DEFLECTION DEFLECTIO N OF A SIMPLY SIMPLY SUPPORTED BEAM Objective: To establish the relationship between deflection and applied load and determine the elastic modulus of the beam specimen from the deflection data. Theory:
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Apparat!: The apparatus consist of:
1. 2. 3. 4. 5. !. ". #.
A supp suppor ortt fra fram me. A pair pair of of pinn pinned ed sup suppo port rt.. A load load han hanger ger. A dial gauge gauge with with 0.01 0.01 mm accuracy to measuring measuring deflection. deflection. eam specimen specimen with constan constantt depth depth and width width throug throughout hout its length. length. A caliper caliper to measure measure the depth and with with of the the beam specimen. specimen. A meter ruler ruler or tape tape measure measure to measure measure the the span of the beam. beam. A set set of of wei weigh ghts ts..
Dia"ra#:
Fi"re $% Loa&' $N
Fi"re (% Meter r)er
Fi"re *% A pair o+ pi,,e& !pport
Fi"re -% Type o+ bea#! !peci#e,
Fi"re .% Setti," the &ia) "a"e rea&i,"
Fi"re /% Ca)iper Proce&re:
1. olt the two $nife edge supports to the support frame using the plate and bolt supplied with the apparatus. The distance between the two supports should be e%ual to the span of the beam to be tested. 2. &easure width and depth of specimen and record the readings 'ta$e measurement at 3 location and record the a(erage reading). 3. *lace the beam specimen on the $nife edge supports. 4. +i, the load hanger at mid-span of the beam. 5. *osition the dial gauge at the mid-span of the beam to measure the resulting deflection. !. et the dial gauge reading to /ero. ". *lace a suitable load on the hanger 'starting with 1) #. ecord the resulting dial gauge reading. . ncrease the load on the load hanger 'by an increment of 1) 10. epeat step # and for a few more load increments of 1 up to a ma,imum total load of 5 on the hanger. 11. epeat the abo(e test to obtain another set of readings using the same beam specimen. 12. epeat the whole procedure from step 1 to 11 for two other beam specimens. Re!)t! o+ A)#i,i#%
pan of tested beam 6 1000 mm 7idth of beam specimen b 6 25.02# mm
8epth of beam specimen d 6 3.#! mm &oment of inertia of beam specimen 6 'bd 3912) 6 123.4 mm 4 8ial gauge reading 1 di(ision 6 0.01 mm &odulus of lasticity 6 "0000 9mm 2 Table: App)ie& Loa&
N 1 2 3 4 5
E0peri#e,ta) De+)ectio,
Te!t $
Te!t (
## 1.04 2.2# 3.31 4.52 5.!
## 1.1! 2.34 3.55 4."" !.02
Theoretica) De+)ectio, ##
Avera"e De+)ectio, ##
1.1 2.31 3.43 4.!45 5.#1
2.413 4.#2! ".23 .!52 12.0!5
Re!)t! o+ Stai,)e!! Stee)%
pan of tested beam 6 1000 mm 7idth of beam specimen b 6 25.04 mm 8epth of beam specimen d 6 3.03 mm &oment of inertia of beam specimen 6 'bd3912) 6 5#.05 mm 4 8ial gauge reading 1 di(ision 6 0.01 mm &odulus of lasticity 6 1#"500 9mm2 Table: App)ie& Loa&
N 1 2 3 4
E0peri#e,ta) De+)ectio,
Te!t $
Te!t (
## 1.1 2.43 3.! 4.!
## 1.1 2.4# 3.!" 5
Theoretica) De+)ectio, ##
Avera"e De+)ectio, ##
1.145 2.455 3.!# 4.#
1.141 3.#2# 5."42 ".!5!
5
!.3
!.4
!.35
.5"
Re!)t! o+ Bro,1e%
pan of tested beam 6 1000 mm 7idth of beam specimen b 6 25.5055 mm 8epth of beam specimen d 6 5.0 mm &oment of inertia of beam specimen 6 'bd3912) 6 2#0.2 mm 4 8ial gauge reading 1 di(ision 6 0.01 mm &odulus of lasticity 6 120000 9mm2 Table: App)ie& Loa&
N 1 2 3 4 5
E0peri#e,ta) De+)ectio,
Te!t $
Te!t (
## 0.!# 1.3" 2.0 2."# 3.45
## 0.!" 1.41 2.22 2.5 3."5
Theoretica) De+)ectio, ##
Avera"e De+)ectio, ##
0.!"5 1.3 2.155 2.#!5 3.!
0.!1 1.23 1.#5# 2.4"# 3.0"
1. ;sing the tabulated data in table abo(e plot the graph of load (erses e,perimental deflection. 2. 8raw the best fit cur(e through the plotted point and hence deduce the relationship between the applied load and the resulting mid span deflection. 3.
1. +rom this e,periment what is the relationship between the applied load and the resulting displacement9deflection. 7hen the applied load increase the resulting displacement9deflection will higher. 2. 7hat does the slope of the graph represents how does it (aries in relation to the load position.
3. =ow do the e,perimental results differ with the theoretical results in terms of
accuracy> riefly e,plain the probable cause of errors and how can it be o(ercome.
