6. Shear and Moment in Beams
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Transcript of 6. Shear and Moment in Beams
SHEAR AND MOMENT IN BEAMS(Lecture 6)
Mechanics of Deformable Bodies (MEC32)
Engr. Derwin Daniel C. Bautista
Instructor, School of CEGE
Mapua Institute of Technology
BEAM
• A structure usually horizontal, acted upon by transverse loads (forces that acts perpendicular to the plane containing the longitudinal axis of the beam).
• Statically Indeterminate Beams
• Beams that are over-supported in the sense that each beam has at least one more reaction than is necessary for support.
BEAM SUPPORTS AND LOADINGS
STATICALLY INDETERMINATE BEAMS
SHEAR AND MOMENT DIAGRAM
• Convenient visual references to the internal forces in a beam
• Internal Forces:
• Beam Shear
• Bending Moment
SHEAR AND MOMENT DIAGRAM
• The slope of the shear diagram at each point is the distributed load intensity at each point.
• The slope of the moment diagram at each point is the shear at each point.
SIGN CONVENTION(Load, Shear, and Moment)
PROBLEMS
• PROBLEM 1
• Draw the shear and moment diagrams for the beam shown.
PROBLEMS
• PROBLEM 2
• Draw the shear and moment diagrams for the beam shown.
PROBLEMS
• PROBLEM 3 and 4
• Draw the shear and moment diagrams for the beam shown.
PROBLEMS
• PROBLEM 5
• Draw the shear and moment diagrams for the beam shown.
PROBLEMS
• PROBLEM 6
• Draw the shear and moment diagrams for the beam shown.
PROBLEMS
• PROBLEM 7
• Draw the shear and moment diagrams for the beam shown.
PROBLEMS
• PROBLEM 8
• Draw the shear and moment diagrams for the beam shown.
PROBLEMS
• PROBLEM 9
• Draw the shear and moment diagrams for the beam shown.
PROBLEMS
• PROBLEM 10
• Draw the shear and moment diagrams for the beam shown.
PROBLEMS
• PROBLEM 12
• Draw the load and the bending moment diagrams that corresponds to the shear diagram shown. Assume no couples are applied to the beam.
REFERENCES
• Pytel, A., & Kiusalaas, J. (2012). Mechanics of Materials (2nd ed.). Cengage Learning.
• Hibbeler, R. (2011). Mechanics of Materials (8th ed.). Prentice Hall.
• Pytel, A., & Singer, F. (1987). Strength of Materials (4th ed.). Harper and Row.