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ANALYSIS OF TRUSS
BY
GP CAPT NC CHATTOPADHYAY
ANALYSIS OF FRAME
• A FRAME IS A STRUCTURE MADE OF SEVERAL BARS/ RODS
WELDED / RIVETTED TOGETHER
• THE BARS ARE ANGLE IRONS/ CHANNELS OF “I” OR “T”
SECTIONS. THESE ARE CALLED MEMBERS
• ON APPLICATION OF LOAD ON TO THE STRUCTURE, THE
MEMBERS REMAIN LOADED WITH TENSILE/ COMPRESSIVE
LOAD
• MEMBERS UNDER TENSION ARE CALLED “TIE”
• MEMBERS UNDER COMPRESSION ARE CALLED “STRUT”
• THE STRUCTURE FORMED BY THE MEMBERS (TIE/ STRUT) IS
CALLED “TRUSS”
• EXTENSIVELY USED IN ROOF, BRIDGE, SHEDS ETC.
TYPES
PERFECT
• STRUCTURE IS MADE OF
MEMBERS JUST SUFFICIENT
TO KEEP IT IN EQUILIBRIUM,
WHEN LOADED WITHOUT
ANY CHANGE OF SHAPE
• n = 2j – 3 where ‘n’ is
the number of
members and ‘J’ no of
joints
• It is efficient and
optimised structure
IMPERFECT
• STRUCTURE IS MADE OF
MEMBERS MORE OR LESSER
THAN THE MINIMUM
NUMBERS NECESSARY TO
KEEP IT IN EQUILIBRIUM,
WHEN LOADED
• n ≠ 2j – 3
• n > 2j – 3 REDUNDANT
• n < 2j – 3 DEFICIENT
• INEFFICIENT STRUCTURE
PERFECT VS IMPERFECT
B
A
C
STRESSES IN A FRAME
• UNDER APPLICATION OF LOAD THE STRUCTURE
TENDS TO DEFORM. THE MATERIAL OF THE FRAME
TENDS TO KEEP THE FRAME RIGID ( PREVENTS
DEFORMATION)
• AN INTERNAL RESISTIVE FORCE IS SET IN IN THE
MATERIAL . THIS INDUCES STRESS.
• σ = INTERNAL RESISTANCE / AREA
• LOAD CAN BE PULL / PUSH (TENSILE/ COMPRESSIVE)
• FOR JOINTS TO BE IN EQUILIBRIUM THE MEMBERS
MAY CARRY ZERO LOAD/ TENSILE/ COMPRESSIVE
LOAD.
CONVENTIONS
• ANALIST HAS TO IDENTIFY THE SITUATION ,
MAKE A MENTAL PICTURE OF THE FORCES
AND DECIDE THE ARROWS.
• A LOAD WITH ARROW AWAY FROM THE
JOINT IS TENSILE
• A LOAD WITH ARROW TOWARDS THE JOINT
IS COMPRESSIVE
ASSUMPTIONS
• THE FRAME IS A PERFECT FRAME
• MEMBERS ARE PIN JOINTED (Every member of
the truss is then in pure compression or pure
tension – shear, bending moment, and other
more complex stresses are all practically zero. )
• LOADS ACT ON THE JOINTS ONLY
• WEIGHT OF THE MEMBER AS COMPARED TO
THE EXTERNAL LOADS IS NEGLIGIBLE AND NOT
CONSIDERED FOR CALCULATIONS.
SOLUTIONS
•
•
•
•
ANALYTICAL
USE OF TRIGONOMETRY/
GEOMETRY/ ALGEBRA
TWO METHODS (JOINT &
SECTION METHODS)
THE METHODS CAN BE
CUMBERSOME AND LENGTHY
AND LEAD TO ERRORS
A COMPARISON ON NEXT
SLIDE
GRAPHICAL
• USE OF CONCEPT OF ENGG DRG
• USE OF SPACE, VECTOR DIAGRAM
AND A LOAD TABLE
• VECTOR DIAGRAM OF EACH JOINT
(MAXWELL DIAGRAM) AND
COMPOSITE VECTOR DIAGRAM
GIVES THE SOLUTION
• SELECT THE 1ST JOINT WITH 2 UNK
FORCES AND THEN PROCEED TO THE
NEXT JOINT
• IT IS SIMPLE , EASY AND FULL PROOF
• INITALLY ANALYTICAL METOD TOBE
USED FOR CALCULATION OF
REACTIONS
ANALYTICAL SOLUTIONS
JOINT METHOD
• FORCES OF EA JOINT IS ANALYSID
ONE BY ONE
• SELECT A JOINT WITH 2 UNK
FORCES
• ANALYSE THE FORCES AT THAT
JOINT MATHEMATEICALLY AND
THEN PROCEED TO THE NEXT
• FOR COMPLEX FRAME THIS
METHOD IS VERY LONG AND CAN
LEAD TO MATHEMATICAL ERRORS
SECTION METHOD
• THE FRAME IS CUT INTO
SECTIONS
• EA SECTION IS THEREAFTER
ANALYSED USING FBD
• MOMENTS OF EACH MEMBER
W.R.T. A REF POINT IS
CALCULATED AND THE
FORCES ARE BVDETERMINED
• SECTION LINE MUST NOT CUT
MORE THAN 3 MEMBERS
• IT IS VERY TEDIOUS FOR
COMPLEX STRUCTURES
LOAD TABLE
• IT IS THE SUMMARY OF ALL LOADS ACTING
ON ALL THE MEMBERS THAT IS DETERMINED
GRAFHICALLY OR ANALYTICALLY
• SAMPLE TABLE
SLNO
MEMBER
LOAD
TYPE
1
AB
W
COMPRESSION
2
BC
X
COMPRESSION
3
CD
Y
TENSION
4
DA
Z
COMPRESSION
LIFE IS COMFORTABLE ….
AS WE PRACTICE