are zero.
∑Fy = 0 Sum of the moments about the Z axis are zero.
∑M = 0
9
Introductory Structural Analysis Problems
Nielsen
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20
Introductory Structural Analysis Problems
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Shear And
Moment Diagrams
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Introductory Structural Analysis Problems
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Introductory Structural Analysis Problems
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Virtual Work Deflections
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50
Introductory Structural Analysis Problems
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Visual Integration Deflections
51
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52
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64
Introductory Structural Analysis Problems
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Force Method With Virtual Work
65
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Force Method With Visual Integration
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Moment Distribution Method
93
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Nielsen
Introduction:
This book is intended as a study aid for students studying Introductory Structural Analysis. The Author has strived to present problems that would be found in a typical engineering class, in a hand drawn style that will be familiar to any student who has put pencil to engineering paper.
If any errors or omissions are discovered, please report them to NieKo Technical Publishing for correction in future editions.
1
Introductory Structural Analysis Problems
Nielsen
2
Introductory Structural Analysis Problems
Nielsen
Problems: Determinate Structures:
Page
1) Equations of Equilibrium a) Beams b) Frames c) Trusses
9
2) Shear and Moment Diagrams a) Beams b) Frames
21
3) Virtual Work – Deflections a) Beams b) Frames c) Trusses
33
4) Visual Integration –Deflections a) Beams b) Frames c) Trusses
51
Indeterminate Structures – Support Reactions Page 1) Force Method with Virtual Work a) Beams b) Frames
65
2) Force Method with Visual Integration a) Beams b) Frames
81
3) Moment Distribution Method a) Beams b) Frames
93
3
Introductory Structural Analysis Problems
Nielsen
4
Introductory Structural Analysis Problems
Nielsen
Notation: A - Area (sq. in.) L – Length (feet or inches) E – Modulus of Elasticity (K/in2) or (ksi) I – Moment of Inertia (in4) k – kips = 1000 lbs. mv – Virtual Moment (kft) M – Real Moment (kft) n – Virtual Axial Force (k) N – Real Axial Force (k) FEM – Fixed End Moment (kft) DF – Distribution Factors FBD – Free Body Diagram ƒ aa – Flexibility Coefficient Δ - Deflection (in)
5
Introductory Structural Analysis Problems
Nielsen
6
Introductory Structural Analysis Problems
Nielsen
7
Introductory Structural Analysis Problems
Nielsen
8
Introductory Structural Analysis Problems
Nielsen
Equations of Equilibrium Statically Determinate Structures Beams Frames Trusses
Since the problems shown deal with 2 dimensional structures, the following equations of equilibrium are used throughout this book. Sum of the forces in the X direction are zero.
∑Fx = 0 Sum of the forces in the Y direction are zero.
∑Fy = 0 Sum of the moments about the Z axis are zero.
∑M = 0
9
Introductory Structural Analysis Problems
Nielsen
10
Introductory Structural Analysis Problems
Nielsen
11
Introductory Structural Analysis Problems
Nielsen
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Introductory Structural Analysis Problems
Nielsen
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Introductory Structural Analysis Problems
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Introductory Structural Analysis Problems
Nielsen
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Introductory Structural Analysis Problems
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Introductory Structural Analysis Problems
Nielsen
17
Introductory Structural Analysis Problems
Nielsen
18
Introductory Structural Analysis Problems
Nielsen
19
Introductory Structural Analysis Problems
Nielsen
20
Introductory Structural Analysis Problems
Nielsen
Shear And
Moment Diagrams
21
Introductory Structural Analysis Problems
Nielsen
22
Introductory Structural Analysis Problems
Nielsen
23
Introductory Structural Analysis Problems
Nielsen
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Introductory Structural Analysis Problems
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Introductory Structural Analysis Problems
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31
Introductory Structural Analysis Problems
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32
Introductory Structural Analysis Problems
Nielsen
Virtual Work Deflections
33
Introductory Structural Analysis Problems
Nielsen
34
Introductory Structural Analysis Problems
Nielsen
35
Introductory Structural Analysis Problems
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Introductory Structural Analysis Problems
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Introductory Structural Analysis Problems
Nielsen
48
Introductory Structural Analysis Problems
Nielsen
49
Introductory Structural Analysis Problems
Nielsen
50
Introductory Structural Analysis Problems
Nielsen
Visual Integration Deflections
51
Introductory Structural Analysis Problems
Nielsen
52
Introductory Structural Analysis Problems
Nielsen
53
Introductory Structural Analysis Problems
Nielsen
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Introductory Structural Analysis Problems
Nielsen
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Introductory Structural Analysis Problems
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64
Introductory Structural Analysis Problems
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Force Method With Virtual Work
65
Introductory Structural Analysis Problems
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Introductory Structural Analysis Problems
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80
Introductory Structural Analysis Problems
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Force Method With Visual Integration
81
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Introductory Structural Analysis Problems
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Moment Distribution Method
93
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