Mechanic of Materials (a short lab)

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remember before u handle this work, this work is so important to me, so i will revise it many times before i turn it in and i will rate u depend on your work quality such as providing correct and full answers and meet all requirements in the attached instructions. Please avoid the Lack of depth in your response.

see the data then complete and answer the attached WORD document fully.

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Mechanic of Materials (a short lab)
combined_load.jpg
Mechanics of Materials Laboratory Dr. M. E. Barkey Department of Aerospace Engineering and Mechanics The University of Alabama Stress State from Combined Loading M. E. Barkey 1 04/06/18 A. Introduction and Objective The objectives of this experiment are to compute a stress state for combined loading and the principal stresses that result from this stress state; measure strains experimentally with a strain gage rosette; calculate stresses from the measured strains and compute the principal stresses from the experimental data. B. Theory 1.0 Stress State from Combined Loading We have studied states of stress from varies types of loads as they are applied independently on a structure. The formulas for the stresses are summarized below: o=F (axial normal stress) (1) (longitudinal bending stress) (2) (pressure vessel stresses) (3) (transverse shearing stress) (4) (torsional shearing stress). (5) Æ o= –My I oh = pr v= VQ It v= Tq , oa = tw pr 2tw Ip For a state of combined loading, the stress states from these individual loads can be superimposed to determine the combined loading stress state. The principle of superposition can be applied as long as the system that you are analyzing remains linear—for our purposes in this class, that means that the material cannot have yielded—i.e. when load is applied and removed, the strains return to nearly the same initial value. M. E. Barkey 2 04/06/18 The following steps should be taken to determine the stress state at the point of interest on your structure: 1) Make a free-body-diagram to determine the reactions (loads and moments) that act at the point of interest in the structure. 2) Determine how each reaction contributes to the stress state at the point of interest. Before these two steps, you can also use statics to simplify the structure by removing various loading arms and replacing them with a statically equivalent force-moment system. Note that forces and moments must be resolved to the centroid of the crosssection of the bar on which you are determining the stress state. Figure 1: Structure subjected to combined loading. M. E. Barkey 3 04/06/18 After the stresses are calculated, principal stress can be calculated by using Mohr’s Circle. 2.0 Strain Gage Rosette Analysis A strain gage rosette is a pattern of two or three strain gages. A strain gage is mounted on the upper surface of the combined loading structure as shown in Figure 2. (The orientation of your gage may be different than shown in the figure.) The 0º45º-90º strain gage rosette can be used to determine a complete state of surface strain (including shear strain) by measuring extensional strains in three (non-colinear) directions. The strains are determined in the gage coordinate system. Figure 2: Strain gage rosette. M. E. Barkey 4 04/06/18 Gage 1, 2, 3 are labelled in Figure 3. Gage 1 is the 0º gage aligned with the x-axis, gage 3 is the 90º gage aligned with the y-axis, and gage 2 is the 45º gage. The gage numbers are manufactured onto the gage but are partially obscured by the wires. The rosette x-y coordinate system is also manufactured onto the gage and are shown highlighted on the figure. Note that the strain gage coordinate system will usually not line up with the axis of the tube. Figure 3: Strain gage rosette and coordinate system. M. E. Barkey 5 04/06/18 The strain components in the strain gage coordinate system are given by the following equations: ss = s1 (6) sy = s3 (7) ysy = 2 s2 — s1 — s3 (8) and the stresses in the rosette coordinate system are found by inverting generalized Hooke’s Law specialized for zero stress in the z-direction: s = ox — u s s = y oy E (9) E —u E ysy = oy cxy G ox (10) E (11) Finally, calculate principal stresses from the measured experimental strains are found by Mohr’s Circle. M. E. Barkey 6 04/06/18 C. Lab Procedure IMPORTANT: The strain gage and wires are very delicate and are time consuming to install. Please handle the test structure carefully to avoid damage. Attached the combined loading structure to the benchtop using bolts and nuts. Check that you and anyone else in the area are wearing safety glasses and closed-toe shoes. The main possible hazard during this lab is a dropped weight. Use a small cable tie to loop through one of the holes on the loading arm if it is not already attached. Use a weight pan, and place a foam pad under the weight pan in case the weight pan fails. Measure the distances l1 (from the load line to the centroid of the tube) and l2 (from the centroid of the tube to the center of the strain gage rosette) as shown in Figure 1. Note that the material is 6061-T6 aluminum tube with an outside diameter of 0.625 inches and a wall thickness of 0.035 inches. Attach the strain gage wires to the P3 strain indicator as a three-wire quarter bridge as shown in Figure 4 below. Wire 1 should be attached to channel 1, wire 2 should be attached to channel 2, wire 3 should be attached to channel 3. Look for markings on the wires to indicate the wire number. Set the gage factor for each channel to 2.02 for test specimens 17-1, 17-2, 17-3, 17-4, 17-5. Verify the settings with the Lab Assistant. Figure 4: P3 strain indicator. M. E. Barkey 7 04/06/18 Balance the strain indicator with the weight pan in place, but with no weights attached. Record the initial strain readings, and take strain readings for the weights listed in the table below. Remove the weights and take a final zero load reading. Raw Measurements Strain Gage Readings (micro‐strain) weight (lbs) 1 2 3 0 2 4 6 8 10 0 IMPORTANT: DO NOT EXCEED 10 lbs WEIGHT Determine the net strain readings for each gage. Net Adjusted Strain Gage Readings (micro‐strain) (Raw ‐ Average Zero) weight (lbs) 1 2 3 0 2 4 6 8 10 0 M. E. Barkey 8 04/06/18 D. Lab Report Check to see if the strain readings are linear with load: plot load on the y-axis and each gage strain reading on the x-axis. All of the gages will be plotted on this same plot. Fit the data for each gage with a straight line (linear regression trend line). Note any deviations from linearity in your discussion. At 10 pounds weight, calculate the strain components in the gage coordinate system using equations (6), (7), (8). Calculate stresses through the use of equations (9), (10), (11). Calculate the in-plane principal stresses by the use of Mohr’s circle. Include these calculations in your lab report. Calculate the stress state at the gage location using the theory—equations (1)-(5) —as appropriate. Include a free body diagram and your calculations in your lab report. Use Mohr’s circle to determine the principal stresses. Compare your calculated and experimental principal stress values at 10 pounds load and determine the percent error; complete the table below. Comparison of Theory and Experiment 10 lbs Sigma_P1 Sigma_P2 Theory Experiment % Error M. E. Barkey 9 04/06/18 E. Questions Why do we need to use 3-D Hooke’s Law to calculate strains for this experiment? Why don’t we use equation v = VQ to calculate shear stress at the gage location? It F. Discussion M. E. Barkey 10 04/06/18

Tutor Answer

TeacherSethGreg
School: UIUC

Attached.

Mechanics of Materials Laboratory
Dr. M. E. Barkey
Department of Aerospace Engineering and Mechanics
The University of Alabama

Stress State from Combined Loading

M. E. Barkey

1

04/06/18

A. Introduction and Objective
The objectives of this experiment are to compute a stress state for combined loading and
the principal stresses that result from this stress state; measure strains experimentally with
a strain gage rosette; calculate stresses from the measured strains and compute the
principal stresses from the experimental data.
B. Theory

1.0 Stress State from Combined Loading

We have studied states of stress from varies types of loads as they are applied
independently on a structure. The formulas for the stresses are summarized below:
o=F

o=

(axial normal stress)

(1)

(longitudinal bending stress)

(2)

(pressure vessel stresses)

(3)

Æ

–My
I

oh =

p r,

oa =

tw

pr
2tw

v =

VQ
It

(transverse shearing stress)

(4)

v =

Tq
Ip

(torsional shearing stress).

(5)

For a state of combined loading, the stress states from these individual loads can be
superimposed to determine the combined loading stress state. The principle of
superposition can be applied as long as the system that you are analyzing remains
linear—for our purposes in this class, that means that the material cannot have
yielded—i.e. when load is applied and removed, the strains return to nearly the same
initial value.

M. E. Barkey

2

04/06/18

The following steps should be taken to determine the stress state at the point of
interest on your structure:

1) Make a free-body-diagram to determine the reactions (loads and moments) that
act at the point of interest in the structure.
2) Determine how each reaction contributes to the stress state at the point of interest.

Before these two steps, you can also use statics to simplify the structure by removing
various loading arms and replacing them with a statically equivalent force-moment
system. Note that forces and moments must be resolved to the centroid of the crosssection of the bar on which you are determining the stress state.

Figure 1: Structure subjected to combined loading.

M...

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Top quality work from this guy! I'll be back!

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