Question

Question 1. Classify each of the structures shown in Figure 1 as statically determinate, statically indeterminate, stable or unstable. If indeterminate, specify the degree of indeterminacy. The supports or connections are to be assumed as stated. (10 marks) Pin Fixed Roller Pin Pin (a) Pin Roller (b) Figure 1

Answer 1

Determinacy →lf m+& <a <aj alf mte = dj → underrigid structure =) Statically determinate → statically indeterminate If m+&> aj Stability If mis <aj stable structure - If mih zaj Unstable structure where m= total no of members. = minimum no. of reactive components required for external stability. = total no of joints. c. (0) 2 3 2 m 2 3 r=6 (masked with red ist) Note: At fixed and there are 3 reactive components ie vestical and horizontal force component and a moment. Rolles support only have vertical force reactive component and hinged a reactive components ie horizontal & vestical force reactive components. suppost have j = 4 m+& 3+6=9.

aj= 2x4 =8 8 .. and mte> aj » Structure is statically indeterminate Structure is unstable. Degree of Indeterminary, I = (m+8) - 2j I = 9-8 I = (112 4 8 3 9 lo 6. 11 m=1 r=3 j = 7 mte=11+3=14 aj 2x7 214 M +8 = aj » The above structure is statically determinate and unstable.