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NEW 375 Lecture03

# NEW 375 Lecture03 - REVISIT ACTIONS ON A CROSS-SECTION OF...

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REVISIT ACTIONS ON A CROSS-SECTION OF AN AXIALLY LOADED MEMBER A

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Normal Stress X Differential Normal Force Differential Area of cross-section σ σ x dA = dF dF = ACTION ON DIFFERENTIAL AREA OF CROSS-SECTION STRESS DIFFERENTIAL FORCE
σ ACTIONS ON TOTAL CROSS-SECTION STRESSES DIFFERENTIAL FORCES d F d A = σ

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σ STRESSES FORCES d F d A = σ VOLUME of STRESS WEDGE = Stress Wedge σ A = P =RESULTANT FORCE Resultant Force P P d F P d A P A = = = σ σ σ c.g. Uniform Stress
FOR AN AXIAL FORCE ACTING THROUGH THE CENTROID OF THE CROSS-SECTION: σ σ = P A a l l o w a b l e Material Property Constant: See Table of Typical Properties of Selected Engineering Materials σ a l l o w a b l e

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FOR AN AXIAL FORCE ACTING THROUGH THE CENTROID OF THE CROSS-SECTION: No. 1 Investigation Problem: Given: P, A, and σ allowable [ material dependent - see table ] Ques: Can the given member safely resist the applied load? Solution: if σ = P/A ≤ σ allow SAFE if σ = P/A > σ allow NOT SAFE σ σ = P A a l l o w a b l e Material Property Constant: See Table of Typical Properties of Selected Engineering Materials σ a l l o w a b l e
FOR AN AXIAL FORCE ACTING THROUGH THE CENTROID OF THE CROSS-SECTION: No. 2 Investigation Problem: Given: A, and σ allowable Ques: What is the maximum axial force P all the member can safely resist ? Solution: P all = A σ allow σ σ = P A a l l o w a b l e

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FOR AN AXIAL FORCE ACTING THROUGH THE CENTROID OF THE CROSS-SECTION: No.3 Design Problem: Given: P, and σ allowable Ques: What is the magnitude of the minimum required cross-sectional area, A req’d , for a member to safely resist the force on the cross-section? Solution: A req’d = P / σ allowable No. 2 Investigation Problem: Given: A, and σ allowable Ques: What is the maximum axial force P all the member can safely resist ?
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NEW 375 Lecture03 - REVISIT ACTIONS ON A CROSS-SECTION OF...

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