Classify each of the structures as statically determinate st

Classify each of the structures as statically determinate, statically indeterminate, stable or unstable. (If Indeterminate, specify the degree of indeterminacy). Gii) pin (iv)

Solution

Ans- i) Since all the three supports are rollers thus the no of unknown reactions is 3 and equilibrium equations are also 3. Thus it is a determinate structure. For stability- If a structure doesn\'t follow a rigid body motion on applying external forces it is said to be stable. If a force will be applied to this structure it will start moving horizontally thus it is unstable.

ii) Since both the supports are fixed thus the no of unknown reactions is 6 and equilibrium equations are 3. Thus it is an indeterminate structure with a degree of indeterminacy 6-3 = 3. For stability- If a structure doesn\'t follow a rigid body motion on applying external forces it is said to be stable. If a force will be applied to this structure it will not show any rigid body motion thus it is stable.

iii) The two supports are roller and one is hinged thus the no of unknown reactions is 4 and equilibrium equations are also 3. Thus it is an indeterminate structure with a degree of indeterminacy 4-3 = 1. For stability- If a structure doesn\'t follow a rigid body motion on applying external forces it is said to be stable. If a force will be applied to this structure it will not move as a rigid body, thus it is stable.

iv) Since both the supports are pin thus the no of unknown reactions is 4 and equilibrium equations are also 3. Thus it is an indeterminate structure with a degree of indeterminacy 4-3 = 1. For stability- If a structure doesn\'t follow a rigid body motion on applying external forces it is said to be stable. If a force will be applied to this structure it will not move thus it is stable.