Test the Strength of Structural Members

7/27/2019 Test the Strength of Structural Members

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4EST THE 3TRENGTH OF

3TRUCTURAL -EMBERS

,EARNING !CTIVITY

/VERVIEW OF THE !CTIVITY

)N THIS LEARNING ACTIVITY WE WILL TEST THE STRENGTHS OF THE CARDBOARD STRUCTURAL MEMBERS WE USED IN OURMODEL OF THE 'RANT 2OAD "RIDGE 7E WILL DESIGN A SERIES OF EXPERIMENTS TO DETERMINE THE STRENGTHS OF THESEMEMBERS IN BOTH TENSION AND COMPRESSION 4HE EXPERIMENTS WILL BE CONDUCTED WITH A SIMPLE TESTING MACHINETHAT USES A LEVER TO APPLY A CONTROLLED FORCE TO A TEST SPECIMEN

4O ANALYZE THE EXPERIMENTAL DATA OBTAINED FROM THE TESTING MACHINE WE WILL LEARN AND APPLY THE PRINCIPLEOF THE LEVER &INALLY WE WILL USE A COMPUTER SPREADSHEET TO GRAPH THE RESULTS OF OUR TESTS 4HESE GRAPHS WILL HELPUS TO OBSERVE HOW VARIOUS PHYSICAL PROPERTIES AFFECT THE STRENGTH OF A STRUCTURAL MEMBER 7E WILL ALSO USE THESEGRAPHS AS A TOOL FOR ANALYZING AND DESIGNING BRIDGES IN ,EARNING !CTIVITIES AND

7HY

4O DESIGN A STRUCTURE AN ENGINEER MUST BE ABLE TO DETERMINE THE STRENGTHS OF THE STRUCTURAL MEMBERS THATCOMPRISE IT )N ,EARNING !CTIVITY WE SAW THAT EXTERNAL LOADS CAUSE INTERNAL FORCES TO DEVELOP IN A STRUCTURE7E ALSO OBSERVED THAT A STRUCTURE CAN SUCCESSFULLY CARRY ITS EXTERNAL LOADS ONLY IF THE INTERNAL MEMBER FORCES ARELESS THAN THE CORRESPONDING MEMBER STRENGTHS 4HUS AN ENGINEER CANT EVALUATE THE LOADCARRYING ABILITY OF THE

STRUCTURE WITHOUT lRST BEING ABLE TO DETERMINE MEMBER STRENGTHS

%NGINEERS DETERMINE THE STRENGTHS OF MEMBERS IN TWO DIFFERENT WAYSTHROUGH EXPERIMENTATION ANDTHROUGH THE APPLICATION OF SCIENTIlC PRINCIPLES 4HE SCIENTIlC STUDY OF STRUCTURAL MEMBERS AND MATERIALS ISCALLED THE MECHANICS OF MATERIALS 4HE MECHANICS OF MATERIALS IS TYPICALLY TAUGHT AS AN ENTIRE UNDERGRADUATE

)T IS NOT INTENDED THAT STUDENTS BUILD THE TESTING MACHINE AS PART OF THIS LEARNING ACTIVITY 4HE DEVICE ISQUITE SIMPLE BUT IT WILL REQUIRE SOME WOODWORKING SKILL TO BUILD $ETAILED DRAWINGS AND DIMENSIONS AREPROVIDED )N !PPENDIX # /NE DEVICE WILL BE ADEQUATE FOR A CLASS OF STUDENTS HOWEVER ONE DEVICE PER FOUROR lVE STUDENTS WILL GREATLY ENHANCE THE OPPORTUNITIES FOR HANDSON PARTICIPATION IN THE LEARNING ACTIVITY/NCE BUILT THE TESTING MACHINE CAN BE REUSED INDElNITELY


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ENGINEERING COURSE AND THUS IS BEYOND THE SCOPE OF THIS BOOK )N THIS LEARNING ACTIVITY WE WILL DETERMINEMEMBER STRENGTHS PRIMARILY THROUGH EXPERIMENTATION (OWEVER BY CAREFULLY EXAMINING TRENDS IN OUR EXPERIMENTAL DATA WE WILL DISCOVER SOME OF THE FUNDAMENTAL PRINCIPLES ON WHICH THE MECHANICS OF MATERIALS IS BASED

7E WILL ALSO LEARN HOW TO DESIGN A SERIES OF EXPERIMENTS TO OBTAIN THE DATA REQUIRED TO SOLVE A PROBLEM 4HEABILITY TO DESIGN AND CONDUCT EXPERIMENTS IS NOT JUST IMPORTANT TO STRUCTURAL ENGINEERSIT IS A CRITICAL SKILL IN A

WIDE VARIETY OF ENGINEERING AND SCIENTIlC lELDS

,EARNING /BJECTIVES

!S A RESULT OF THIS LEARNING ACTIVITY YOU WILL BE ABLE TO DO THE FOLLOWING

#ALCULATE THE CROSSSECTIONAL AREA OF A STRUCTURAL MEMBER

$ESCRIBE THE YIELDING RUPTURE AND BUCKLING FAILURE MODES

%XPLAIN THE FACTORS THAT AFFECT THE TENSILE STRENGTH AND THE COMPRESSIVE STRENGTH OF A STRUCTURAL MEMBER

$ESIGN A TESTING PROGRAM TO DETERMINE THE STRENGTH OF STRUCTURAL MEMBERS

$ETERMINE THE TENSILE STRENGTH AND THE COMPRESSIVE STRENGTH OF STRUCTURAL MEMBERS THROUGH EXPERIMENTATION

%XPLAIN THE PRINCIPLE OF THE LEVER AND APPLY THIS PRINCIPLE TO THE ANALYSIS OF EXPERIMENTAL DATA 5SE A COMPUTER SPREADSHEET TO ANALYZE AND GRAPH EXPERIMENTAL DATA

+EY 4ERMS

4O SUCCESSFULLY COMPLETE THIS LEARNING ACTIVITY YOU MUST UNDERSTAND THE FOLLOWING KEY TERMS AND CONCEPTSFROM ,EARNING !CTIVITY

MEMBER LOAD TENSION STRENGTH

FORCE INTERNAL FORCE COMPRESSION FAILURE

)NFORMATION

#ROSS3ECTION AND #ROSS3ECTIONAL !REA

/NE OF THE MOST IMPORTANT CHARACTERISTICS AFFECTING THE STRENGTH OF A STRUCTURAL MEMBER IS ITS CROSSSECTION! CROSSSECTION IS THE TWODIMENSIONAL SHAPE YOU SEE WHEN YOU LOOK AT THE END OF A MEMBER )N THE

ILLUSTRATION BELOW FOR EXAMPLE THE SOLID ROD HAS A CIRCULAR CROSSSECTION AND THE SOLID BAR HAS A RECTANGULARCROSSSECTION

#ROSS3ECTIONW

H

4YPICAL 3TRUCTURAL -EMBERS

W

H

3OLID 2OD3OLID "AR

(OLLOW 4UBE

3HAPE

3OLID 2OD 3OLID "AR (OLLOW 4UBE 3HAPE

4YPICAL STRUCTURAL MEMBERS AND THEIR CROSSSECTIONS


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4HE CROSSSECTIONAL AREA IS THE SURFACE AREA OF THE CROSSSECTION &OR EXAMPLE THE CROSSSECTIONAL AREA OF THESOLID BAR ON THE PREVIOUS PAGE IS THE AREA OF THE BLACK RECTANGLE 4O CALCULATE IT YOU WOULD MULTIPLY THE WIDTH W BYTHE HEIGHT H 4HE CROSSSECTIONAL AREA IS ALWAYS EXPRESSED IN UNITS OF LENGTH SQUAREDFOR EXAMPLE SQUAREINCHES OR SQUARE MILLIMETERS

4ENSILE 3TRENGTH

)N ,EARNING !CTIVITY WE DElNED STRENGTH AS THE MAXIMUM INTERNAL FORCE A MEMBER CAN CARRY BEFORE IT

FAILS 4HE INTERNAL FORCE IN A STRUCTURAL MEMBER CAN BE EITHER TENSION OR COMPRESSION "ECAUSE THE FAILURE OF ASTRUCTURAL MEMBER IN TENSION IS VERY DIFFERENT FROM ITS FAILURE IN COMPRESSION WE MUST CONSIDER THE TENSILESTRENGTH AND COMPRESSIVE STRENGTH SEPARATELY

4ENSILE STRENGTH IS THE MAXIMUM TENSION FORCE A MEMBER CAN CARRYBEFORE IT FAILS !S THIS DElNITION SUGGESTS ONE WAY TO DETERMINE THE TENSILESTRENGTH OF A MEMBER IS TO LOAD IT IN TENSION UNTIL IT FAILSTHAT IS PULL ONTHE MEMBER FROM BOTH ENDS UNTIL IT PHYSICALLY BREAKS IN TWOTHEN MEASURE THE AMOUNT OF FORCE THAT CAUSED THE FAILURE

3UPPOSE WE WANTED TO TEST THE TENSILE STRENGTH OF A CARBON STEEL BAR#ARBON STEEL IS ONE OF THE MOST COMMON MATERIALS USED IN STRUCTURES )T ISA MIXTURE OF IRON AND A VERY SMALL AMOUNT OF CARBONLESS THAN &OR

OUR CARBON STEEL TEST SPECIMEN WE WILL USE THE BAR SHOWN HERE )T HAS A SQUARE CROSSSECTION MEASURING INCHON EACH SIDE 4HIS CROSSSECTION IS TYPICALLY DESIGNATED v X v hONE INCH BY ONE INCHv AND ITS CROSSSECTIONALAREA IS SQUARE INCH

3TEEL IS QUITE STRONG 4O BREAK A STEEL BAREVEN THIS RELATIVELY SMALL ONEWE WILL NEED A SPECIAL MACHINE LIKE THE ONEPICTURED BELOW 4HIS HYDRAULIC TESTING MACHINE IS CAPABLE OFSTRETCHING A TEST SPECIMEN WITH MANY THOUSANDS OF POUNDS 4HEMACHINE CAN MEASURE BOTH THE LOAD ON THE SPECIMEN AND ITSCORRESPONDING DEFORMATIONTHE INCREASE IN THE LENGTH OF THEBAR AS IT IS STRETCHED

4O DETERMINE THE TENSILE STRENGTH OF AMEMBER PULL ON IT FROM BOTH ENDS UNTIL ITBREAKS IN TWO

! HYDRAULIC TESTING MACHINE

4O TEST THE BAR WE WILL CLAMP ITS ENDS INTO THE MACHINE AND GRADUALLY INCREASE THE LOAD UNTIL THE STEEL FAILS!S THE LOAD IS APPLIED THE MACHINE WILL CONTINUOUSLY MEASURE AND RECORD BOTH THE LOAD AND THE DEFORMATION OFTHE SPECIMEN )F WE PLOT THESE DATA ON A GRAPH THE RESULT WILL LOOK SOMETHING LIKE THIS

v

v

v


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,OADDEFORMATION CURVE FOR A v X v CARBON STEEL BAR

,OAD

POUNDS

$EFORMATION INCHES

89IELD 0OINT 2UPTURE

5LTIMATE 3TRENGTH

9IELD 3TRENGTH

,OAD

POUNDS

$EFORMATION INCHES

89IELD 0OINT

89IELD 0OINT

5LTIMATE 3TRENGTH

9IELD 3TRENGTH

5LTIMATE 3TRENGTH

9IELD 3TRENGTH

4HIS GRAPH IS CALLED A LOADDEFORMATION CURVE )T SHOWS US HOW THE MEMBER DEFORMSAND ULTIMATELY HOW ITFAILSAS THE LOAD IS INCREASED ! CAREFUL EXAMINATION OF THE LOADDEFORMATION CURVE WILL TELL US A LOT ABOUTCARBON STEEL ,ETS EXAMINE THE CURVE FROM LEFT TO RIGHT 4HE LOADDEFORMATION CURVE ORIGINATES IN THE LOWERLEFTHAND CORNER OF THE GRAPH WHICH TELLS US THAT THE DEFORMATION IS ZERO WHEN THE LOAD IS ZERO 4HIS CERTAINLYMAKES SENSE 4HE BAR WONT START TO STRETCH UNTIL WE APPLY A FORCE TO IT !S WE FOLLOW THE CURVE UP AND TO THERIGHT WE NOTICE THAT THE CURVE IS ALMOST PERFECTLY STRAIGHT FROM ZERO ALL THE WAY UP TO ABOUT POUNDS 4HESTRAIGHT LINE MEANS THAT THE DEFORMATION INCREASES IN DIRECT PROPORTION TO THE LOAD &OR EXAMPLE THE DEFORMATION AT POUNDS IS EXACTLY TWICE AS LARGE AS THE DEFORMATION AT POUNDS )N THIS LINEAR PART OF THELOADDEFORMATION CURVE THE BEHAVIOR OF THE STEEL BAR IS SAID TO BE ELASTIC %LASTIC BEHAVIOR MEANS THAT IF THELOAD IS REMOVED THE DEFORMATION WILL ALSO RETURN TO ZERO 7HEN A MEMBER IS ELASTIC IT ALWAYS RETURNS TO ITSORIGINAL LENGTH AFTER IT IS UNLOADED 4HIS PARTICULAR STEEL BAR WILL REMAIN ELASTIC AS LONG AS THE LOAD ON IT IS KEPTBELOW POUNDS 7HEN THE LOAD DOES REACH POUNDS THE DEFORMATION OF THE BAR IS JUST OVER v4HE TOTAL LENGTH OF THE BAR HAS INCREASED FROM v TO vA CHANGE OF ONLY ABOUT ONE TENTH OF ONE PERCENT

!S THE LOAD IS INCREASED BEYOND POUNDS THE BEHAVIOR OF THE BAR CHANGES RATHER ABRUPTLY 4HERE ISSUDDENLY A HUGE INCREASE IN DEFORMATION WITH VIRTUALLY NO CHANGE IN THE LOAD 4HE STEEL IS BEGINNING TO FAIL7HEN A MATERIAL UNDERGOES LARGE DEFORMATIONS WITH LITTLE CHANGE IN LOAD IT IS SAID TO BE YIELDING 4HE POINT ONTHE LOADDEFORMATION CURVE WHERE YIELDING BEGINS IS CALLED THE YIELD POINT AND THE FORCE AT WHICH YIELDINGOCCURS IS CALLED THE YIELD STRENGTH "EYOND THE YIELD POINT THE STEEL STRETCHES LIKE TAFFY !ND UNLIKE THE ELASTICBEHAVIOR WE OBSERVED EARLIER ANY DEFORMATION THAT OCCURS BEYOND THE YIELD POINT WILL NOT DISAPPEAR AFTER THELOAD IS REMOVED 4HIS PERMANENT ELONGATION OF THE MEMBER IS CALLED PLASTIC DEFORMATION .OTE THAT AS THEPLASTIC DEFORMATION INCREASES THE BAR EVENTUALLY BEGINS TO CARRY MORE LOAD 4HE LOAD PEAKS AT POUNDS

WHICH IS CALLED THE ULTIMATE STRENGTH OF THE MEMBER !FTER FURTHER PLASTIC DEFORMATION THE SPECIMEN lNALLYBREAKS INTO TWO PIECES 4HIS FAILURE MODE IS CALLED A RUPTURE

3O WHAT IS THE TENSILE STRENGTH OF THIS STEEL MEMBER )S IT THE YIELD STRENGTH OR THE ULTIMATE STRENGTH 3INCE

THE TENSILE STRENGTH IS THE FORCE AT WHICH THE MEMBER FAILS THE ANSWER TO THIS QUESTION DEPENDS ON HOW THESTRUCTURAL ENGINEER CHOOSES TO DElNE hFAILUREv &OR MOST PRACTICAL STRUCTURAL APPLICATIONS THE ENGINEER WOULDPROBABLY WANT TO ENSURE THAT THE MEMBER DOES NOT YIELD )N SUCH CASEShFAILUREv WOULD BE DElNED AS YIELDINGAND THE TENSILE STRENGTH WOULD BE POUNDSTHE YIELD STRENGTH )N SOME CASES HOWEVER THE ENGINEERMIGHT ONLY WANT TO ENSURE THAT THE MEMBER DOES NOT RUPTURE )N SUCH CASES THE TENSILE STRENGTH WOULD BE POUNDSTHE ULTIMATE STRENGTH 4HIS LATTER DElNITION OF FAILURE MIGHT BE APPROPRIATE FOR EXAMPLE WHENTHE ENGINEER IS DESIGNING FOR THE EFFECT OF AN EXTRAORDINARY EVENT LIKE A MAJOR EARTHQUAKE )N SUCH CASES THEENGINEER MIGHT BE WILLING TO ACCEPT SOME PLASTIC DEFORMATION OF THE STRUCTURE AS LONG AS IT DOES NOT COLLAPSE

4HE TEST MACHINE MEASURES THE LOAD APPLIED TO THE BAR 7HAT WE ARE REALLY INTERESTED IN HOWEVER IS THEINTERNAL FORCE IN THE BAR &ORTUNATELY IN THIS TEST THE MAGNITUDE OF THE LOAD AND THE INTERNAL MEMBER FORCEARE EXACTLY EQUAL #AN YOU EXPLAIN WHY


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4HIS IS AN IMPORTANT AND OFTEN MISUNDERSTOOD POINTIN STRUCTURAL ENGINEERING THERE IS OFTEN NO SINGLE UNIVERSALLY ACCEPTED DElNITION OF hFAILUREv 2ATHER THE ENGINEER MUST EXERCISE HIS OR HER PROFESSIONAL JUDGMENT TODETERMINE THE CONDITIONS UNDER WHICH A STRUCTURE OR A COMPONENT OF A STRUCTURE NO LONGER WILL FUNCTION ASINTENDED

/NE OTHER CHARACTERISTIC OF THE LOADDEFORMATION CURVE FOR THE CARBON STEEL BAR IS WORTH MENTIONING .OTETHAT AT RUPTURE THE BAR HAS DEFORMED TWO FULL INCHES OF ITS ORIGINAL LENGTH 4HIS CAPACITY TO UNDERGO VERYLARGE PLASTIC DEFORMATION AFTER YIELDING IS CALLED DUCTILITY $UCTILITY IS ONE OF THE MOST BENElCIAL PROPERTIES OFSTEEL AND IT IS ONE OF THE MOST IMPORTANT REASONS WHY STEEL IS SO WIDELY USED IN STRUCTURES 7HEN A DUCTILEMEMBER BEGINS TO FAIL ITS LARGE PLASTIC DEFORMATION PROVIDES AN OBVIOUS WARNING THAT SOMETHING IS WRONG WITHTHE STRUCTURE 4HIS WARNING PROVIDES AN OPPORTUNITY TO EVACUATE PEOPLE AND MAKE EMERGENCY REPAIRS BEFORETHE STRUCTURE COLLAPSES &OR THIS REASON DUCTILITY GREATLY ENHANCESSTRUCTURAL SAFETY

.OT ALL STRUCTURAL MATERIALS ARE DUCTILE -ATERIALS THAT DO NOTUNDERGO LARGE PLASTIC DEFORMATION PRIOR TO FAILURE ARE CALLEDBRITTLE MATERIALS ! TYPICAL LOADDEFORMATION CURVE FOR A BRITTLEMATERIAL IS SHOWN AT RIGHT .OTE THAT THE MATERIAL RUPTURES WITHOUT YIELDING AND THUS WITHOUT GIVING ANY WARNING THAT A FAILURE ISABOUT TO OCCUR &OR THIS REASON BRITTLE MATERIALS ARE GENERALLYUNDESIRABLE FOR STRUCTURAL MEMBERS #AST IRON IS A BRITTLE MATERIAL

WHICH EXPLAINS WHY CAST IRON HAS BEEN ENTIRELY REPLACED BY STEELIN MODERN STRUCTURES #ONCRETE IS A BRITTLE MATERIAL WHICHEXPLAINS IN PART WHY CONCRETE IS ALWAYS REINFORCED WITH STEELBARS WHEN IT IS USED AS A STRUCTURAL MATERIAL

7E HAVE SEEN HOW ONE PARTICULAR STRUCTURAL MEMBER MADE OFONE PARTICULAR MATERIAL CAN BE TESTED TO DETERMINE ITS TENSILESTRENGTH )F WE WERE TO REPEAT THIS TEST WITH MANY DIFFERENTMEMBERSDIFFERENT SIZES DIFFERENT CROSSSECTIONS AND DIFFERENTMATERIALSSOME PATTERNS WOULD BEGIN TO EMERGE ! CAREFULANALYSIS OF THESE PATTERNS WOULD REVEAL THE FOLLOWING FACTS ABOUTTHE TENSILE STRENGTH OF STRUCTURAL MEMBERS

4ENSILE STRENGTH DEPENDS ON THE CROSSSECTIONAL AREA OF A MEMBER !S THE CROSSSECTIONAL AREA INCREASESTHE TENSILE STRENGTH INCREASES IN DIRECT PROPORTION TO THE AREA )F THE CROSSSECTION OF OUR CARBON STEEL BAR

WERE CHANGED FROM v X v TO v X v THE CROSS SECTIONAL AREA WOULD INCREASE FROM SQUARE INCH TO SQUAREINCHES AND THE YIELD STRENGTH WOULD INCREASE FROM POUNDS TO ABOUT POUNDSFOUR TIMESGREATER

4ENSILE STRENGTH DEPENDS ON THE TYPE OF MATERIAL THE MEMBER IS MADE OF %VERY MATERIAL HAS ITS OWN CHARACTERISTIC STRENGTH MEASURED IN UNITS OF FORCE PER AREA FOR EXAMPLE POUNDS PER SQUARE INCH OR NEWTONS PERSQUARE METER 4HE YIELD STRENGTH OF CARBON STEEL IS POUNDS PER SQUARE INCH /THER TYPES OF STEEL

WITH YIELD STRENGTHS OF POUNDS PER SQUARE INCH AND HIGHER ARE COMMON 4HE TENSILE STRENGTH OF AMEMBERCAN BE CALCULATED BY MULTIPLYING THE TENSILE STRENGTH OF THE MATERIALBY THE CROSSSECTIONAL AREA OFTHE MEMBER

4ENSILE STRENGTH DOES NOT DEPEND ON THE LENGTH OF A MEMBER )F WE USED THE SAME v X v CROSSSECTION BUT

CHANGED THE LENGTH OF OUR SPECIMEN FROM v TO v THE TENSILE STRENGTH WOULD REMAIN EXACTLY THE SAME

4ENSILE STRENGTH DOES NOT DEPEND ON THE SHAPE OF THE CROSSSECTION )F WE TESTED A HOLLOW TUBE OR CIRCULARROD WITH A CROSSSECTIONAL AREA OF SQUARE INCH WE WOULD lND THAT ITS TENSILE STRENGTH IS EXACTLY THE SAME ASTHE v X v SQUARE STEEL BAR

4HESE OBSERVATIONS WILL GUIDE THE DESIGN OF OUR OWN TESTING PROGRAM LATER IN THIS LEARNING ACTIVITY

#OMPRESSIVE 3TRENGTH

#OMPRESSIVE STRENGTH IS THE MAXIMUM COMPRESSION FORCE A MEMBER CAN CARRY BEFORE IT FAILS 7E CANDETERMINE THE COMPRESSIVE STRENGTH OF A STRUCTURAL MEMBER BY LOADING IT IN COMPRESSION UNTIL IT FAILS THEN

,OAD

$EFORMATION

8

2UPTURE

5LTIMATE3TRENGTH

,OAD

$EFORMATION

8

2UPTURE

5LTIMATE3TRENGTH

,OADDEFORMATION CURVE FOR A BRITTLE MATERIAL


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MEASURING THE AMOUNT OF FORCE REQUIRED TO CAUSE THE FAILURE

4O UNDERSTAND HOW A STRUCTURAL MEMBER FAILS IN COMPRESSION TRY THE FOLLOWING SIMPLEEXPERIMENT (OLD A YARDSTICK OR METER STICK VERTICALLY WITH ITS BOTTOM END ON THE mOOR.OW PUT THE STICK IN COMPRESSION BY PUSHING DOWNWARD ON ITS TOP END 'RADUALLY INCREASETHE COMPRESSION FORCE !T SOME POINT THE STICK WILL SUDDENLY BEND SIDEWAYSIN ENGINEERING TERMS IT WILL BUCKLE "UCKLING IS A FAILURE THAT OCCURS WHEN COMPRESSION CAUSES AMEMBER TO SUDDENLY BEND SIDEWAYS PERPENDICULAR TO THE DIRECTION OF THE APPLIED LOAD"UCKLING IS THE MOST COMMON FAILURE MODE FOR STRUCTURAL MEMBERS IN COMPRESSION 7HENA MEMBER FAILS BY BUCKLING ITS COMPRESSIVE STRENGTH IS THE INTERNAL FORCE AT WHICH BUCKLINGOCCURS

4RY REPEATING THE SAME EXPERIMENT WITH A INCH WOODEN RULER 5NLESS YOURE REALLYSTRONG YOULL PROBABLY lND THAT YOU CANT PUSH HARD ENOUGH ON THE INCH RULER TO MAKE ITBUCKLE 4HIS OBSERVATION SUGGESTS AN IMPORTANT CHARACTERISTIC OF BUCKLING FAILURES 3HORTERMEMBERS HAVE GREATER COMPRESSIVE STRENGTH THAN LONGER ONES

.OW SUPPOSE WE WANTED TO TEST THE COMPRESSIVE STRENGTH OF A v X v CARBON STEEL BAR!GAIN WE WOULD NEED TO USE OUR HYDRAULIC TESTING MACHINE TO LOAD THE BAR )T WOULD TAKE ABOUT POUNDSOF COMPRESSIVE FORCE TO CAUSE THE vLONG BAR TO BUCKLE 2ECOGNIZING THAT THE COMPRESSIVE STRENGTH OF THE BARDEPENDS ON ITS LENGTH WE WOULD NEED TO TEST A SERIES OF v X v SQUARE BARS EACH WITH A DIFFERENT LENGTH 7E

WOULD lND THAT INCREASING THE LENGTH OF THE BAR TO v WOULD CAUSE A SUBSTANTIAL REDUCTION IN ITS STRENGTHTOABOUT POUNDS ! v BAR WOULD FAIL AT AROUND POUNDS )F WE TESTED MEMBERS WITH LENGTHS UP TOv AND PLOTTED THE RESULTS ON A GRAPH OF COMPRESSIVE STRENGTH VS LENGTH THE RESULT WOULD LOOK LIKE THIS

,ENGTH INCHES

#OMP

RESSIVE3TRENGTHPOUNDS

#OMPRESSIVE STRENGTH VS LENGTH FOR A vXv CARBON STEEL BAR

4HIS GRAPH VIVIDLY ILLUSTRATES THE EFFECT OF MEMBER LENGTH ON COMPRESSIVE STRENGTH .OTE THAT AN vMEMBER IS LESS THAN ONETENTH AS STRONG AS A v MEMBER EVEN THOUGH THEIR CROSSSECTIONS ARE IDENTICAL

(OW DO THE SIZE AND SHAPE OF THE CROSSSECTION AFFECT COMPRESSIVE STRENGTH )N ,EARNING !CTIVITY WEOBSERVED THAT HOLLOW TUBES SEEM TO BE MORE EFFECTIVE THAN SOLID BARS AT CARRYING COMPRESSION ,ETS TEST THATOBSERVATION NOW WITH ANOTHER SIMPLE EXPERIMENT 5SING THE SAME lLEFOLDER CARDBOARD YOU USED TO BUILD THE'RANT 2OAD "RIDGE CUT OUT TWO IDENTICAL RECTANGLES MEASURING CENTIMETERS WIDE AND CENTIMETERS LONG &OLDONE OF THE TWO RECTANGLES INTO A SQUARE TUBE MEASURING CM X CM 'LUE THE EDGES TOGETHER AS WE DID WHEN WEPREFABRICATED THE SQUARE TUBES IN ,EARNING !CTIVITY 4HE SECOND RECTANGLE SHOULD REMAIN UNFOLDEDACMWIDE hBARv WITH A LENGTH OF CM 7E NOW HAVE TWO STRUCTURAL MEMBERSA BAR AND A TUBE "OTH ARE THESAME LENGTH AND BOTH USE EXACTLYTHE SAME AMOUNT OF MATERIAL 0LACE EACH ONE WITH ITS ENDS BETWEEN YOUR


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THUMB AND FORElNGER AND SQUEEZE 9OULL lNDTHAT THE mAT RECTANGULAR hBARv BUCKLES WITH ONLYTHE SLIGHTEST COMPRESSIVE FORCE /N THE OTHERHAND THE TUBE IS AMAZINGLY STRONGALMOSTIMPOSSIBLE TO BUCKLE WITH ONE HAND 4HIS SIMPLETEST CLEARLY DEMONSTRATES ANOTHER IMPORTANTCHARACTERISTIC OF BUCKLING FAILURES ! HOLLOW TUBEHAS SIGNIlCANTLY HIGHER COMPRESSIVE STRENGTH THANA SOLID BAR USING THE SAME AMOUNT OF MATERIAL

.OW LETS DO THE SAME SORT OF EXPERIMENT WITHACTUAL STEEL STRUCTURAL MEMBERS /UR GOAL IS TOINVESTIGATE HOW THE CROSSSECTIONAL AREA ANDCROSSSECTION SHAPE AFFECT THE COMPRESSIVESTRENGTH 7E CAN ACCOMPLISH THIS GOAL BY TESTINGA SERIES OF STEEL SPECIMENS WITH VARIOUS AREAS ANDSHAPES THEN COMPARING THE RESULTS 3INCE WE WILL BE STUDYING THE EFFECTS OF TWO DIFFERENT VARIABLESCROSSSECTIONAL AREA AND SHAPEWE WILL NEED TO DESIGN THE EXPERIMENTS CAREFULLY )T IS IMPORTANT THAT SUCCESSIVE TESTSCHANGE ONLY ONE VARIABLE AT A TIME SO WE CAN LOGICALLY COMPARE THE RESULTS AND DETERMINE THE EFFECT OF EACHVARIABLE

&OR EXAMPLE CONSIDER THE FOLLOWING lVE CARBON STEEL TEST SPECIMENS

! CARDBOARD BAR BUCKLES WITH

ONLY A SLIGHT LOAD

! CARDBOARD TUBE IS AMAZINGLYSTRONG IN COMPRESSION

3PECIMEN ! IS THE SAME v X v SOLID SQUARE BAR WEHAVE BEEN USING THROUGHOUT THIS LEARNING ACTIVITY4HE TEST RESULTS FOR THIS BAR WILL PROVIDE A BASIS FORCOMPARISON WITH THE OTHER SPECIMENS

3PECIMEN " IS A HOLLOW TUBE MEASURING v Xv 4HE THICKNESS OF THE TUBE WALLS IS vv 4HESE DIMENSIONS RESULT IN A CROSSSECTIONAL AREA OF EXACTLY SQUARE INCHTHE SAME AS3PECIMEN ! "ECAUSE THEIR CROSSSECTIONAL AREASARE EQUAL WE CAN COMPARE THE TEST RESULTS FROM3PECIMENS ! AND " TO DETERMINE THE EFFECT OFCROSSSECTION SHAPE ON COMPRESSIVE STRENGTH

3PECIMEN # IS A v X v SOLID BAR 4HESEDIMENSIONS RESULT IN A CROSSSECTIONAL AREA OF SQUARE INCHESEXACTLY HALF THE AREA OF 3PECIMEN! 3INCE 3PECIMENS ! AND # HAVE THE SAME SHAPE

WE CAN COMPARE THE TWO SETS OF TEST RESULTS TODETERMINE THE EFFECT OF CROSSSECTIONAL AREA ONSTRENGTH

3PECIMEN $ IS A v X v SOLID BAR ,IKE 3PECIMEN# THIS BAR HAS A CROSSSECTIONAL AREA OF SQUAREINCHES HOWEVER THE CROSSSECTION OF 3PECIMEN $

IS RECTANGULAR RATHER THAN SQUARE 4HUS WE CANCOMPARE THE TEST RESULTS FROM 3PECIMENS # AND $TO FURTHER EXAMINE THE EFFECT OF CROSSSECTIONSHAPE ON STRENGTH

3PECIMEN % IS A v X v HOLLOW TUBE WITH WALLSv THICK )TS CROSSSECTIONAL AREA IS EXACTLY SQUARE INCH 7E CAN COMPARE THE TEST RESULTS FROM3PECIMENS # AND % TO DETERMINE THE EFFECT OFCROSSSECTION SHAPE 7E CAN COMPARE THE RESULTSFROM 3PECIMENS ! AND % TO DETERMINE THE EFFECT OFCROSSSECTIONAL AREA

#ARBON STEEL TEST SPECIMENS USED TO DETERMINE HOW CROSSSECTIONAL

AREA AND SHAPE AFFECT COMPRESSIVE STRENGTH

v

v

,ENGTH

v ,ENGTH

v

v,ENGTH

v

v

vv

,ENGTH

,ENGTH

vv

v

v

v

,ENGTH

v

v

,ENGTH

v ,ENGTH

v

v ,ENGTH

v

v,ENGTH

v

v,ENGTH

v

v

vv

,ENGTH

v

vv

,ENGTH

,ENGTH

vv

v

,ENGTH

vv

v


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11#AN YOU CALCULATE THE CROSSSECTIONAL AREAS OF THESE MEMBERS

3HOW THAT THE CROSSSECTIONAL AREA IS EXACTLY SQUARE INCH FOR 3PECI

MENS ! AND " AND EXACTLY SQUARE INCH FOR 3PECIMENS # $ AND %

)F WE DO A SERIES OF COMPRESSION STRENGTH TESTS ON EACH OF THESE lVE SPECIMENS USING A VARIETY OF DIFFERENTLENGTHS THE RESULTS WILL LOOK LIKE THIS

,ENGTH INCHES

" X TUBE

! X BAR

# X BAR

$ X TUBE

% X TUBE

! CAREFUL COMPARISON OF THESE lVE STRENGTH VS LENGTH CURVES WILL CONlRM SEVERAL OF OUR EARLIER OBSERVATIONSABOUT COMPRESSIVE STRENGTH AND WILL LEAD US TO SEVERAL NEW ONES AS WELL

#OMPRESSIVE STRENGTH DEPENDS ON THE LENGTH OF THE MEMBER &OR ALL lVE SPECIMENS INCREASING THE LENGTHCAUSES A SUBSTANTIAL REDUCTION IN THE COMPRESSIVE STRENGTH

#OMPRESSIVE STRENGTH DEPENDS ON THE SHAPE OF THE CROSSSECTION ! COMPARISON OF THE RESULTS FOR 3PECIMENS ! AND " CLEARLY SHOWS THAT A HOLLOW TUBE HAS A SUBSTANTIALLY HIGHER COMPRESSIVE STRENGTH THAN A SOLIDBAR FOR A GIVEN LENGTH AND CROSSSECTIONAL AREA 4HE RESULTS FOR 3PECIMENS # AND % CONlRM THIS OBSERVATION4HE RESULTS FOR 3PECIMENS # AND $ INDICATE THAT A SQUARE BAR HAS SOMEWHAT HIGHER STRENGTH THAN A RECTANGULAR BAR WITH THE SAME AREA

#OMPRESSIVE STRENGTH DEPENDS ON THE CROSSSECTIONAL AREA OF THE MEMBER 4HE RESULTS FOR 3PECIMENS ! AND# INDICATE THAT INCREASING THE CROSSSECTIONAL AREA OF A MEMBER INCREASES ITS COMPRESSIVE STRENGTH 4HERESULTS FOR " AND % INDICATE THAT THIS SAME CONCLUSION IS VALID FOR TUBES .OTE THAT UNLIKE TENSILE STRENGTHTHE COMPRESSIVE STRENGTH IS NOT PROPORTIONAL TO THE CROSSSECTIONAL AREA &OR EXAMPLE DOUBLING THE AREAGENERALLY WILL NOT DOUBLE THE STRENGTH

#OMPRESSIVE STRENGTH DEPENDS ON THE MATERIAL THE MEMBER IS MADE OF 4HIS SERIES OF TESTS USES ONLYCARBON STEEL HOWEVER IF WE REPEATED THESE EXPERIMENTS WITH SPECIMENS MADE OF OTHER MATERIALS WE WOULDlND THAT STRONGER STIFFER MATERIALS HAVE HIGHER COMPRESSIVE STRENGTH THAN WEAKER MORE mEXIBLE ONES


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117HAT CAN WE LEARN FROM A COMPARISON OF 3PECIMENS ! AND %

#OMPARE THE COMPRESSIVE STRENGTH VS LENGTH CURVES FOR 3PECIMENS

! AND % ON THE GRAPH ABOVE 7HAT CONCLUSION CAN YOU DRAW FROM THIS

COMPARISON

4HE 0RINCIPLE OF THE ,EVER

7HEN ACTUAL STRUCTURAL MEMBERS ARE TESTED IN A LABORATORY POWERFUL HYDRAULIC MACHINES ARE USED TO PERFORM THE TESTS 7E DONT HAVE HYDRAULIC POWER AVAILABLE FOR THIS PROJECT BUT WE DO HAVE THE POWER OF THE LEVERTO HELP US APPLY A LARGE CONTROLLED MEASURABLE TENSION OR COMPRESSION FORCE TO A CARDBOARD STRUCTURALMEMBER 4HE SIMPLE TESTING MACHINE WE WILL USE IN THIS LEARNING ACTIVITY IS BASED ON THE PRINCIPLE OF THE LEVER THUS TO UNDERSTAND HOW THE MACHINE WORKS YOU WILL NEED TO UNDERSTANDHOW A LEVER WORKS

3UPPOSE YOU ARE DOING A LANDSCAPING PROJECT AND YOU ENCOUNTER A POUND ROCK THATMUST BE MOVED 4HE ONLY hTOOLSv AVAILABLE ARE A FOOT LONG STEEL PIPE AND A SHORTLOG (OW CAN YOU MOVE THE ROCK !S THE PICTURE SUGGESTS YOU CANMOVE THE ROCK QUITE EASILY BY USING THE STEEL PIPE AS A LEVERAND THE LOG AS A FULCRUM ! LEVER IS A SIMPLE MACHINE CONSISTING OF A BAR OR ROD THAT ROTATES ON A PIVOT 4HE PIVOT IS CALLEDA FULCRUM 7HEN YOU APPLY A DOWNWARD FORCE TO ONE END OFTHE LEVER THE LEVER PIVOTS ON THE FULCRUM AND APPLIES ANUPWARD FORCE TO THE ROCK AT THE OTHER END

4HE DIAGRAM BELOW SHOWS THE FORCES ACTING ON THE LEVER &

REPRESENTS THE DOWNWARD FORCE YOU ARE APPLYINGTO ONE END OF THE LEVER AND &

REPRESENTS THE WEIGHT OF THE ROCK PUSHING DOWN ON THE OTHER END 3INCE THE

LEVER IS LIFTING THE ROCK &

ALSO REPRESENTS THE UPWARD FORCE APPLIED BY THE LEVER TO THE ROCK ,

IS THE DISTANCE

FROM THE FORCE & TO THE FULCRUM , IS THE DISTANCE FROM THE FORCE & TO THE FULCRUM

4HE PRINCIPLE OF THE LEVERSTATES THAT

)N OUR EXAMPLE WE KNOW THAT THE WEIGHT OF THE ROCK & IS POUNDS ,ETS PLACE THE LOG THE FULCRUM ONE

FOOT AWAY FROM THE ROCK 3INCE THE STEEL PIPE THE LEVER IS SIX FEET LONG THEN ,

IS AND ,

IS 7HAT FORCE DOYOU NEED TO APPLY TO THE LONG END OF THE LEVER TO LIFT THE ROCK )F YOU SUBSTITUTE THE KNOWN VALUES OF ,

,

AND

&

INTO THE EQUATION ABOVE AND SOLVE FOR & YOU WILL lND THAT YOU CAN LIFT THE POUND ROCK WITH A FORCE OF ONLY

POUNDS

5SING A LEVER TO MOVE A HEAVY ROCK

,

,

&

&

,

,

&

&


10/28

115SING THIS LEVER HOW MUCH WEIGHT COULD YOU LIFT WITH POUNDS

3UPPOSE YOU NEED TO MOVE ANOTHER ROCK WITH THIS LEVER 5SING THE

SAME BAR AND FULCRUM LOCATION YOU PUSH DOWNWARD WITH A FORCE OF

POUNDS TO LIFT THE ROCK (OW MUCH DOES THE ROCK WEIGH

4HIS SIMPLE EXAMPLE SHOWS HOW A LEVER CAN BE USED TO SIGNIlCANTLY INCREASE THE AMOUNT OF FORCE THAT CAN BEAPPLIED TO AN OBJECT )T ALSO SHOWS HOW WE CAN USE THE PRINCIPLE OF THE LEVER TO PRECISELY CALCULATE THE AMOUNTOF FORCE APPLIED TO AN OBJECT 4HE TESTING MACHINE WE WILL BE USING TO CONDUCT STRENGTH TESTS IS A DIRECT APPLICATION OF THIS PRINCIPLE

#ONVERTING -ASS TO 7EIGHT

7EIGHTIS A FORCE THUS WE EXPRESS THE WEIGHT OF AN OBJECT IN UNITS OF FORCE )N THE LEVER EXAMPLE ABOVE THEWEIGHT OF THE ROCK AND THE FORCES APPLIED TO THE LEVER ARE EXPRESSED IN POUNDSTHE STANDARD MEASURE OF FORCEIN THE 53 #USTOMARY SYSTEM OF UNITS

4HE EXPERIMENTS CONDUCTED IN THIS LEARNING ACTIVITY USE METRIC UNITS ALSO CALLED 3) UNITS 3) STANDS FOR3YSTEME )NTERNATIONAL $ETERMINING THE WEIGHT OF AN OBJECT IN 3) UNITS IS A BIT MORE COMPLICATED THAN DOING ITIN 53 UNITS 7HEN YOU hWEIGHv AN OBJECT ON A METRIC SCALE THE NUMBER YOU READ FROM THE SCALE IS USUALLY INGRAMS OR KILOGRAMS WHICH ARE UNITS OF MASS NOT FORCE 4HUS WHEN YOU hWEIGHv AN OBJECT ON A METRIC SCALEYOU ACTUALLY DO NOT MEASURE ITS WEIGHT 9OU MEASURE ITS MASS

4O DETERMINE THE WEIGHT OF THIS OBJECT YOU MUST CONVERT ITS MASS TO A FORCE USING THE EQUATION

)N THIS EQUATION 7IS THE WEIGHT OF THE OBJECT MIS ITS MASS AND GIS THE ACCELERATION OF GRAVITY )N 3) UNITS G METERSSEC )F YOU EXPRESS THE MASS MIN KILOGRAMS THEN THE WEIGHT 7WILL BE IN NEWTONS

117HAT IS THE WEIGHT OF A KILOGRAM MASS

)N ,EARNING !CTIVITY WE USED A KILOGRAM STACK OF BOOKS TO LOAD

THE 'RANT 2OAD "RIDGE (OW MUCH DID THIS STACK OF BOOKS WEIGH

7E WILL USE THIS MASSTOWEIGHT CONVERSION EXTENSIVELY WHEN WE ANALYZE THE EXPERIMENTAL DATA COLLECTED ASPART OF THIS LEARNING ACTIVITY


11/28

4HE 0ROBLEM

4HE .EED

4HE 4OWN %NGINEER OF (AUPTVILLE .EW 9ORK HAS DECIDED TO CONDUCT A STRUCTURAL EVALUATION OF THE 'RANT2OAD "RIDGE TO ENSURE THAT IT CAN SAFELY CARRY THE REQUIRED HIGHWAY LOADS "EFORE HE CAN BEGIN ANALYZING THESTRUCTURE HE WILL NEED TO OBTAIN INFORMATION ABOUT THE STRENGTHS OF THE VARIOUS STRUCTURAL MEMBERS USED IN THEMAIN TRUSSES (E DECIDES TO HIRE A MATERIALS TESTING LABORATORY TO DESIGN AND CONDUCT AN EXPERIMENTAL TESTINGPROGRAM TO PROVIDE THE NECESSARY INFORMATION

9OUR *OB

9OUR MATERIALS TESTING COMPANY 5NIVERSAL 3TRUCTURAL -ATERIALS !SSESSMENT )NC HAS BEEN HIRED BY THE

(AUPTVILLE 4OWN %NGINEER TO PROVIDE EXPERIMENTAL DATA IN SUPPORT OF HIS STRUCTURAL EVALUATION OF THE 'RANT 2OAD"RIDGE 9OUR JOB IS TO DESIGN AND CONDUCT A PROGRAM OF EXPERIMENTATION TO DETERMINE THE STRENGTHS OF ALLSTRUCTURAL MEMBERS USED IN THE MAIN TRUSSES OF THE BRIDGE !S A TECHNICAL SPECIALIST YOU ARE RESPONSIBLE FORPROVIDING YOUR CLIENT WITH COMPLETE ACCURATE DATA AND PRESENTING THAT DATA IN A MANNER THAT IS BOTH UNDERSTANDABLE AND USABLE

4HE 3OLUTION

4HE 0LAN

/UR PLAN TO PROVIDE THE (AUPTVILLE %NGINEER WITH THE INFORMATION HE NEEDS IS AS FOLLOWS

&AMILIARIZE WITH THE TESTING MACHINE THAT WE WILL USE FOR OUR EXPERIMENTS

$ESIGN A TESTING PROGRAM

-AKE THE TEST SPECIMENS

#ONDUCT TENSION AND COMPRESSION STRENGTH TESTS

!NALYZE AND GRAPH THE EXPERIMENTAL DATA

4HE PRODUCT OF OUR WORK WILL BE A SERIES OF GRAPHS THAT THE (AUPTVILLE %NGINEER CAN USE AS THE BASIS FOR HISSTRUCTURAL EVALUATION

4HE 4ESTING -ACHINE

$ESCRIPTION4HIS SIMPLE LEVERBASED TESTING MACHINE WILL ALLOW YOU TO APPLY A CONTROLLED TENSION OR COMPRESSION FORCE TO

A TEST SPECIMEN AND MEASURE THAT FORCE WITH REASONABLE ACCURACY 4HOUGH YOU DO NOT NEED TO BUILD THEMACHINE YOU SHOULD UNDERSTAND HOW IT WORKS IN ORDER TO USE IT PROPERLY AND TO ACHIEVE ACCURATE RESULTS

4HE CONlGURATION AND COMPONENT PARTS OF THE TESTING MACHINE ARE ILLUSTRATED IN THE DRAWING BELOW 4HELOADING ARM IS FASTENED TO THE POSTS WITH A STEEL BOLT WHICH SERVES AS A PIVOT 4HE 4,INE AND #,INE ARE VERTICALMARKS ON THE LOADING ARM INDICATING THE POINTS WHERE THE TENSION AND COMPRESSION SPECIMENS WILL BE FASTENEDFOR TESTING &ELT PADS ARE FASTENED TO THE UNDERSIDE OF THE LOADING ARM AND THE TOP SIDE OF THE BASE AT THE #,INE4HESE PADS WILL ENSURE THAT COMPRESSION TEST SPECIMENS ARE UNIFORMLY LOADED 4HE TEMPORARY SUPPORTIS A

WOODEN POST THAT IS USED TO SUPPORT THE LOADING ARM WHILE A TENSION SPECIMEN IS BEING CLAMPED INTO POSITION

4HE ,EARNING !CTIVITY


12/28

#OMPONENT PARTS OF THE TESTING MACHINE

4HE PHOTO BELOW SHOWS EVERYTHING YOU WILL NEED TO CONDUCT THE TENSILE AND COMPRESSIVE STRENGTH EXPERIMENTS

0IVOT

,OADING !RM.OTCH

4EMPORARY3UPPORT

"ASE0OST

# ,INE

4,INE

&ELT

0ADS

0IVOT

,OADING !RM.OTCH

4EMPORARY3UPPORT

"ASE0OST

# ,INE

4,INE

&ELT

0ADS

4HE TESTING MACHINE

4WO SMALL CLAMPSv 1UICK'RIP CLAMPS ARERECOMMENDED

/NE ADDITIONAL CLAMP TO ATTACHTHE MACHINE TO A TABLETOP

! PLASTIC BUCKET WITH HANDLE!BOUT KG OF SANDSHOWN HERE IN A SECOND BUCKET

! SCOOP A SMALL GARDENINGSHOVEL WORKS WELL

! METRIC SCALE CAPABLE OFMEASURING THE MASS OF AN OBJECTACCURATELY TO THE NEAREST GRAM

4HE SCALE SHOULD HAVE A CAPACITYOF AT LEAST GRAMS

! SMALL SHEET OF vTHICK BALSA WOOD


13/28

(OW THE -ACHINE 7ORKS7HEN YOU TEST THE TENSILE STRENGTH OF A CARDBOARD STRUCTURAL MEMBER YOU WILL CLAMP THE TOP OF THE TEST

SPECIMEN TO THE LOADING ARM AT THE 4,INE 4HE BOTTOM OF THE SPECIMEN WILL BE CLAMPED TO THE BASE 9OU WILLHANG THE PLASTIC BUCKET FROM THE NOTCH AT THE END OF THE LOADING ARM THEN SLOWLY lLL IT WITH SAND UNTIL THESPECIMEN RUPTURES !FTER THE FAILURE YOU WILL WEIGH THE BUCKET AND SAND AND APPLY THE PRINCIPLE OF THE LEVERTODETERMINE THE INTERNAL FORCE IN THE SPECIMEN AT THE INSTANT OF FAILURE 4HE PRINCIPLE OF THE LEVER SAYS THAT

)N THIS EQUATION 4IS THE INTERNAL FORCE IN THE TEST SPECIMEN AND 7IS THE WEIGHT OF THE BUCKET AND SAND3INCE ,

AND ,

CAN BE MEASURED DIRECTLY FROM YOUR TESTING MACHINE AND 7IS DETERMINED EXPERIMENTALLY WE CAN

SOLVE THIS EQUATION FOR THE UNKNOWN INTERNAL FORCE 4 4HE RESULT IS

4HE PROCEDURE FOR TESTING COMPRESSION MEMBERS IS THE SAME EXCEPT THAT THE SPECIMEN WILL BE PLACED AT THE#,INE INSTEAD OF THE 4,INE 7HEN WE APPLY THE PRINCIPLE OF THE LEVER TO lND THE UNKNOWN INTERNAL COMPRES

SION FORCE #IN THE SPECIMEN WE GET

.OTE THAT THE PRINCIPLE OF THE LEVER APPLIES EVEN WHEN BOTH FORCES ARE ON THE SAME SIDE OF THE FULCRUM

$ESIGN THE 4ESTING 0ROGRAM

.OW THAT THE TESTING MACHINE IS READY TO GO YOU ARE PROBABLY ANXIOUS TO START DOING SOME EXPERIMENTS "UTBEFORE WE CAN START TESTING WE lRST NEED TO DESIGN THE TESTING PROGRAM 4HE OBJECTIVES OF THIS PLANNING PROCESSARE TO

%NSURE THAT WE GET ACCURATE DATA

%NSURE THAT WE GET THE RIGHT KINDS OF DATA TO SUPPORT THE PROJECTS WE WILL BE DOING LATER AND

%NSURE THAT WE DO NOT WASTE TIME OR MATERIAL BY DOING UNNECESSARY TESTS

4O ACCOMPLISH THESE OBJECTIVES WE MUST APPLY SOME OF THE OBSERVATIONS WE MADE EARLIER ABOUT THE TENSILESTRENGTH AND COMPRESSIVE STRENGTH OF STRUCTURAL MEMBERS 3PECIlCALLY WE NEED TO LOOK AT EACH OF THE FACTORSON WHICH THE TENSILE AND COMPRESSIVE STRENGTH DEPEND AND VARY THESE FACTORS SYSTEMATICALLY IN OUR TESTS !S AMINIMUM THE RANGE OF VALUES FOR EACH FACTOR MUST BE ADEQUATE TO ANALYZE EVERY MEMBER IN THE 'RANT 2OAD"RIDGE

4HE LOGICAL THOUGHT PROCESS LEADING TO THE DESIGN OF OUR TESTING PROGRAM IS AS FOLLOWS

4ENSILE STRENGTH DEPENDS ON THE CROSSSECTIONAL AREA OF A MEMBER 4HEREFORE WE MUST CREATE TEST SPECIMENS WITH A VARIETY OF DIFFERENT CROSSSECTIONAL AREAS 4HE CROSSSECTIONAL AREA OF A RECTANGULAR MEMBER ISSIMPLY ITS WIDTH TIMES ITS THICKNESS 3INCE ALL OF OUR SPECIMENS WILL HAVE THE SAME THICKNESS THE THICKNESSOF THE CARDBOARD WE NEED TO CREATE TEST SPECIMENS WITH A VARIETY OF DIFFERENT WIDTHS

4ENSILE STRENGTH DOES NOT DEPEND ON THE LENGTH OF A MEMBER 4HEREFORE ALL OF OUR TENSION TEST SPECIMENSCAN BE THE SAME LENGTH 7E WILL USE CENTIMETERS BECAUSE THIS LENGTH lTS THE TESTING MACHINE NICELY

4ENSILE STRENGTH DOES NOT DEPEND ON THE SHAPE OF THE CROSSSECTION 4HEREFORE ALL OF OUR TENSION TESTSPECIMENS CAN HAVE THE SAME TYPE OF CROSSSECTION 7E WILL USE A SIMPLE RECTANGULAR hBARv


14/28

CM

CM

CM

WIDTH

CM

CM

CM

WIDTH

#OMPRESSIVE STRENGTH DEPENDS OF THE SHAPE AND SIZE OF THE CROSSSECTION 4HEREFORE WE MUST CREATECOMPRESSION TEST SPECIMENS FOR EACH OF THE DIFFERENT CROSSSECTIONS WE PLAN TO USE IN OUR STRUCTURE 7E WILLTEST RECTANGULAR TUBES WITH THE SAME DIMENSIONS AS THE TUBES USED IN THE 'RANT 2OAD "RIDGE MODEL

#OMPRESSIVE STRENGTH DEPENDS OF THE LENGTH OF THE MEMBER 4HEREFORE WE MUST CREATE TEST SPECIMENSWITH THE FULL RANGE OF DIFFERENT LENGTHS WE PLAN TO USE IN OUR STRUCTURE 7E WILL USE LENGTHS FROM TO CENTIMETERS

4ENSILE AND COMPRESSIVE STRENGTH BOTH DEPEND ON THE MATERIAL THE MEMBER IS MADE OF 4HEREFORE TO DO ATRULY COMPREHENSIVE TESTING PROGRAM WE WOULD NEED TO CREATE TEST SPECIMENS OF VARIOUS DIFFERENT MATERIALS 3INCE OUR PROJECTS WILL ALL USE THE SAME TYPE OF CARDBOARD HOWEVER WE WILL ONLY TEST THIS ONE MATERIAL

)N DESIGNING THE TESTING PROGRAM WE MUST ALSO CONSIDER THE EFFECTS OF EXPERIMENTAL ERROR AND THE NATURALVARIABILITY OF THE PROPERTIES WE ARE ATTEMPTING TO MEASURE 4HERE ARE MANY POSSIBLE SOURCES OF EXPERIMENTALERROR IN OUR TEST SETUP 7E WILL DISCUSS THEM IN DETAIL LATER 3OME OF THESE CAN BE CONTROLLED BY CONDUCTINGTHE TESTS VERY CAREFULLY BUT NO MATTER HOW CAREFUL WE ARE OUR EXPERIMENTAL DATA WILL EXHIBIT SOME NATURALVARIABILITY &OR THIS REASON WE SHOULD REPEAT EACH OF OUR EXPERIMENTS SEVERAL TIMES AND AVERAGE THE RESULTS2EPEATING EACH EXPERIMENT SEVERAL TIMES IS ESPECIALLY IMPORTANT FOR THE COMPRESSION TESTS WHICH ARE INHERENTLYMORE VARIABLE THAN THE TENSION TESTS

4AKING ALL OF THESE FACTORS INTO ACCOUNT OUR TESTING PROGRAM WILL CONSIST OF THE FOLLOWING EXPERIMENTS

-AKE THE 4EST 3PECIMENS

4HE CONlGURATION OF A TYPICAL TENSION TEST SPECIMEN IS SHOWN BELOW 4HE MEMBER ITSELF IS A STRIP OF CARDBOARD CENTIMETERS LONG SLICED FROM A lLE FOLDER JUST AS WE DID IN ,EARNING !CTIVITY 'LUED ONTO EACH ENDOF THE MEMBER IS A CENTIMETER SQUARE OF CARDBOARD WHICH PROVIDES A SURFACE FOR THE CLAMPS TO GRIP WHEN THESPECIMEN IS PLACED IN THE TESTING MACHINE

4EST #ROSS3ECTION ,ENGTH .UMBER OF3PECIMENS

4 MMWIDE BAR CM

4 MMWIDE BAR CM

4 MMWIDE BAR CM

# MM X MM TUBE CM

# MM X MM TUBE CM

# MM X MM TUBE CM

# MM X MM TUBE CM

# MM X MM TUBE CM

# MM X MM TUBE CM

4ENSION TEST SPECIMEN


15/28

-AKING A TENSION TEST SPECIMEN

2EINFORCING THE ENDS OF A COMPRESSION TEST SPECIMEN

4O MAKE A TENSION TEST SPECIMEN APPLY GLUE TOONE OF THE CARDBOARD SQUARES 0LACE THE MEMBER ONTOTHE GLUE AND HOLD IT IN POSITION UNTIL THE GLUE SETS2EPEAT FOR THE OPPOSITE END OF THE MEMBER AS SHOWNAT RIGHT

4O MAKE THE COMPRESSION TEST SPECIMENS START BYLAYING OUT AND FABRICATING CARDBOARD TUBES OF THEREQUIRED SIZES EXACTLY AS WE DID IN ,EARNING !CTIVITY

4HEN REINFORCE THE ENDS OF EACH MEMBER BYCOATING A MMWIDE STRIP OF CARDBOARD WITH GLUE AND

WRAPPING THE STRIP AROUND THE ENTIRE PERIMETER OF THEMEMBER AT EACH END 4HIS PROCEDURE IS ILLUSTRATED INTHE PHOTO AT RIGHT 4HE PURPOSE OF THIS REINFORCEMENTIS TO ENSURE THAT THE ENDS OF THE MEMBER DO NOT CRUSH

WHEN THEY ARE COMPRESSED BY THE TESTING MACHINE

4HE PICTURE AT RIGHT SHOWS ONE COMPLETE SET OF TEST

SPECIMENSTHREE BARS OF DIFFERENT WIDTHS AND TWOTUBULAR CROSSSECTIONS EACH IN THREE DIFFERENT LENGTHS


16/28

#ONDUCT THE 4ENSION 4ESTS

5SE THE FOLLOWING PROCEDURE TO TEST EACH OF YOURTENSION SPECIMENS

4O PREPARE FOR YOUR lRST TEST CLAMP THE TESTINGMACHINE TO THE EDGE OF A TABLE WITH THE LONG ENDOF THE LOADING ARM OVERHANGING AS SHOWN 0LACETHE TEMPORARY SUPPORT UNDER THE LOADING ARM AND

HANG A BUCKET FROM THE NOTCH AT THE END OF THELOADING ARM 0UT A CHAIR OR STOOL BELOW THE BUCKETAND IF NECESSARY STACK BOOKS ON THE CHAIR SO THATTHE SPACE BETWEEN THE TOP OF THE STACK AND THEBOTTOM OF THE BUCKET IS ONLY ABOUT TWO INCHES7HEN A TEST SPECIMEN BREAKS THE BUCKET WILL FALL

WE DONT WANT IT TO FALL VERY FAR

0LACE ONE OF THE MM TENSION SPECIMENS 4EST 4INTO POSITION CENTERED ON THE 4,INE

#LAMP THE TOP OF THE SPECIMEN TO THE LOADING ARMAND THE BOTTOM OF THE SPECIMEN TO THE BASE%NSURE THAT THE SPECIMEN REMAINS STRAIGHT ANDVERTICAL 4HE CLAMPS MUST BE TIGHT SO THE SPECIMEN WONT SLIP


17/28

11)S CARDBOARD DUCTILE OR BRITTLE

$ID YOUR TEST SPECIMEN FAIL IN A DUCTILE OR BRITTLE MANNER 7HAT DOES

THIS CHARACTERISTIC TELL YOU ABOUT THE SUITABILITY OF CARDBOARD AS A

STRUCTURAL MATERIAL

2EMOVE THE TEMPORARY SUPPORT AND GENTLY ALLOWTHE WEIGHT OF THE BUCKET TO PULL THE SPECIMENTIGHT .OW BEGIN THE LOADING PROCESS &ILL THESCOOP WITH SAND THEN SLOWLY POUR THE SAND FROMTHE SCOOP INTO THE BUCKET 7AIT SECONDS THENADD A SECOND SCOOP OF SAND 7AIT SECONDS ANDADD A THIRD SCOOP #ONTINUE THIS PROCESS ALWAYS

WAITING SECONDS BETWEEN SCOOPS UNTIL THESPECIMEN BREAKS

4HE FAILURE OF THE SPECIMEN WILL HAPPEN SUDDENLY

WITHOUT WARNINGOFTEN DURING ONE OF THE SECOND PAUSES IN THE LOADING PROCESS (OWEVER IFTHE FAILURE DOES OCCUR WHILE YOU ARE ADDING SANDSTOP IMMEDIATELY 4HE SAND IN THE BUCKET SHOULDBE THE EXACT AMOUNT THAT CAUSED THE FAILURE TOOCCUR

,IFT THE BUCKET OFF OF THE TESTING MACHINE PLACE ITON THE SCALE AND RECORD THE MASS

.OW EMPTY THE BUCKET AND REPEAT THE PROCESS FOREACH OF YOUR TENSION SPECIMENS &OR EACH TEST KEEPCAREFUL RECORDS OF THE SPECIMEN SIZE AND THE MASS OFTHE BUCKET AND SAND


18/28

117HY IS IT NECESSARY FOR THE LOADING ARM TO BE BALANCED

7HEN THE TESTING MACHINE WAS BUILT THE LOADING ARM WAS BALANCED

ON THE PIVOT SEE !PPENDIX # )F THE LOADING ARM HAD NOT BEEN

BALANCED HOW WOULD IT AFFECT YOUR EXPERIMENTAL RESULTS

!NALYZE AND 'RAPH THE 4ENSION $ATA

4O ANALYZE OUR EXPERIMENTAL DATA WE NEED TO CALCULATE THE ACTUAL TENSILE STRENGTH THAT WE MEASURED IN EACHTEST THEN CREATE A GRAPH OF TENSILE STRENGTH VS MEMBER WIDTH 4HIS GRAPH WILL GIVE US THE CAPABILITY TO DETERMINE THE TENSILE STRENGTH FOR ANYMEMBER WIDTH NOT JUST THE SPECIlC WIDTHS WE TESTED 4HE ANALYSIS AND GRAPHING CAN BE PERFORMED MOST EASILY AND ACCURATELY BY USING A COMPUTER SPREADSHEET

#ALCULATE THE 4ENSILE 3TRENGTH&OR EACH TENSION TEST YOU DETERMINED THE MASS OF THE BUCKET AND SAND THAT CAUSED THE SPECIMEN TO FAIL )N

ORDER TO DETERMINE THE TENSILE STRENGTH YOU MUST

#ONVERT THE MASS TO WEIGHT USING THE EQUATION

WHERE GIS METERSSECOND AND MMUST BE EXPRESSED IN KILOGRAMS

!PPLY THE PRINCIPLE OF THE LEVER TO DETERMINE THE FORCE IN THE SPECIMEN AT FAILURE USING THE EQUATION

"ECAUSE THESE CALCULATIONS MUST BE PERFORMED FOR EACH INDIVIDUAL TEST THE ANALYSIS CAN BE DONE VERY EFlCIENTLY WITH A SPREADSHEET 4HE RESULTS SHOULD LOOK SOMETHING LIKE THIS

4EST -EMBER -ASS OF 7EIGHT OF 4ENSILE

.UMBER 7IDTH "UCKET 3AND "UCKET 3AND 3TRENGTH

MM G . .

4

4 4

4

4 4

4

4

4


19/28

)N THIS SPREADSHEET THE BLACK CELLS ARE HEADINGS THE WHITE CELLS ARE FOR ENTRY OF EXPERIMENTAL DATA AND THEGRAY CELLS ARE CALCULATED AUTOMATICALLY 4HE CELL FORMULAS REQUIRED TO CREATE THIS SPREADSHEET WITH -ICROSOFT%XCEL LOOK LIKE THIS

.OTE THAT THE SPREADSHEET IS SET UP TO ALLOW ANYVALUES OF ,

AND ,

TO BE ENTERED 4HIS IS IMPORTANT BECAUSETHE ACTUAL MEASUREMENTS ,

AND ,

FOR YOUR TESTING MACHINE ARE LIKELY TO BE DIFFERENT FROM THESE VALUES .OTE

ALSO THAT THE MASS WAS RECORDED IN GRAMS SO IT HAD TO BE CONVERTED TO KILOGRAMS DIVIDED BY AS PART OF THEWEIGHT CALCULATION

11#AN YOU VERIFY THESE SPREADSHEET CALCULATIONS

7HENEVER YOU USE A COMPUTER TO SOLVE A NUMERICAL PROBLEM YOU

SHOULD VERIFY THAT THE CALCULATIONS ARE BEING DONE CORRECTLY /NE WAY

TO VERIFY COMPUTER RESULTS IS TO PERFORM ONE COMPLETE SET OF CALCULATIONS BY HAND AND COMPARE YOUR ANSWER WITH THE ONE THE COMPUTER

CALCULATED 3ELECT ANY ONE OF THE TENSION TEST RESULTS ABOVE CALCULATE

THE TENSILE STRENGTH BY HAND AND COMPARE YOUR RESULTS TO THE COM

PUTER SOLUTION !RE THE COMPUTER RESULTS CORRECT

#REATE A 'RAPH OF 4ENSILE 3TRENGTH VS -EMBER 7IDTH

/NCE THE SPREADSHEET IS SET UP IT IS A RELATIVELY SIMPLE TASK TO CREATE A GRAPH OF TENSILE STRENGTH VS MEMBERWIDTH 4HE BEST TYPE OF GRAPH FOR THIS TYPE OF DATA IS AN hXY SCATTER PLOTv WITH NO LINE CONNECTING THE DATAPOINTS 5SE MEMBER WIDTH FOR THE XAXIS AND TENSILE STRENGTH FOR THE YAXIS 4HE PROCEDURE FOR CREATING THISGRAPH DEPENDS OF THE SPREADSHEET SOFTWARE YOU ARE USING #HECK THE PROGRAMS h(ELPv MENU FOR INSTRUCTIONS4HE RESULT SHOULD LOOK SOMETHING LIKE THE GRAPH ON THE FOLLOWING PAGE %ACH hv SYMBOL REPRESENTS ONE TEST


20/28

4ENSILE 3TRENGTH VS -EMBER ,ENGTH FOR CARDBOARD MEMBERS EXPERIMENTAL DATA

-EMBER 7IDTH MM

4ENSILE3TREN

GTHNEWTONS

-EMBER 7IDTH MM

4ENSILE3TRENGTHNEWTONS

4REND ,INE

4ENSILE 3TRENGTH VS -EMBER ,ENGTH FOR CARDBOARD MEMBERS EXPERIMENTAL DATA WITH TREND LINE

!S YOU MIGHT EXPECT THERE IS SOMEhSCATTERv IN OUR EXPERIMENTAL DATAA CLEAR INDICATION OF BOTH EXPERIMENTAL ERROR AND NATURAL VARIABILITY IN THE TENSILE STRENGTH OF A MATERIAL .ONETHELESS THE DATA POINTS ALL APPEARTO LIE ALONG A STRAIGHT LINE 4HIS OBSERVATION SUGGESTS THAT THERE IS A LINEAR RELATIONSHIP BETWEEN MEMBER WIDTHAND TENSILE STRENGTH 7E CAN REPRESENT THIS LINEAR RELATIONSHIP BY DRAWING A hBEST lTv STRAIGHT LINE DIRECTLY ONTHE XY SCATTER PLOT -ANY SPREADSHEET PROGRAMS CAN DO THIS AUTOMATICALLY USING A FUNCTION CALLED hTREND LINEvOR hLINEAR REGRESSIONv !GAIN CHECK THE h(ELPv MENU OF YOUR SPREADSHEET PROGRAM TO SEE IF EITHER OF THESEFUNCTIONS IS AVAILABLE )F NOT YOU CAN PRINT A COPY OF THE GRAPH YOU JUST CREATED THEN USE A PENCIL AND RULER TODRAW A STRAIGHT LINE THAT BEST lTS YOUR DATA 7HETHER YOU DRAW THE LINE YOURSELF OR USE THE SPREADSHEET TO DO ITYOU MUST ENSURE THAT THE TREND LINE PASSES THROUGH THE POINT 7E KNOW THAT A MEMBER WITH ZERO WIDTHMUSTHAVE ZERO STRENGTH SO THE POINT MUSTLIE ON THE TREND LINE )N A SPREADSHEET PROGRAM THIS IS NORMALLYACCOMPLISHED BY SETTING THE YINTERCEPT OF THE TREND LINE TO ZERO 4HE RESULT SHOULD LOOK LIKE THIS


21/28

.OTICE THAT THIS CHART CAN BE USED AS A POWERFUL DESIGN TOOL %VEN THOUGH YOU ONLY PERFORMED TESTS ONSPECIMENS OF THREE DIFFERENT WIDTHS YOU CAN NOW EASILY DETERMINE THE TENSILE STRENGTH OF A MEMBER WITH ANY

WIDTH BETWEEN AND MM 4O USE THE CORRECT MATHEMATICAL TERM YOU CAN INTERPOLATE ANY POINT ON THE GRAPH9OU COULD ALSO GUESS AT THE STRENGTH OF A MEMBER WITH A WIDTH LARGER THAN MM IN OTHER WORDS YOU COULDEXTRAPOLATE FROM THE GRAPH "UT BE CAREFUL %XTRAPOLATION CAN BE DANGEROUS *UST BECAUSE OUR DATA APPEAR TOBE HIGHLY LINEAR IN THE RANGE FROM TO MM DOESNT MEAN THAT THE RELATIONSHIP BETWEEN MEMBER WIDTH ANDTENSILE STRENGTH WILL CONTINUE TO BE LINEAR FOR LARGER WIDTHS

11#AN YOU USE THE GRAPH TO DETERMINE TENSILE STRENGTH

7HAT IS THE TENSILE STRENGTH OF A CARDBOARD MEMBER MILLIMETERS

WIDE 7HAT IS THE STRENGTH OF A DOUBLE MILLIMETER BAR LIKE THE ONES

WE USED IN THE 'RANT 2OAD "RIDGE MODEL

/N AN !CTUAL "RIDGE 0ROJECT

(OW DO ENGINEERS OBTAIN DATA FROMEXPERIMENTAL STRENGTH TESTING

4HE SORT OF STRENGTH TESTING WE HAVE BEEN DOING IN THIS LEARNING

ACTIVITY IS GENERALLY NOT PERFORMED AS PART OF THE DESIGN PROCESS FOR INDIVIDUAL

STRUCTURES 2ATHER TESTING IS DONE BY RESEARCHERS IN UNIVERSITIES IN GOVERNMENT

LABORATORIES AND IN INDUSTRY 4HE RESULTS OF THESE TESTS ARE INCORPORATED INTO BOOKS

CALLED DESIGN CODES WHICH ARE PUBLISHED BY PROFESSIONAL SOCIETIES AND MADE AVAIL

ABLE TO ENGINEERS &OR EXAMPLE THE !MERICAN )NSTITUTE OF 3TEEL #ONSTRUCTION PUB

LISHES A DESIGN CODE FOR STEEL STRUCTURES 4HE !MERICAN #ONCRETE )NSTITUTE PUBLISHES A

DESIGN CODE FOR CONCRETE STRUCTURES 4HESE CODES ARE UPDATED FREQUENTLY SO THAT

PRACTICING ENGINEERS CAN HAVE ACCESS TO THE MOST CURRENT RESEARCH RESULTS WITHOUT

ACTUALLY HAVING TO DEVELOP AND CONDUCT EXPERIMENTS FOR EACH PROJECT


22/28

4EST THE #OMPRESSION 3PECIMENS

4O CONDUCT THE COMPRESSION TESTS SET UP THETESTING MACHINE IN THE SAME WAY YOU DID FOR THETENSION TESTS 0LACE ONE OF THE CMLONG SPECIMENS 4EST # AT THE h#,INEv BETWEEN THELOADING ARM AND THE BASE "OTH THE TOP ANDBOTTOM OF THE SPECIMEN SHOULD BE RESTING ON THE

FELT PADS

/NCE THE SPECIMEN IS IN PLACE APPLY LOAD JUST ASYOU DID FOR THE TENSION TESTS !DD SAND TO THEBUCKET ONE SCOOP AT A TIME PAUSING SECONDSBETWEEN SCOOPS

7HEN THE SPECIMEN BUCKLES REMOVE THE BUCKETPLACE IT ON THE SCALE AND RECORD THE MASS

%MPTY THE BUCKET AND REPEAT THE PROCESS FOR EACHOF YOUR COMPRESSION SPECIMENS &OR EACH TESTKEEP CAREFUL RECORDS OF THE SPECIMEN SIZE ANDLENGTH AND THE MASS OF THE BUCKET AND SAND

4O MOUNT THE CMLONG AND CMLONG SPECIMENSA MINOR ADJUSTMENT TO THE TESTING MACHINE WILL BEREQUIRED )T IS VERY IMPORTANTTHAT THE LOADING ARMBE EXACTLY HORIZONTAL AT THE START OF EACH TESTOTHERWISE THE FOUR SIDES OF THE TUBE WILL NOT BELOADED EQUALLY &OR THE SHORTER SPECIMENS IT ISNECESSARY TO BLOCK UP THE BASE OF THE MEMBER

WITH BOOKS OR PIECES OF WOOD UNTIL THE LOADINGARM IS LEVEL 5SE THE CMLONG TEMPORARYSUPPORT AS A GAGE 5SE SHIMS MADE OF v BALSA

WOOD TO MAKE lNE ADJUSTMENTS TO THE HEIGHT OFTHE SPECIMEN "ECAUSE BALSA IS SOFT THESE SHIMS

WILL ALSO PERFORM THE FUNCTION OF THE LOWER FELTPAD WHICH IS NOW COVERED UP


23/28

117HAT ARE SOME POSSIBLE SOURCES OF ERROR IN THESE EXPERIMENTS

.OW THAT YOU HAVE COMPLETED THE TENSION AND COMPRESSION TESTS

THINK ABOUT SOME OF THE FACTORS THAT MIGHT CAUSE YOUR RESULTS TO BE

INACCURATE ,IST AT LEAST lVE POSSIBLE SOURCES OF EXPERIMENTAL ERROR IN

THESE TESTS 7HICH SOURCES OF ERROR DO YOU THINK HAVE THE GREATESTEFFECT ON YOUR RESULTS (OW CAN YOU MINIMIZE THEM

!NALYZE AND 'RAPH THE #OMPRESSION $ATA

4O ANALYZE OUR EXPERIMENTAL DATA WE WILL lRST CALCULATE THE ACTUAL COMPRESSIVE STRENGTH MEASURED IN EACHTEST THEN USE THESE DATA TO CREATE A COMPRESSIVE STRENGTH VS LENGTH GRAPH FOR EACH CROSSSECTION !GAIN THESETASKS ARE BEST PERFORMED WITH A COMPUTER SPREADSHEET

#ALCULATE THE #OMPRESSIVE 3TRENGTH!S LONG AS THE DISTANCE FROM THE #,INE TO THE PIVOT OF YOUR TESTING MACHINE IS EXACTLY EQUAL TO ,

WE CAN

CALCULATE THE COMPRESSIVE STRENGTH #USING THE EQUATION

7E CAN USE A SLIGHTLY MODIlED VERSION OF OUR TENSION SPREADSHEET TO DO THE DATA ANALYSIS 4HE RESULT SHOULDLOOK LIKE THIS

4EST 3IZE ,ENGTH -ASS OF 7EIGHT OF #OMPRESSIVE

.UMBER "UCKET 3AND "UCKET 3AND 3TRENGTH

MM CM G . .

# X

# #

#

#

#

#

#

#

# X #

#

#

# #

#

#

#


24/28

#OMPRESSIVE 3TRENGTH VS ,ENGTH FOR A MM X MM CARDBOARD TUBE EXPERIMENTAL DATA

#OMPRESSIVE 3TRENGTH VS ,ENGTH FOR A MM X MM CARDBOARD TUBE EXPERIMENTAL DATA

#REATE A 'RAPH OF #OMPRESSIVE 3TRENGTH VS ,ENGTH4HE COMPRESSIVE STRENGTH OF A TUBE IS AFFECTED BY BOTH THE SIZE OF ITS CROSSSECTION AND THE LENGTH OF THE

MEMBER 4HUS WE NEED TO CREATE A SERIES OF STRENGTH VS LENGTH GRAPHS ONE FOR EACH DIFFERENT CROSSSECTION!GAIN WE WILL USE THE hXY SCATTER PLOTv WITH MEMBER LENGTH AS THE XAXIS AND COMPRESSIVE STRENGTH AS THEYAXIS 4HE RESULTING GRAPHS FOR THE MM X MM AND MM X MM CROSSSECTIONS SHOULD LOOK LIKE THIS

,ENGTH CM

#OMPRESSIVE3TRENGTHNEWTONS

,ENGTH CM



25/28

11 #AN YOU USE THE GRAPH TO DETERMINE COMPRESSIVE STRENGTH

7HAT IS THE COMPRESSIVE STRENGTH OF A MM X MM TUBE THAT IS

CM LONG 7HAT IS THE COMPRESSIVE STRENGTH OF AN MM X MM

TUBE THAT IS CM LONG

#OMPRESSIVE 3TRENGTH VS ,ENGTH FOR CARDBOARD TUBES EXPERIMENTAL DATA WITH POLYNOMIAL TREND LINES

.OTE ALSO THAT THE EXPERIMENTAL DATA PLOTTED ON THE COMPRESSION STRENGTH GRAPHS DO NOT SEEM TO BE ASSTRONGLY LINEAR AS THE TENSION STRENGTH DATA WERE )NDEED THE RELATIONSHIP BETWEEN COMPRESSIVE STRENGTH ANDLENGTH IS NOTLINEAR SO IT WOULD BE INCORRECT TO REPRESENT THEM WITH A LINEAR TREND LINE )NSTEAD WE SHOULD USE AhBEST lTv CURVE TO REPRESENT THE DATA 4HE GRAPH BELOW SHOWS BOTH SETS OF DATA WITH POLYNOMIAL TREND LINESADDED !GAIN IF YOURE SPREADSHEET DOES NOT HAVE THIS CAPABILITY YOU CAN PRINT THE TWO GRAPHS ABOVE ANDSKETCH IN THE hBEST lTv CURVES BY HAND

,ENGTH CM


MM X MM TUBE

MM X MM TUBE

,IKE THE TENSILE STRENGTH GRAPH YOU DEVELOPED EARLIER THIS IS AN IMPORTANT DESIGN TOOL /F COURSE THIS GRAPHIS ONLY USEFUL FOR TWO PARTICULAR MEMBER SIZESTHE MM X MM TUBE AND MM X MM TUBE )F YOU WANTEDTO USE A DIFFERENT SIZE MEMBER IN A DESIGN YOU WOULD NEED TO RUN ANOTHER SERIES OF TESTS AND PRODUCE A CORRESPONDING CHART FOR THAT CROSSSECTION

#ONCLUSION)N DOING THIS PROJECT YOU HAD AN OPPORTUNITY TO LEARN ABOUT STRUCTURAL MEMBERS HOW THEY FAIL AND HOW

THEIR VARIOUS CHARACTERISTICS AFFECT THEIR STRENGTH 9OU LEARNED ABOUT DESIGNING EXPERIMENTS AND YOU SAW THATTHE DATA OBTAINED FROM WELLDESIGNED EXPERIMENTS CAN BE USED TO PREDICT THE STRENGTHS OF STRUCTURAL MEMBERS

WITH REASONABLE ACCURACY -OST IMPORTANT YOU PRODUCED A SERIES OF GRAPHS THAT WE WILL SOON USE TO ANALYZE ANDDESIGN MODEL TRUSS BRIDGES


26/28

!NSWERS TO THE 1UESTIONS

#AN YOU CALCULATE THE CROSSSECTIONAL AREAS OF THESE MEMBERS )N THE CASE OF SOLID SQUARE OR RECTANGULARMEMBERS THE CROSSSECTIONAL AREA IS THE WIDTH TIMES THE HEIGHT OF THE MEMBER

&OR THE v X v BAR 3PECIMEN ! THE AREA IS

&OR v X v BAR 3PECIMEN # THE AREA IS

&OR THE v X v BAR 3PECIMEN $ THE AREA IS

)N THE CASE OF HOLLOW TUBES THE EASIEST METHOD IS TO CALCULATE THE CROSSSECTIONAL AREA AS IF THE BAR WERE SOLID

THEN SUBTRACT THE AREA OF THE HOLE &OR THE v X v TUBE 3PECIMEN " THE AREA IS

.OTE THAT THE hHOLEv IN THE CROSS SECTION MEASURES v WHICH IS DETERMINEDBY SUBTRACTING TWO TIMES THE WALL THICKNESS v FROM v

&OR THE v X v TUBE 3PECIMEN % THE AREA IS

7HAT CAN WE LEARN FROM A COMPARISON OF 3PECIMENS ! AND % &OR ANY LENGTH GREATER THAN ABOUT v THE HOLLOWTUBE % IS STRONGER THAN THE SOLID BAR !EVEN THOUGH THE TUBE USES ONLY HALF AS MUCH STEEL 4HIS OBSERVATIONCLEARLY DEMONSTRATES THAT HOLLOW SHAPES ARE GENERALLY MUCH MORE ECONOMICAL THAN SOLID ONES FOR STRUCTURALMEMBERS IN COMPRESSION

5SING THIS LEVER HOW MUCH WEIGHT COULD YOU LIFT WITH POUNDS 4HE PRINCIPLE OF THE LEVERSTATES THAT &,

&

,

)N THIS CASE WE KNOW &

IS POUNDS ,

IS AND ,

IS )F WE SOLVE FOR &

AND SUBSTITUTE THESE KNOWN VALUESWE GET

.OTE THAT THE PRINCIPLE OF THE LEVER CAN BE USED TO DETERMINE THE MAGNITUDE OF EITHERFORCE ACTING ON THE LEVER

v

v

v

v

v

v


27/28

7HAT IS THE WEIGHT OF A KILOGRAM MASS 4O lND THE WEIGHT OF A KILOGRAM MASS USE THE EQUATION

)S CARDBOARD DUCTILE OR BRITTLE #ARDBOARD FAILS SUDDENLY WITH NO WARNING AND WITH NO EVIDENCE OF YIELDINGBEFORE RUPTURE 4HEREFORE IT IS A BRITTLE MATERIAL AND WOULD NOT BE APPROPRIATE FOR USE IN ACTUAL STRUCTURES

7HY WAS IT NECESSARY TO BALANCE THE LOADING ARM )F THE LOADING ARM WERE NOT BALANCED THEN THE WEIGHT OFTHE ARM ITSELF WOULD AFFECT THE FORCE IN THE SPECIMEN &OR EXAMPLE IF THE LONG SIDE OF THE LOADING ARM WEREHEAVIER THAN THE SHORT END EVEN WITH THE CLAMP ATTACHED THEN THE WEIGHT OF THE LOADING ARM WOULD ADD TOTHE INTERNAL FORCE IN THE SPECIMEN "UT THAT FORCE WOULD NOT BE ACCOUNTED FOR IN OUR ANALYSIS OF EXPERIMENTAL DATA BECAUSE THE EQUATION 47,

,

ASSUMES THAT 7AND 4ARE THE ONLY FORCES ACTING ON THE LOADING

ARM 4HUS AN IMPROPERLY BALANCED LOADING ARM COULD BE A SIGNIlCANT SOURCE OF EXPERIMENTAL ERROR

#AN YOU VERIFY THESE SPREADSHEET CALCULATIONS 4HE FOLLOWING CALCULATIONS ARE A MANUAL VERIlCATION OF THE TESTRESULT FOR THE lRST SPECIMEN

'IVEN,

CM

,

CM

-ASS OF BUCKET AND SAND GRAMS KILOGRAM

#ONVERT MASS TO WEIGHT

!PPLY THE PRINCIPLE OF THE LEVER

4HIS ANSWER MATCHES THE SPREADSHEET RESULT EXACTLY

#AN YOU USE THE GRAPH TO DETERMINE TENSILE STRENGTH

! CARDBOARD MEMBER MM WIDE SHOULD HAVE A TENSILE STRENGTH OF ABOUT NEWTONS

! SINGLE MM BAR SHOULD HAVE A TENSILE STRENGTH OF ABOUT NEWTONS 4HE DOUBLED MM BAR HAS TWICETHE CROSSSECTIONAL AREA AND THEREFORE TWICE THE STRENGTHABOUT NEWTONS

7HAT ARE SOME POSSIBLE SOURCES OF ERROR IN THESE EXPERIMENTS 3OME POSSIBLE SOURCES OF ERROR INCLUDE

)NACCURATE FABRICATION OF THE TEST SPECIMENS

)NACCURATE POSITIONING OF THE SPECIMENS IN THE TESTING MACHINE

)NACCURATE MEASUREMENT OF ,

AND ,

)NACCURATE MEASUREMENT OF THE WEIGHT OF SAND IN THE BUCKET

)MPROPERLY CALIBRATED SCALE

,OADING ARM NOT BALANCED


28/28

0OOR EXPERIMENTAL PROCEDURE SUCH AS ADDING SAND TOO RAPIDLY ADDING SAND AFTER THE SPECIMEN HASFAILED OR NOT ENSURING THAT THE LOADING ARM IS HORIZONTAL AT THE START OF THE TEST

&RICTION AT THE PIVOT OF THE LOADING ARM

/F THESE SOURCES OF ERROR INACCURACY IN THE FABRICATION AND POSITIONING OF TEST SPECIMENS IS PROBABLY MOSTCRITICAL )F A MM TENSION SPECIMEN IS ACTUALLY ONLY MM WIDE THE MEASURED TENSILE STRENGTH WILL BE TOOSMALL BY PERCENT )F A COMPRESSION SPECIMEN IS NOT PLACED EXACTLY VERTICALLY IN THE TESTING MACHINE ALLFOUR SIDES OF THE TUBE WILL NOT BE LOADED UNIFORMLY THE MEMBER WILL FAIL PREMATURELY AND THE MEASUREDCOMPRESSIVE STRENGTH WILL BE MUCH TOO LOW .ONE OF THESE SOURCES OF ERROR CAN BE ELIMINATED BUT THEY CANBE MINIMIZED BY FABRICATING TEST SPECIMENS AS PRECISELY AS POSSIBLE AND BY CAREFUL ATTENTION TO PROPEREXPERIMENTAL PROCEDURES

#AN YOU USE THE GRAPH TO DETERMINE COMPRESSIVE STRENGTH

4HE COMPRESSIVE STRENGTH OF A MM X MM TUBE WITH A LENGTH OF CM IS APPROXIMATELY NEWTONS

4HERE IS NO STRENGTH VS LENGTH GRAPH FOR AN MM X MM TUBE .ONETHELESS BECAUSE THIS MEMBER SIZEFALLS BETWEEN THE MM X MM TUBE AND THE MM X MM TUBE WE CAN REASONABLY INTERPOLATEBETWEEN THE TWO CURVES 4HE COMPRESSIVE STRENGTH OF AN MM X MM TUBE WITH A LENGTH OF CM COULDBE ESTIMATED AT APPROXIMATELY NEWTONS

3OME )DEAS FOR %NHANCING THIS ,EARNING !CTIVITY/NCE STUDENTS HAVE COMPLETED THE BASIC STRENGTH TESTS DESCRIBED ABOVE HAVE THEM DEVELOP AND PERFORM

EXPERIMENTS TO ANSWER QUESTIONS LIKE THESE

!RE DIFFERENT CROSSSECTION SHAPESTRIANGLES SHAPES AND CIRCULAR TUBES FOR EXAMPLEMORE OR LESSEFlCIENT THAN SQUARE TUBES IN CARRYING COMPRESSION

$O TWO MM BARS REALLY HAVE THE SAME STRENGTH AS ONE MM BAR

#AN THE TENSILE STRENGTH OF A CARDBOARD MEMBER BE IMPROVED BY COATING IT WITH GLUE

7HAT IS THE TENSILE STRENGTH OF A PIECE OF LICORICE 4HE COMPRESSIVE STRENGTH OF A PRETZEL STICK

"ETTER YET HAVE THE STUDENTS FORMULATE THEIR OWN QUESTIONS THEN DESIGN EXPERIMENTS TO lND THE ANSWERS!FTER STUDENTS HAVE COMPLETED A SERIES OF TENSILE STRENGTH AND COMPRESSIVE STRENGTH EXPERIMENTS ASK THEM

TO ASSESS THE DESIGN OF THE TESTING MACHINE 7ORKING IN TEAMS THE STUDENTS SHOULD STUDY AND DISCUSS THEOPERATION OF THE DEVICE THEN RECOMMEND AT LEAST THREE IMPROVEMENTS TO ITS CONlGURATION THAT WILL IMPROVE THEACCURACY OF THE EXPERIMENTAL RESULTS OR IMPROVE THE USERFRIENDLINESS OF THE MACHINE 4HIS EXERCISE WILL HELP TOREINFORCE WHAT THE STUDENTS HAVE ALREADY LEARNED ABOUT TENSILE STRENGTH COMPRESSIVE STRENGTH LEVERS ANDEXPERIMENTAL ERROR )T WILL ALSO GET THEM THINKING ABOUT DESIGNTHE SUBJECT OF TWO FUTURE LEARNING ACTIVITIES

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Test the Strength of Structural Members