Chapter 4

Question 1

Stability and Determinacy of Beams

Answer 1

3 + c = r determinate
3 + c > r unstable externally
3 + c < r indeterminate

Where:
r = number of unknown reactions
c = equation of internal conditions for beams:
c = 1.0 for internal hinge
c = 2.0 for internal roller

Question 2

Stability and Determinacy of Frames

Answer 2

3b + r = 3n + s determinate
3b + r > 3n + s indeterminate
3b + r < 3n + s unstable externally

Where:
b = number of bars/segments/members
r = number of unknown reactions
n = number of joints or nodes
s = equation of internal conditions for frames:
s = 1.0 for internal hinge
s = 2.0 for internal roller

Question 3

Stability and Determinacy of Trusses

Answer 3

r + b = 2n determinate
r + b > 2n indeterminate and internally unstable
r + b < 2n statically unstable but determinate

Where:
b = number of bars/segments/members
r = number of unknown reactions
n = number of joints or nodes