Beam Deflection
Laboratory Three: Parallam Beam Deflection
Lab Group - 1st Mondays, Late: Jesse Bertrand, Ryan Carmichael, Anne Krikorian, Noah Marks, Ann Murray Report by Ryan Carmichael and Anne Krikorian
E6 Laboratory Report – Submitted 12 May 2008 Department of Engineering, Swarthmore College
Abstract:
In this laboratory, we determined six different values for the Elastic Flexural Modulus of a 4-by10 (100” x 3.50” x 9.46”) Parallam wood-composite test beam. To accomplish this, we loaded the beam at 1/3 span with 1200 psi in five load increments in both the upright (9.46 inch side vertical) and flat (9.46 inch side horizontal) orientations. We then used three different leastsquare methods (utilizing Matlab and Kaleidagraph) on the data for each orientation to fit the data, resulting in the following:
E: Upright Orientation Units Method One Method Two Method Three
E: Flat Orientation 10 ksi 103 ksi
3
0.981 ± 0.100 1.253 ± 0.198 1.065 ± 0.247
1.880 ± 0.046 2.080 ± 0.083 1.881 ± 0.106
1
Purpose:
The purpose of this lab is to determine the flexural elastic modulus of a Parallam woodcomposite beam by examining its behavior when simply supported and under flexural stress, and to analyze deflection data using different least-squares methods to fit theoretical deflection curves.
Theory:
In theory, a beam’s deflection can be mapped by the governing equation of beam flexure: EI d2y/dx2 = M(x), where E is the elastic modulus, I is the second moment of inertia about the neutral axis of the beam (the value of which changes significantly according to orientation), y is deflection, and M(x) is bending moment in the beam. This equation requires that several assumptions be made about the beam: 1) Geometric Assumption: the beam must be a straight, prismatic member with at least one axis of symmetry. 2) Material assumption: the beam must be linear, elastic, isotropic, and homogeneous, and the modulus of elasticity in tension must equal the modulus of elasticity in
Lab Group - 1st Mondays, Late: Jesse Bertrand, Ryan Carmichael, Anne Krikorian, Noah Marks, Ann Murray Report by Ryan Carmichael and Anne Krikorian
E6 Laboratory Report – Submitted 12 May 2008 Department of Engineering, Swarthmore College
Abstract:
In this laboratory, we determined six different values for the Elastic Flexural Modulus of a 4-by10 (100” x 3.50” x 9.46”) Parallam wood-composite test beam. To accomplish this, we loaded the beam at 1/3 span with 1200 psi in five load increments in both the upright (9.46 inch side vertical) and flat (9.46 inch side horizontal) orientations. We then used three different leastsquare methods (utilizing Matlab and Kaleidagraph) on the data for each orientation to fit the data, resulting in the following:
E: Upright Orientation Units Method One Method Two Method Three
E: Flat Orientation 10 ksi 103 ksi
3
0.981 ± 0.100 1.253 ± 0.198 1.065 ± 0.247
1.880 ± 0.046 2.080 ± 0.083 1.881 ± 0.106
1
Purpose:
The purpose of this lab is to determine the flexural elastic modulus of a Parallam woodcomposite beam by examining its behavior when simply supported and under flexural stress, and to analyze deflection data using different least-squares methods to fit theoretical deflection curves.
Theory:
In theory, a beam’s deflection can be mapped by the governing equation of beam flexure: EI d2y/dx2 = M(x), where E is the elastic modulus, I is the second moment of inertia about the neutral axis of the beam (the value of which changes significantly according to orientation), y is deflection, and M(x) is bending moment in the beam. This equation requires that several assumptions be made about the beam: 1) Geometric Assumption: the beam must be a straight, prismatic member with at least one axis of symmetry. 2) Material assumption: the beam must be linear, elastic, isotropic, and homogeneous, and the modulus of elasticity in tension must equal the modulus of elasticity in