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.
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