MecMovies 4.0 : M2.5: Shear Strain in a Plate

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The figure shows a triangular plate P Q R S before and after deformation. The base of the triangle is Q R S and it is fixed to the ceiling. The length of the segment Q R is 900 millimeters and the length of the segment R S is 300 millimeters. The apex of the triangular plate is P. The height of the plate is 519.615 millimeters. The angle at Q is 30 degrees and the angle at S is 60 degrees. After deformation, the apex P, extends downwards by 1 millimeter and the height of the plate is 520.615 millimeters. Angle Q P R becomes alpha and angle R P S becomes beta.

Use this length and the original plate dimensions to calculate α and β on the sketch.

$\tan α = \frac{900 mm}{520.615 mm} ∴ α = 1.046365 rad$

$\tan β = \frac{300 mm}{520.615 mm} ∴ β = 0.522767 rad$