Question

 Classify each of the plane trusses shown in Fig. Q1.1 as unstable, statically determinate, or statically indeterminate. Explain your answer for each. If the truss is statically indeterminate, then determine the degree of static indeterminacy.

Answer 1

Conditions for static determinacy and stability of trusses:

Let: m = number of members in the truss

r = number of external support reactions for the truss

j = number of nodes in the truss.

1. m + r = 2j is statically determine

2. m + r < 2j is statically unstable

3. m+r > 2j is statically indeterminate

Q1.

a.

m = 2,

r = 3,

j = 3

m+r = 2+3 = 5

2j = 2*3 = 6

m+r < 2j

This plane is statically unstable

b.

m = 9

r = 3

j = 6

m + r = 9 + 3 = 12

2 j = 2 * 6 = 12

m + r = 2 j

This plane truss is statically determinate

c.  

m = 3

r = 4

j = 4

m + r = 3 + 4 = 7

2 j = 2 * 4 = 8

m + r < 2 j

This plane truss is statically unstable

D.

m = 17

r = 3

j = 9

m + r = 17 + 3 = 20

2 j = 2 * 9 = 18

m + r > 2 j

This plane is statically indeterminate

The degree of static inderminacy = m + r - 2 j

= 17 + 3 - 2 * 9

= 2

E.

m = 24

r = 6

j = 15

m + r = 24 + 6 = 30

2 j = 2 * 15 = 30

m + r = 2 j

This plane is statically determinate

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