Engineering of Measurement

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Engineering of Measurement
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Engineering of Measurement
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Engineering of Measurement
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WIDENER UNIVERSITY School of Engineering Department of Mechanical Engineering ME 303 - Mechanical Measurement Laboratory Experiment No. 3 FORCES IN TRUSS MEMBERS I. INTRODUCTION When a section of a truss is subjected to an external load, the members of that truss section assume loads which are related to the applied external load by the geometry of the truss and the magnitude, location, and direction of the applied load. Consider a simple truss loaded as shown. Principles of statically determinate loads are used to determine analytically forces in each member of the truss. SFx = 0: FAC sin q 1 - FBC sin q 2 = 0 SFy = 0: FAC cosq 1 + FBC cosq 2 = P (1) ( 2) From these two equations, FAC and FBC may be determined. FAC = P sin q 2 sin (q 1 + q 2 ) FBC = P sin q 1 sin (q 1 + q 2 ) The force in member AB is: FAB = FAC sin q 1 = FBC sin q 2 Reactions at A and B are: RA = P l BC sin q 2 = FAC cosq 1 l AB RB = P l AC sin q 1 l AB = FBC cosq 2 The stress in a member, say “i” is: si = Fi Ai where: Fi - force in the i-th member Ai - cross sectional area of the i-th member 1 or, using Hooke’s law: e i Ei = Fi Ai where: ei - applied strain Ei - modulus of elasticity of the material. Thus, the force in the i-th member can be found if ei , Ei and Ai are known. II. Fi = Ei Ai ei EXPERIMENT A. Objectives - Experimental determination of forces in truss members subjected to external loads. - Familiarization with strain gage measurement. B. Equipment - Tinius Olsen testing machine - Digital strain equipment - Vernier calipers C. D. Specimens - Three pin connected triangular trusses will be tested, as shown below. Each truss is instrumented with strain gages. Experimental Procedure For each truss: 1. Check all strain gages for broken leads. 2. Measure length and cross-section of each member. 3. Find the yielding load PY for the material of the truss. 4. Check the critical buckling load Pcr for the truss. 5. Set up a truss in the Tinius Olsen testing machine (make sure that loads and reactions do not interfere with free loading of members - see sketch below). 6. Connect the strain gages to the bridge and strain indicator per instruction manual. 7. Apply five loads to the truss starting with the smallest load which gives a suitable strain reading. The maximum load shall not exceed a 50% PY or 50% Pcr. The load increments shall be equally spaced between the first and fifth reading. Record the applied load and corresponding strain readings in all members. E. Results - Calculate analytically theoretical forces in each member of a truss using Method of Joints. Draw FBD for each joint and derive expressions for all theoretical forces in terms of the applied load P: FiTH = f (P). Find forces in truss members corresponding to each experimentally applied load. Compare the experimental and theoretical results (calculate % difference).. Discuss the results and possible errors. Note: Material: 4140 Alloy Steel E = 29.2 x 106 psi sY = 61 ksi Cross-sectional dimensions of an “ideal” truss: 1”x0.25 2 Date: __________ Team: __________ 1. _________ 2. _________ 3. _________ 4. _________ 5. _________ ME 303 Experiment #4 FORCES IN TRUSS MEMBERS Experimental Data Material: 4140 Alloy Steel E = 29.2 x 106 psi sY = 61 ksi Truss: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ei x 10-6 P [lb] AB Front Back AC Ave. Front Back BC Ave. Front Back Ave. Truss: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ei x 10-6 P [lb] AB Front Back AC Ave. Front Back BC Ave. Front Back Ave. Truss: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ei x 10-6 P [lb] AB Front Back AC Ave. Front Back BC Ave. Front Back Ave. 3 Measurements for Trusses 30,60,90 60,60,60 45,45,90 Width Thickness Length 0.9965 0.249 5.9655 0.979 0.256 10.3955 0.997 0.2525 11.9655 Width In. Thickness In. 1.0035 0.251 1.0065 0.2475 1.0025 0.251 Width Thickness Length 12.6055 12.85 Pin Diameter 12.85 Length 1.0205 0.249 12.025 0.9975 0.2495 8.708 1.001 0.251 8.708 0.2445 Load (lb) gauge 1 gauge 2 0 -59 250 500 gauge 3 gauge 4 -17 -12.5 0 -58 7 7 -68 -47 26 4 -112 750 -34 41 -6 -151 1000 -21 55 -18 -188 1250 -8 69 -29 -225 gauge 5 gauge 6 0 0 13 -60 12 -107 7 -150 -1 -191 -12 -229 *all gauge readings are measured in microstrain Load (lb) gauge 1 gauge 2 gauge 3 gauge 4 0 -55 -13 -9 0 250 -56 -13 42 -121 500 -56 -14 48 -196 750 -56 -14 28 -245 1000 -57 -14 5 -289 1250 -58 -14 -20 -334 gauge 5 gauge 6 *all gauge readings are measured in microstrain 0 -2 2 -9 2 -9 2 -9 3 -12 3 -9 Load (lb) gauge 1 gauge 2 gauge 3 gauge 4 0 -62 -20 -11 -1 250 14 -81 19 -67 500 35 -87 23 -107 750 52 -89 25 -144 1000 68 -85 24 -179 1250 81 -78 21 -210 gauge 5 gauge 6 *all gauge readings are measured in microstrain -1 -16 -7 -56 -17 -92 -27 -129 -37 -164 -49 -197 ...
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