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GRAPHICAL METHOD. BY GP CAPT NC CHATTOPADHYAY. ANALYSIS OF FORCE SYSTEMS. ANALYTICAL. GRAPHICAL. USE OF GEOMETRY, VECTORS, TRIANGLE AND POLYGON LAW EASILY APPLIED TO ALL KINDS/ NATURE/ QUANTITY OF FORCES EXTENSIVELY USED IN ANALYSING ENGG STRUCTURES AND COMPLEX FRAMES

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graphical method

GRAPHICAL METHOD

BY

GP CAPT NC CHATTOPADHYAY

analysis of force systems
ANALYSIS OF FORCE SYSTEMS

ANALYTICAL

GRAPHICAL

USE OF GEOMETRY, VECTORS, TRIANGLE AND POLYGON LAW

EASILY APPLIED TO ALL KINDS/ NATURE/ QUANTITY OF FORCES

EXTENSIVELY USED IN ANALYSING ENGG STRUCTURES AND COMPLEX FRAMES

COMPARITIVELY EASY TO UNDERSTAND/ ANALYSE COMPLEX FORCE SYSTEM

  • USE OF ALGEBRA,GEOMETRY, TRIGONOMETRY
  • LAWS OF MECHANICS

- PARALLELOGRAM

- LAMI

-VARIGNON

- EQUILLIBRIUM CONDITIONS

  • EASY TO SOLVE TO THREE FORCES
  • CUMBERSOME FOR MULTIPLE FORCE SYSTEM
graphical method1
GRAPHICAL METHOD
  • IT IS SIMILAR TO POLYGON LAW OF FORCES
  • FORCES ARE REPRESENTED IN THEIR RELATIVE POSITION/ EXACT ORIENTATION
  • ENTIRE FORCE SYSTEM IS REPRESENTED BY TWO DIAGRAMS VIZ- SPACE DIAGRAM AND VECTOR DIAGRAM
space diagram
SPACE DIAGRAM
  • IT IS A DIAGRAMATIC REPRESENTATION OF VARIOUS LOADS WITH THEIR MAGNITUDES, LINES OF ACTION AND POINTS OF APPLICATION
  • A SYSTEM OF NOTATION CALEED ” BOW’S NOTATION” IS FOLLOWED TO REPRESENT THE FORCES IN SPACE DIAGRM.

A

B

C

Rb

Ra

bow s notation
BOW’S NOTATION
  • TO NOTIFY ALL FORCES ACTING IN THE SYETEM
  • EACH FORCE IN THE SPACE DIAGRAM IS REPRESENTED BY A PAIR OF LETTERS / NUMERALS. CAPITAL LETTERS ARE PREFERED AS SMALL LETTERS WILL BE USED IN THE VECTOR DIAGRAM
  • CHOOSING OF LETTERS IS FLEXIBLE VIZ ABCDE…, PQRST…
  • TO AVOID CONFUSION NUMERALS 123.. ARE NOT PREFERED
  • THIS SCHEME OF NOTATION WILL BE USED IN ANALYSIS OF STRUCTURES / FRAMES/TRUSS
example
EXAMPLE

F2

C

B

D

F1

A

F3

vector diagram
VECTOR DIAGRAM
  • IT IS A VECTOR REPRESENTATION OF THE ENTIRE FORCE SYSTEM, CONSIDERING ALL FORCES ONE BY ONE IN THEIR RELATIVE POSITION ( AS IN SPACE DIAGRAM) ALONG THE SIDES OF A POLYGON KEEPING THEIR MAGNITUDE AND DIRECTION UNCHJANGED
  • START FROM ANY ARBITRARY / CONVENIENT POINT BY THE SIDE OF THE SPACE DIAGRAM
  • ADD THE FORCES ONE BY ONE CHOOSING A SUITABLE SCALE
  • CLOSING SIDE WILL REPRESENT RESULTANT
  • EXTENSIVE USE OF PARALLEL LINES USING SET SQUARES
  • EXTENSIVE USE IN ANALYSING A TRUSS (NEXT CLASS)
practice
PRACTICE ……
  • TRY TO SOLVE THE WORKED OUT EXAMPLES OF THE BOOK TO GAIN CONFIDENCE
  • THEN ONLY U SHOULD TRY UNSOLVED QUESTIONS
  • CHOOSE APPROPRIATE SCALE FOR THE SPACE AND VECTOR DIAGRAMS TO KEEP THE PAIR OF DIAGRAMS ON THE SAME PAGE SIDE BY SIDE.