In some extent, we are doing characterization of our loading frame. means we will have to set its limitation also for the further testing of structural models prototype and separate component so there are so many other aspects also about which we will have to understand rather they having strength related significance or not. In that case, we have to follow IS 14877 Part-1 for its geometrical characterization. First of all the test was performed is flatness of top surface.
5.1 Flatness of top surface
As per 14877 Part-1 permissible limit for flatness of top surface can be calculate by formula given bellow
For Grade-1=.015+(.04*L1)/1000
For Grade-2=.03+(.06*L1)/1000
For Grade-3=.06+(.08*L1)/1000
Table 5.1 readings of flatness of top surfaces
S.no. distance from left column undulations in mm
Permissible values
1 100 0.06
Grade1
0.085
2 200 0.08
3 250 0.03
4 400 0.07
Grade2
0.135
5 600 0.14
6 750 0.09
7 900 0.13
8 925 0.09
9 1210 0.10
Grade3
0.20
10 1570 0.17
11 1690 0.12
12 1760 0.09
So by the interpretation of results obtain maximum undulations in the top surface exeed to Grade 1 and Grade2 respectively but they are within Grade3 limit. So its top surface is of grade 3 type of hydraulic press.
5.2 Flatness of bottom surface
For theoretical limits of bottom surface, we will use same formula as earlier for top surface.
Table 5.2 readings of flatness of bottom surfaces
S.no. distance from left column(mm) Undulations in( mm) Permissible limits
1 100 0.06
Grade1
0.085
2 250 0.08
3 370 0.03
4 460 0.07
Grade2
0.135
5 600 0.14
6 780 0.09
7 910 0.13
8 925 0.09
9 1280 0.10
Grade3
0.20
10 1520 0.16
11 1630 0.12
12 1730 0.09
5.3 Parallelism
For this there following two criteria’s.
For Grade-1=0.03+(0.08*L2)/1000
But not less than 0.06
For Grade-2=0.06+(0.12*L2)/1000
But not less than 0.12
For Grade-3=0.12+(0.17*L2)/1000
But not less than 0.20
Table 5.3 Readings of Parallelism surfaces
S.no. distance from left (mm) undulations in mm Permissible limits
1 100 0.13
Grade1
0.17
2 250 0.28
3 370 0.12
4 460 0.31
Grade2
0.27
5 620 0.34
6 810 0.24
7 920 0.26
8 960 0.14
9 1250 0.1
Grade3
0.4175
10 1535 0.38
11 1630 0.35
12 1730 0.29
So we had seen experimental values as well as theoretical values with help of which we can say that our loading frame is characterize as Grade3 type as per IS-14877 part1 defines for straight sided hydraulic press.
5.4 Strain Analysis
For functioning as a hydraulic press or a testing machine, it should possess minimum flexibility as minimum as possible. So our loading frame should be as rigid as possible is desired.
Here first we have to do the theoretical calculation for our box type-loading frame for calculation of distributed moment over the joints. Because it’s a symmetrical frame with symmetrical loading conditions so carry over moment will be canceled due to symmitricity of box frame so the step included in calculation are as follows.
Its corners ware welded so we can assume it as rigid jointed frame. so its line diagram will be as shown bellow.
Fig.5.1Line diagram of frame
Fixed end moments Mab= wl/8
Mba=-wl/8
Similarly Mdc=- wl/8
Mcd= wl/8
And because there is no such load or moment on span DA and BC so
Mda=Mad=0
And Mbc=Mcb=0
All corners ware assumed to be rigid so stiffness of each member
Kab=Kba=Kbc=Kcb=Kcd=Kdc=Kda=Kad= 4EI/L
So Distribution factor for AB= 18/43
Distribution factor for AB= 25/43
So ultimately after calculation of moment distribution we got the expression for moment magnitude is.
Mab=Mba=Mbc=Mcb=Mcd=Mdc=Mad=Mda= 25wl/344
Final moment on top of top beam at mid span is
M=61wl/344
And now we can also calculate stress with the help of bending equation i.e. . . .
M/I=o/y=E/R
On which o=MY/I
Moreover, with help of stress we can find strain occur at top of flange of top beam by help of relation given in hook’s law.
ℇ=o/E
for column because there is not any load in whole span only fixed end moment will be distributed over whole span. So at mid where we are finding strain only this moment will acting. And rest of calculation of strain are same as for beam.
Experimental calculation of strain
Because the output which was founded from strain gauge and ultimately from data logger are in form of voltage signals in ppm unit. So we have to convert it in to proper strain format. For that formula should be used is as follows.
strain in (micro strain)=(4*(initial reading-final reading))/Gn
Strain in beams
We have done the experiments and results of both with percentage are shown in table given bellow. Based on which we can do comparative study of actual and theoretical results. With help of which we can conclude several things like strain displacement fixity of supports etc.
Table 5.4 readings of strain in beam
S.no.
load in KN strain in top flange experimental (micro strain) strain in top flange theoretical (micro strain)
%Error
1 0 0 0 0%
2 51.14 35.23 37.03 -4.88%
3 102.24 74.35 74.049 0.40%
4 149.2 110.33 108.06 2.10%
5 199.88 151.20 144.78 4.44%
6 249.90 187.13 180.99 3.39%
7 299.60 226.84 216.98 4.53%
8 349.20 256.96 252.91 1.59%
9 400.58 298.36 290.01 2.87%
After the results, we had seen that there is some difference between these two strain values of results. So bar chart considering comparative results of both shown bellow.
Fig.5.2 comparison of strains between experimental and theoretical
There could be two reason behind this difference between these two readings of strain.
Due to error in measurement
Due to fixity of the supports or joints
However, we can check reliability of our sensing and instrumentation system by plotting graph between load and strain, which is ultimately load verses displacement plot. Graph between load and displacement shown bellow.
Fig.5.3 plot between load and strain
Here we found linear relation between load and displacement, which was desired so we can believe on our setup and reading at some extent.
Strain in columns
Because there is no load in span of column, so not any excess bending moment will act on both of them and there is only fixed end moment and shear force because we
know that there is negligible chances that steel column will fail due to shear force. So total moment in whole column will be-
M=25wl/344
Distributed in span of column.
Table bellow shows comparison between experimental and theoretical values of strain in right column.
S.no
load in KN strain in extreme flange fiber(micro strain) theoretical values of strain (micro strain)
1 0 0 0
2 51.14 1.51 10.9297
3 102.24 13.58 21.8506
4 149.20 9.35 31.8864
5 199.9 4.95 42.7201
6 249.91 4.27 53.4096
7 299.60 22.01 64.028
8 349.20 28.47 74.6301
9 400.58 32.18 85.612
Table 5.5 readings of strain in right column
So to find differences between theoretical and experimental values we had plot a bar chart between experimental vales of strain. Shown bellow.
Fig.5.4 comparison of strains between experimental and theoretical
Table 5.6 readings of strain in left column
S.no
load in KN strain in extreme flange fiber(micro strain) theoretical values of strain (micro strain)
1 0 0 0
2 51.14 1.87 10.92
3 102.24 14.02 21.85
4 149.18 10.06 31.89
5 199.89 7.52 42.72
6 249.91 7.89 53.41
7 299.61 20.76 64.02
8 349.19 29.81 74.63
9 400.57 34.89 85.61
We have also done comperative study of results founded theoritically and experimentally for respective values of loads.
Fig.5.5 comparison of strains between experimental and theoretical
5.5 Deflection analysis
for verifying the frame in structural aspect there is one more study we have done. It was study of deflection at various characteristic loads. For obtaining theoretical values we used moment distribution first to find moment and then for finding the deflection we used energy method.
Deflection of top beam δ=.0064wl*l* l/EI
So we have don e comparative study of result founded from experiments and thory.
Table 5.7 Results of deflections
S.no
load in KN Experimental deflection (mm) Theoretical deflection (mm)
1 0 0 0
2 51.14 0.031 0.028
3 102.24 0.057 0.056
4 149.19 0.088 0.081
5 199.89 0.1102 0.11
6 249.90 0.1386 0.13
7 299.6 0.1647 0.16
8 349.19 0.1981 0.19
9 400.56 0.2206 0.22
Bar chart indicating towards comparison of theatrical and experimental data shown bellow.
Fig.5.6 comparative results of deflection
Fig.5.7 plot of load verses experimental deflection data
5.6 SUMMARIZED RESULTS AND DISCUSSIONS
Characterization of frame had been done satisfactorily and results are as expected were within the limits means acceptable.
As per geometrical specification our frame comes under the Grade-3 as define in Indian standard code IS 14877 part-1.
And as per structural performance basis its result are also satisfying codal provision of IS-15747 2007 i.e. maximum deflection as a hydraulic press is .17mm for per 1000 mm of span length.
In comparative study there were some discrepancies for them there may be of two conclusions.
It may be due to error in experimental setup
Or may be due to design fault because it is impossible to form a rigid joint or connection in actual practice and our all calculation are done by assuming as all joints are rigid.
2.2 Critique
Since lot of work has been done on SHM of steel frame for both static condition the type of testing methods from analog to digital .
Further work has been done on structural analysis and optimization of loading frame and hydraulic presses we plant to replicate that for our loading frame
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