HW

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Exam 3 on Friday December 4th

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Reading and Homework Due

Today:

Pros and Cons of SID Structures; Force Method of Analysis

CENE 376 Fall 2015

Sometimes the utilization of a statically determinate structural system is based on practical considerations for construction - what can be easily built, or what is feasible.

• Why are Statically Indeterminate Structures Used?

12/02/15 S.I.D. Structures & Force Method

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A S.I.D. beam will be capable of carrying more load as compared to a determinate beam of the same cross section size.

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A S.I.D. beam will have smaller transverse deflections than a S.D. beam of the same section size.

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Statically Indeterminate Structures are "more efficient" than comparable S.D. structures…•

Statically Indeterminate Structures are "safer" as a generalization because they possess redundancy. In a S.I.D. structure, if one location fails do to overload, the structure remains stable and can still carry additional loading; it does not collapse. Collapse occurs as soon as n s < 0.

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Method to solve for unknown member forces/moments in a S.I.D. structure.• Involves releasing as many unknown forces/moments as equal to ns and writing compatibility equations to solve for the unknown (released) actions (forces/moments).

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Compatibility equations are equations that state that the structural deformations must be compatible with the boundary conditions.

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"Flexibility" = displacement caused by a unit force (or rotation caused by a unit moment)•

Analysis of Statically Indeterminate Structures by the "Force Method of Analysis"

Many elements of a wood framed structure are statically determinate - common to find S.D.• Reinforced concrete structures are typically S.I.D. because of monolithic nature of construction

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Steel framed structures are commonly both S.I.D. and S.D.•

Have higher load carrying capacity than S.D. structure○

Be stiffer: less deformation for a given load than S.D. structure○

For the same individual member sizes, a S.I.D. structure will:•

OR, S.I.D. structures can use smaller member sizes than S.D. structure•

Summary: S.I.D. versus S.D. Structures

Example:

Given: Find: Determine the BMD

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Example:

Given: Find: Determine the BMD

using the Force Method of

Analysis.

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Determine the degree of static indeterminacy, ns1. Make system statically determinate by releasing ns redundant forces (or moments)…introduce mechanisms to make these releases.

2.

Draw each "system" (the "0": released structure with original loads, the "1": the released structure 3.

Force Method of Analysis Procedure

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Draw each "system" (the "0": released structure with original loads, the "1": the released structure with a unit positive force or moment at location of release), the deformations at the location where the releases was introduced, and the BMD.

3.

For each system, solve for the unknown deformations, fij at locations of releases.4. Write compatibility equation.5. Determine bending moments and shears by superposition.6.

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