Reliability Analysis Of Shear Strength Of A

“Reliability Analysis of Shear Strength of a RCC Beam by Point Estimate Method” By

Rakesh Kumar S STRUCTURAL ENGINEERING

Under the guidance of

Dr Devaraj V Professor UVCE ,Bangalore university

INTRODUCTION



THE



THE SAFETY OF STRUCTURE STRUCTURE.



THE PERFORMANCE OF THE STRUCTURE IS ASSESSED BY ITS SAFETY, SERVICEABILITY AND ECONOMY.

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INPUT VARIABLES ARE NEVER CERTAIN, PRECISE AND COMPLETE. THIS IS WHERE, RELIABILITY PLAYS AN IMPORTANT ROLE.

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“RELIABILITY IS THE PROBABILITY OF AN ITEM PERFORMING ITS INTENDED FUNCTION OVER A GIVEN PERIOD OF TIME UNDER THE OPERATING CONDITIONS ENCOUNTERED”.

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EVALUATION OF SAFETY OF STRUCTURES IS A TASK OF MUCH IMPORTANCE, IT HAS BEEN THE HIGHEST PRIORITY FOR ANY ENGINEER. DEPENDS ON THE RESISTANCE,R

AND THE LOAD,S ACTING ON THE

METHODS OF ASSESSING RELIABILTITY 

FIRST ORDER SECOND MOMENT METHOD.



POINT ESTIMATE METHOD.

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HASOFER LIND METHOD.

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MONTE CARLO SIMULATION TECHNIQUE.

POINT ESTIMATE METHOD   

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FIRST PRESENTED BY ROSEN BLUETH IN 1975 AND LATER EXTENDED BY HIM IN 1981,HAS SEEN CONSIDERABLE USE AND EXPANSION. AN ANALOGY HAS BEEN ESTABLISHED BETWEEN A PROBABILITY DISTRIBUTION AND A DISTRIBUTED VERTICAL LOAD ON A HORIZONTAL RIGID BEAM. THE EXPECTED VALUE WAS THE ANALOG OF THE POINT OF EQUILIBRIUM AND THE STANDARD DEVAITION WAS ITS RADIUS OF GYRATION, WHICH SUPPLY INFORMATION CONCERNING CENTRAL TENDENCY AND SCATTER OF VARIABLE. ROSENBLUETH SUGGESTED THAT THIS INFORMATION CAN BE EXTRACTED WITH RIGID BEAM SUPPORTED ON TWO REACTIONS,P– ACTING AT X=X– AND P+ ACTING AT X+.

SHEAR STRENGTH FORMULATION

 MARGIN

OF SAFETY= RESISTANACE-

LOAD  IN RELIABILITY ANALYSIS OF SHEAR STRENGTH, 

      

 RELIABILITY, 

 WHERE

MEAN VALUES ARE CALCULATED AS =

    AND

SIMILARLY OTHERS ARE CALCULATED BY REPLACING Fy.  NUMBER OF ITERATIONS DEPENDS ON NUMBER OF VARIABLES PRESENT IN EACH EQUATION, AND IS CALCULATED AS , 



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HERE REISTANCE EQUATION AS 8 VARIABLES AND LOAD AS 2 VARIABLES, AND ITERATIONS ARE DONE AS FOLLOWS:-

Upper bound and lower bound values are calculated as and calculated for other variables also  Upper bound 



 Lower

bound



 NOW

AFTER COMPUTING THE ABOVE VALUES, WE HAVE TO COMPUTE THE RELIABILITY INDEX  AND CALCULATE PROBABLITY OF FAILURE.

MODEL CALCULATION  RELIABILITY

ANALYSIS OF SHEAR STRENGTH OF RCC BEAM BY POINT ESTIMATE MEATHOD.

 

=95 N/mm2 =1.25mm

=8 variable

RESULTS AND DISCUSSIONS  THE

RELIABILITY INDEX OBTAINED IS 7.31 , WHICH IS GREATER THAN TARGET MEAN STRENGTH OF 3.5, HENCE SAFE.  PROBABILITY OF SAFETY IS MORE THAN 100%.

conclusions  THE

RELIABILITY INDEX OBTAINED IS 7.31 , WHICH IS SAFE.  POINT ESTIMATE METHOD IS EASIEST METHOD, WHICH INVOLVES SIMPLE MATHE MATICAL CALCULATIONS.  DESIGNS MADE UNDER THE CODE AND OTHER STANDARD PROVISIONS ARE UNECONOMICAL RATHER MORE SAFE. 

REFERENCES 1.MILTON E HARR, RELIABILITY – BASED DESIGN IN CIVIL ENGINEERING, MCGRAW-HILL BOOK COMPANY,INC,NEW YORK,1987. 2.RANGANATHAN R, STRUCTURAL RELIABILITY ANALYSIS AND DESIGN, JAICO PUBLISHING HOUSE,1999. 

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