SME
Structural Analysis · Problem type
Determinate, indeterminate or unstable
Use this for “A six-panel Pratt truss sits on a pin and a roller. Is it statically determinate?”
Diagram
m + r − 2j = 21 + 3 − 24 = 0: statically determinate, so the joints alone give every force.
This is an example. Type your own values to start a new problem.
m
=
4
×
n
−
3
j
=
2
×
n
D
=
m
+
r
−
2
×
j
Formulas
m
=
4
×
n
−
3
21 = 4 × 6 − 3
j
=
2
×
n
12 = 2 × 6
D
=
m
+
r
−
2
×
j
0 = 21 + 3 − 2 × 12
Assumptions
•
A Pratt truss with end posts: m = 4n − 3 members and j = 2n joints for n panels.
•
A pin gives 2 reactions and a roller 1; each joint gives 2 equilibrium equations.
•
D < 0 is unstable, 0 determinate, > 0 indeterminate; a 0 can still be unstable when members are badly arranged.
Step-by-step
WE KNOW
n = 6, r = 3
FIND
members (m), joints (j), degree of indeterminacy (D)
Step 1 · Find members (m)
Use m = 4 × n − 3
n
bottom
chords,
n
−
2
top
chords,
2
end
posts,
n
−
1
verticals
and
n
−
2
diagonals.
m
=
4
×
6
−
3
m
=
24
−
3
m
=
21
Step 2 · Find joints (j)
Use j = 2 × n
n
+
1
lower
joints
and
n
−
1
upper
ones.
j
=
2
×
6
j
=
12
Step 3 · Find degree of indeterminacy (D)
Use D = m + r − 2 × j
Unknowns (member forces and reactions) minus equations (two at each joint); a 0 still needs a stable arrangement.
D
=
21
+
3
−
2
×
12
D
=
21
+
3
−
24
D
=
0
Check
Put the numbers back in. Both sides should match.
21 = 4 × 6 − 3 ✓
12 = 2 × 6 ✓
0 = 21 + 3 − 2 × 12 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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Determinate structures
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