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**Unformatted text preview: **1w if. “‘3 Unitrersit}r of Alberta Department of Civil and Environmental Engineering Cir E 1'?“ Laboratory 7' Name: Lil:
Dare: Hark:
Loo Sﬁcﬂ-ﬂﬂ.‘ BENDTNG TEST 11 DBJECTWES To verify the assumption that ﬂexural strains uarjr linearly with the distance from the
neutral axis. To illustrate elastic and inelastic bending behaviour.
To calculate the modulus of elasticitj.r and the yield strength using bending tests. To predict member strength based on measured material properties and simple beam
theory. To apply the test results to a practical problem. T2 TEST PROCEDURE 12.1 Aluminum I—Beam, Elastic Bending Test 1. Place and align the I—beam in the testing machine, as shown schematically in
Figure 11. Connect the strain gauges to the strain indicator.
Apply an initial load of ID l-zN to seat the beam and the load and reaction devices Unload the beam and zero the strain gauges and load dial. Record zero readings. Record strain readings for gauges at locations 1 through 5 for loads of It) El, 2!] El,
30' W and 46 Hi. Unload and then record the zero readings. Laboratory 5' Cir! E 2W 2 12.2 Rectangular Steel Beam, Inelastic Bending Test 1. 2. hall-sure and reeord the cross—sectional dimensions of the test specimen Place and align the specimen in the testing machine= as shown schematically in
Figure T2. Connect the strain gauges and LVDT‘s to the data acquisition system. Apply an initial load of about ltlﬂﬁ’ the estimated yield load in order to S-l' the
specimen. Unload and zero the instruments.
Apply load continuously. Continue loading until strain values at the extreme tension or compression ﬁbres are
at least ﬁve times the yield strain 13 RECORD lICJIF TEST DATA AND ANALYSIS OF TEST RESULTS 13.1 Aluminum I—Beam, Elastic Bendgg' Test [3} [13} {C} {d} {E} The locations of strain gauges 1 through 5, cross-sectional dimensions, geometric properties and material properties are given in Figure ?.1. Record the strain gauge readings on Data Sheet 11. Compute theoretical strains at gauge locations 1 through 5 for loads of it] IrN and
4-D IrN hased on material and geometric properties and the elastic ﬂexural formula
discussed in class. Based on the strains measured by gauges l and 5 at a load level of 4-D er, calculate
the modulus of elasticity E and eompare it with the value of E given in Fig. T. 1. Plot both the Insured {experimental} and computed {theoretical} strain distributions
for loads ofhoth 2!] m and 4!] kN. Use a scale ofES mm= 25E! microstrain {us} on the x—axis and use full scale for the cross—sectional depth on the y—axis. Lahel the
axesandeunres. All theseplots aretobedoneonthe same graph. 13.2 Rectangular Steel Beam, Inelastic Bending Test [3} The measured {average} dimensions of the rectangular bar are as follows. heamdepth, d= mm
beam width, h = m Laboratory 7 Chi 270 3 7.4 (b) (C) (d) (e) (f) (g) (h) (i) The material properties of this beam have been determined from a uniaxial tension
testonacouponmade ﬁoruabarofthesameheat. Modulus of elasticity, E = MPa
Static yield strength, °y = MPa
Ultimate strength, ou = MPa
(if available) Using the measured cross-sectional dimensions, calculate the values of A, 1‘, S, and
Z” wherex isthe axis ofbending. Drawaﬁeebodydiagramofthebeamandusethistoderiveanequationforthe
maximum moment, M, as a function of the machine load P. Two strain gauges have been attached to the top and bottom of the rectangular section to measure extreme ﬁbre strain, as shown in Fig 7.2. Write the equation that relates
extreme ﬁbre strain to curvature of the beam. Predict values of My and Mp based on measured material properties and calculated
values Sx and 2,. Calculate the corresponding loads, Py and Pp, that cause yielding
of the extreme ﬁbres and yielding of the whole cross-section. A graph of the moment vs. curvature behaviour for the beam will be handed out. The graph contains two curves. In the ﬁrst, moment is calculated as in part ((1). In the
second, a correction for the second order effects is included in the moment calculation. At large curvatures, the load points move inwards and the support points
move outwards, resulting in an increase in the shear span. Calculate the magnitude of
the second order effect for this test- label the locations of MM MYpredicted= Mm and MW on the corrected
moment vs. curvature plot. Determine the slope of the initial linearly elastic portion of the moment vs. curvature
plot. Compare this to the product E1 DISCUSSION 7.4. 1 7.4.2 Comment on the measured and computed strain distributions obtained in the elastic
bending test. Compare the yield and maximum moments obtained in the Inelastic Bending Test
with your predicted values. Commmt on the diﬁ‘erences. Lahomrm}! F Cit! E 2W 4 7".5 APPLICATION OF RESULTS A manufacturer produces 12 m long mild steel bars hating the sme cross—section and
material proportion as the section used for the inelastic bending test. It is proposed to load the bars onto trucks using a crane that will pick up the bars only at their centres. The stresses during
this operation are not to exceed 56% of the yield strength. Determine the maximum moment, calculate the maximum stress in the cross—section [neglect shear stresses}, and eompare this with
the jrield strength. Use the yield strength given in Section ?_3_2[b} and the density of rolled steel, "1' = T350 kge'm3. Is the proposed loading procedure acceptable? If not, suggest a solution to the
mamrfacturer‘s problem. Suggest improvements even if the procedure is aceeptable. a=25_4 mm; b= ?ﬁ_3mm
d= lﬂl} mm; t=li5mm
w=4_?mm llK =2_542 31105 mm4
E= T2 DUI] LIFE] Figure ?_1 Schematic of set—up of elastic bending test and cross—section of aluminum I—beam Figure T2 Schematic of set-up of inelastic bending test and cross—section of steel beam Laﬁamrm]: F Cir E 2 Fl? 5 Name: Date:
Data Sheet 7.1 Strain Gauge Readings Strain Indicator Endings, a 1D"5 mm-‘mm, {pa} LuadeN -------- Measured Strains Measured Stajn= Strain Readin —Asrera us Zero Readin- ...

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