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The degree of static indeterminancy for statically determinate beam is equal to
1
2
0
3
0
A structure is classified as statically determinate if all its internal forces and support reactions can be determined using only the equations of static equilibrium. By definition, for such structures, the degree of static indeterminacy (DsтАЛ) is always zero.
A structure is classified as statically determinate if all its internal forces and support reactions can be determined using only the equations of static equilibrium. By definition, for such structures, the degree of static indeterminacy (DsтАЛ) is always zero.
DsтАЛ=rтИТe тАФ General formula for static indeterminacy
DsтАЛ=0 тАФ Condition for static determinacy
Static indeterminacy (DsтАЛ) is calculated as the total number of unknown reactions (r) minus the number of available equilibrium equations (e). For a plane beam, equilibrium equations are тИСFxтАЛ=0, тИСFyтАЛ=0, and тИСM=0 (e=3). When r=e, the structure is statically determinate, resulting in DsтАЛ=rтИТe=0.
A structure is determinate when the number of unknowns equals the number of equilibrium conditions.
Indeterminate structures require additional compatibility equations for solving support reactions.
For beams, e=3 (in 2D space) generally.
Easier to analyze manually.
Forces are independent of material properties and cross-sectional dimensions.
Generally less redundant compared to indeterminate structures.
Failure of a single support leads to global collapse.
Simply supported beams
Cantilever beams
Overhanging beams
If DsтАЛ>0, the structure is statically indeterminate (hyperstatic).
If DsтАЛ<0, the structure is geometrically unstable (mechanism).
C is correct тАФ The degree of static indeterminacy for any statically determinate structure is defined as zero.
Always check for internal hinges or rollers when calculating DsтАЛ, as they provide additional condition equations (eextraтАЛ) which effectively reduce the degree of indeterminacy.
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