ANALYSIS OF TRUSS

1. ANALYSIS OF TRUSS BY GP CAPT NC CHATTOPADHYAY

4. 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.

5. TYPES PERFECT 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 • 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

6. PERFECT VS IMPERFECT B A C

7. 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.

8. 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

9. 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.

11. SOLUTIONS ANALYTICAL 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 • 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

13. ANALYTICAL SOLUTIONS JOINT METHOD 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 • 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

15. LOAD TABLE • IT IS THE SUMMARY OF ALL LOADS ACTING ON ALL THE MEMBERS THAT IS DETERMINED GRAFHICALLY OR ANALYTICALLY • SAMPLE TABLE

16. LIFE IS COMFORTABLE …. AS WE PRACTICE