4 30 points For each truss shown below check internal stabil

4. (30 points) For each truss shown below, check internal stability and state whether each truss is statically unstable, statically determinate or statically indeterminate. Calculate the degree of static indeterminacy if applicable

Solution

a) If (m+r>=2j) then it is stable other wise unstable

m= number of members

r=number of reactions

j=number of joints

17+3>2*9 Hence stable.

Statically Indeterminate.

Degree of indeterminacy = m+r-2j =17+3-2*9 =20-18 =2

b) If (m+r>=2j) then it is stable other wise unstable

m= number of members

r=number of reactions

j=number of joints

12+3>2*7 Hence stable.

Statically Indeterminate.

Degree of indeterminacy = m+r-2j =12+3-2*7 =15-14 =1

c) If (m+r>=2j) then it is stable other wise unstable

m= number of members

r=number of reactions

j=number of joints

25+4>2*14 Hence stable.

Statically Indeterminate.

Degree of indeterminacy = m+r-2j =25+4-2*14 =29-28 =1

d) If (m+r>=2j) then it is stable other wise unstable

m= number of members

r=number of reactions

j=number of joints

24+6>2*15 Hence stable.

Statically determinate.

Degree of indeterminacy = m+r-2j =24+6-2*15 =30-30 =0