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.