GRAPHICAL METHOD BY GP CAPT NC CHATTOPADHYAY ANALYSIS

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 F 2 C B D F 3 A F 1

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?