Chapter 4: Pure Bending - Union Collegeminerva.union.edu/bucinelr/mer214/LectureNotes/MER21… ·...
Transcript of Chapter 4: Pure Bending - Union Collegeminerva.union.edu/bucinelr/mer214/LectureNotes/MER21… ·...
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Chapter 4:Pure Bending
Composite BeamsEccentric Axial Loading
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Composite Beam
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Redefining Cross-Section
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
4
Composite Beam ProcedureDraw Shear and Bending Moment diagramsCreate an equivalent cross-sectionFind the centroid of the equivalent cross-sectionDetermine the stress distribution of the equivalent cross-sectionTransform the stress in the equivalent cross-section back to the origionalcross-section
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Example 1
A beam section composed of aluminum (E=10 Msi) and steel (E=30 Msi) are bonded together as shown. If the section is undergoing a positive bending moment of Mz=10000 lb-in, determine the resulting stress distribution.
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Example Solution
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Eccentric Axial Loading
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Super-Impose Stress Distribution
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Example 2
The eccentric axial force acts a distance 30mm below the top surface of the steel bar. Determine the stress distribution at the designated cross-section and draw the distribution.
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Solution
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Unsymmetrical bending
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Circular Cross-Section
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Circular Cross-Section
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Rectangular Cross-Section
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Rectangular Cross-Section
Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering
Union College, Schenectady, NY
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Example
Determine the angle between the resultant moment and the z axis, the neutral axis, the value and location of the maximum compressive stress normal to the surface and the value and location of the maximum tensile stress normal to the surface.