Defination,Analysis of frames,stresses in frame,convention, assumptions, solutions(analytical), Learning outcomes

1. ANALYSIS OF TRUSS

2. Syed Raheel Zafar

3. WHAT IS TRUSS?
• A truss is a structure comprising one or more
triangular units constructed with straight
members whose ends are connected at joints.
• If all the bars lie in a plane, the structure is a
planar truss.
• The main parts of a planar truss.

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
• MEMBERS UNDER COMPRESSION
• THE STRUCTURE FORMED BY THE MEMBERS IS CALLED
“TRUSS”
• EXTENSIVELY USED IN ROOF, BRIDGE, SHEDS ETC.

5. 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.

6. CONVENTIONS
• ANALYST 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

7. ASSUMPTIONS
MEMBERS ARE RIGIDILY JOINT (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.

8. 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

9. 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

10. LEARNING OUTCOME
• Types of joints and supports
• Zero force members
• Material choice
• Factor of safety
• Design analysis
• Trial and error