Lab #6 Report due TODAY Individual Data Processing and Individual Write Up Lab #6 Report is due TODAY by midnight Answer Multiple Choice Questions ONLINE TODAY Answer Student Survey ONLINE TODAY Submit the Lab Report #6 in the drawer labeled “Strength of Materials I Lab” beneath M. E. Mail Folders

Lab #6 Report due Today Cover Page + Abstract Data Sheet Spreadsheet including Material Properties Plot #1: Elastic Modulus Plot #2: Poisson’s Ratio Plot #3: Axial Strains Plot #4: Transverse Strains Plot #5: Shear Strains Comments and Conclusions

Lab #7 Due Dates Lab #7 Multiple Choice Questions by midnight Saturday (05/03/14) Lab #7 Answers will be posted by 11am on Sunday (05/04/14) Final Quiz next week will have 20 questions selected from Lab #1  #7 Lab Report #7 and Student Survey will be due next on the class day

Deflection of a Cantilevered Beam Measure deflection of a cantilevered beam due to a Point Load at different distances from the fixed support Determine the elastic modulus of the beam material, and compare it with values from the handbook and Lab #5 Compare the measured deflections with values calculated from theory

Key Relation in Bending At any location x along the longitudinal axis of the beam:  (x) is the curvature of the beam  (x) is the radius of curvature of the beam M(x) is the internal bending moment E is the elastic modulus of the beam material I is the moment of inertia of the beam cross-section

Curvature of a curve y(x) If deflections y(x) are small, then the slopes |y’(x)| << 1.

Cantilevered Beam under its own weight (=w per unit length)

Deflection of a Cantilevered Beam under its own weight

Cantilevered Beam with a Point Load P at a distance q

Deflection of a Cantilevered Beam with point load P

Deflection of a cantilevered beam with a point load P

Summary of Deflection Formulas Only uniformly distributed load w Both w and point load P Only point load P

Deflection at x = q Only uniformly distributed load w Both w and point load P Only point load P

Data Sheet

Processing Data P (lb) = - P(mm) *10 *0.2248

Plot #1: y versus P

Fitting Straight Lines to y versus P =slope(y-values, x-values) =intercept(y-values, x-values) =rsq(y-values, x-values)

Plot #2: q 3 versus slope q 3 = (3EI) * slope

Determining Elastic Modulus E Use LINEST function =bh 3 /12=Gradient/3I Mass Density (look it up) =  * b * h q 3 = (3EI) * slope

Materials Properties Table

Naming Parameters Emod w

Visual Basic Module select click If you don’t see the “Developer” tab in the menubar, then select File  Options  Customize Ribbons

New VBA Module On Menubar: Insert  Module

Theoretical Deflections Importing named parameter values Must name worksheet as “Data” Defining VBA function Defw

Using the VBA function Defw(q, P) = defw (q, P) Deflection due to Beam weight (remember we zeroed both indicators)

Implementing Singularity Function n

VBA Function DefwP(q, P) Underscore is Line Continuation Character Singularity function

Theoretical Deflections = DefwP(q, P) – y 0

Comparing Measured & Theoretical Deflections =Theoretical - Measured

Plot #3: Differences

Spreadsheet (Two Pages)

Lab #6 Report due TODAY Individual Data Processing and Individual Write Up Lab #6 Report is due TODAY by midnight Answer Multiple Choice Questions ONLINE TODAY Answer Student Survey ONLINE TODAY Submit the Lab Report #6 in the drawer labeled “Strength of Materials I Lab” beneath M. E. Mail Folders

Lab #6 Report due Today Cover Page + Abstract Data Sheet Spreadsheet including Material Properties Plot #1: Elastic Modulus Plot #2: Poisson’s Ratio Plot #3: Axial Strains Plot #4: Transverse Strains Plot #5: Shear Strains Comments and Conclusions

Lab #7 Report due Next Week Cover Page + Abstract Data Sheet Spreadsheet (2 pages) Plot #1: Deflections versus P Plot #2: q 3 versus slopes Plot #3: Differences versus P Material Properties Table Comments and Conclusions

Lab #7 Due Dates Lab #7 Multiple Choice Questions by midnight Saturday (05/03/14) Lab #7 Answers will be posted by 11am on Sunday (05/04/14) Final Quiz next week will have 20 questions selected from Lab #1  #7 Lab Report #7 and Student Survey will be due next on the class day