CIVE+1160+Ch04

CIVE+1160+Ch04 - Ch.4: Axially Loaded Members College of...

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CIVE 1160 Summer 2011 College of Engineering Ch.4: Axially Loaded Members Frames and other support systems are fabricated so that component members are loaded in tension or compression only, that is without bending or twisting. The loading in the members is parallel to the longer axis, that is axial load is applied to the member. We will apply what we learned about stress, strain and material properties.
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CIVE 1160 Summer 2011 College of Engineering Axial : How it fits in the big picture. Basic case We will use stress to estimate “How  strong?” We will use strain to estimate “How stiff?” Based on assumptions that are  validated by experiment, we will develop   = f(load, geometry)  = f(load, geometry, material) We will introduce the solution to  statically indeterminate problems 
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CIVE 1160 Summer 2011 College of Engineering Basic Assumption: Uniformity of Strain (stress) Saint-Venant’s principle states that the stress distribution will be not be uniform near the point of application of the load and will become uniform with distance. After a distance from the loading the stress will become uniform regardless of how the loads are applied. We will compute stresses and deformations in axially loaded members assuming that the strains (stresses) are uniform.
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CIVE 1160 Summer 2011 College of Engineering Stress  = P/A  = f(load, geometry)
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CIVE 1160 Summer 2011 College of Engineering Elastic Deformation The relative displacement of one end of the member with respect to the other end is δ . For a segment of length dx the relative displacement of the segment ends is d δ . Assuming elastic behavior (E = constant): A(x)E P(x)dx E A(x) P(x) E = = = δ ε σ d dx d Fig 4-2
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CIVE 1160 Summer 2011 College of Engineering Integration Over Length L Integration of the previous equation: For P(x) = constant and A(x) = constant : For members that are piecewise linear: = L 0 A(x)E P(x)dx δ EA PL AE PL L = = = 0 dx AE P = AE PL
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CIVE 1160 Summer 2011 College of Engineering Sign Convention Cut a section between each applied force to determine the magnitude and direction of the resultant internal force. If
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CIVE+1160+Ch04 - Ch.4: Axially Loaded Members College of...

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