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

2

Composite Beam

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenectady, NY

3

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

5

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

7

Eccentric Axial Loading

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenectady, NY

8

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

10

Solution

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenectady, NY

11

Unsymmetrical bending

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenectady, NY

12

Circular Cross-Section

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenectady, NY

13

Circular Cross-Section

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenectady, NY

14

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.