L4 - Static Indeterminate Problems Statically...

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Static Indeterminate Problems Statically indeterminate: • internal forces and reactions cannot be determined from statics alone. • More supports than required to maintain equilibrium.
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Statically indeterminant P A B Draw free body diagram P F A F B 0 AB FF F P = +− =
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0 AB FF F P = +− = 2 unknowns 1 equation Cannot be solved w/ statics Need another equation
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Can be solved w/ internal forces P F A F B L1 L2 F A F B F B 1 1 A FL AE δ= 2 2 B AE δ=− F A
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Compatibility Equation: P A B 1 1 A FL AE δ= 2 2 B AE δ=− 12 0 δ δδ = += 0 AB AE AE = 0 FF F P = +− =
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superposition P A B P A A B = + Deformation due to loading Deformation due to support
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P A 2 1 P 2 =0 P 1 =P P P 1 1 PL AE δ= 2 0 1 12 loading PL AE δδ δ =+ = F B
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A B F B F B B reaction FL AE δ =− 1 B total loading reaction P LF L AE AE δδ =+ =
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Thermal Strain Thermal strain: • Change in length due to temperature change • No stress associated from thermal
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L4 - Static Indeterminate Problems Statically...

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