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GRAPHICAL METHOD

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GRAPHICAL METHOD Powered By Docstoc
					GRAPHICAL METHOD

            BY
GP CAPT NC CHATTOPADHYAY
       ANALYSIS OF FORCE SYSTEMS
           ANALYTICAL                      GRAPHICAL
• USE OF ALGEBRA,GEOMETRY,        • USE OF GEOMETRY, VECTORS,
  TRIGONOMETRY                      TRIANGLE AND POLYGON LAW
• LAWS OF MECHANICS               • EASILY APPLIED TO ALL KINDS/
                                    NATURE/ QUANTITY OF FORCES
  - PARALLELOGRAM
                                  • EXTENSIVELY USED IN
  - LAMI                            ANALYSING ENGG STRUCTURES
  -VARIGNON                         AND COMPLEX FRAMES
  - EQUILLIBRIUM CONDITIONS       • COMPARITIVELY EASY TO
                                    UNDERSTAND/ ANALYSE
• EASY TO SOLVE TO THREE FORCES
                                    COMPLEX FORCE SYSTEM
• CUMBERSOME FOR MULTIPLE
  FORCE SYSTEM
        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
CAN WE THINK OF…..
              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
                Ra        Rb
           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
    F2




C
             B
         D


                   F1
    F3   A
              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 ……
• 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.
CAN WE NOW FOLLOW ……..
 THE RULES OF THE GAME?

				
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