# GRAPHICAL METHOD by nikeborome

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• pg 1
```									GRAPHICAL METHOD

BY
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.