ME 101: Engineering Mechanics

A. Narayana Reddy

Department of Mechanical Engineering,Indian Institute of Technology Guwahati,

Guwahati - 781039, India.

Beams and cables

Previous discussiondetermining external forces acting on a structure

determining forces which hold together the various members of astructure

Current discussionDetermining the internal forces (i.e., tension/compression, shear, andbending) which hold together the various parts of a given member.

Beams and cablesBeams - usually long, straight, prismatic members designed to supportloads applied at various points along the member

Cables - flexible members capable of withstanding only tension,designed to support concentrated or distributed loads

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 2 / 33

Beams

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 3 / 33

Internal forces in beams

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 4 / 33

Example

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 5 / 33

Example

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 6 / 33

Example

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 7 / 33

Example

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 8 / 33

Example

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 9 / 33

Beams with different type of loads

(c) Distributed load with discontinuity

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 10 / 33

Statically determinate and indeterminate beams

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 11 / 33

Distributed loads

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 12 / 33

General distributed load

The reaction forces can be evaluated by replacing the distrubuted load with the concentrated load R at centroid.

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 13 / 33

Example-1

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 14 / 33

Example-2

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 15 / 33

Example-3

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 16 / 33

Internal effects

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 17 / 33

Internal effects

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 18 / 33

Internal effects

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 19 / 33

Sign convention

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 20 / 33

Sign convention

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 21 / 33

Shear force and bending moment diagrams

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 22 / 33

Shear force and bending moment diagrams

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 23 / 33

Example-1

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 24 / 33

Example-1

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 25 / 33

Example-1

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 26 / 33

Example-2

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 27 / 33

Example-2

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 28 / 33

Example-2

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 29 / 33

Example-2

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 30 / 33

Example-2

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 31 / 33

Relation between shear force and bending moment

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 32 / 33

Relation between shear force and bending moment

Lecture 5 A Narayana Reddy Indian Institute of Technology Guwahati 33 / 33