L06_Statically Indeterminate- 10

L06_Statically Indeterminate- 10 - EAS 209-Fall 2010...

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EAS 209-Fall 2010 Instructors: Christine Human 8/24/2010 1 06-Statically Indeterminate Lecture 6 Statically Indeterminate Structures Today’s Objectives: Be able to recognize a statically indeterminate structure Analyze statically indeterminate structures subjected to axial loading Consider temperature effects Today’s Homework: EAS 209-Fall 2010 Instructors: Christine Human 8/24/2010 2 06-Statically Indeterminate Statically Indeterminate Structure– reactions and internal member forces cannot be determined from statics alone. No. of Unknowns> No. of Equilibrium Equations A structure will be statically indeterminate whenever it is held by more supports than are required to maintain its equilibrium To obtain a second equation we can consider the deflections of the member. Sum forces in y-direction Σ F y : R A + R B = P Only one equilibrium equation relating the two unknowns, R A and R B . Note that Σ F x or Σ M do not help us here NEED ADDITONAL INFORMATION

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EAS 209-Fall 2010 Instructors: Christine Human 8/24/2010 3 06-Statically Indeterminate Since we know that the total displacement of the bar must be zero due to the fixed end supports 0 0 2 1 = + = = + = AE L N AE L N BC AC BC AC δ From FBD we do know that N AC = R A and N BC =- R B from which 0 0 2 1 2 1 = = = L R L R AE L R AE L R B A B A Combining the above equation based on displacement compatibility with the equilibrium condition we can solve for the reactions () 1 2 1 2 1 2 2 1 0 L L L P R L L L P R L R P L R P R R B A A A B A + = + = = = + Determine member forces and stresses as before.
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L06_Statically Indeterminate- 10 - EAS 209-Fall 2010...

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