ANALYSIS OF TRUSS

BYGP 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.

TYPESPERFECT

• 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

A

B

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