GRAPHICAL METHOD
BY
GP CAPT NC CHATTOPADHYAY
ANALYSIS OF FORCE SYSTEMS
ANALYTICAL
• 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
• 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
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
Ra
Rb
C
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?