ANALYSIS OF TRUSS

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ANALYSIS OF TRUSS

• BY
• GP CAPT NC CHATTOPADHYAY

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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.

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TYPES

• IMPERFECT

• 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

• STRUCTURE IS MADE OF MEMBERS MORE OR LESSER THAN
  THE MINIMUM NUMBERS NECESSARY TO KEEP IT IN
  EQUILIBRIUM, WHEN LOADED
• n ? 2j 3
• n gt 2j 3 REDUNDANT
• n lt 2j 3 DEFICIENT
• INEFFICIENT STRUCTURE

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PERFECT VS IMPERFECT
B
A
C
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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.
• s 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.

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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

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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.

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SOLUTIONS

• ANALYTICAL

• GRAPHICAL

• 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

• 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

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ANALYTICAL SOLUTIONS

• JOINT METHOD

• SECTION 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

• 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

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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
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LIFE IS COMFORTABLE . AS WE PRACTICE