3. A cantilever beam is fixed at the end x₁ = L and occupies the region 0 ≤ x₁ ≤ Land -H ≤ X₂ ≤ H. The beam is under uni

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3 A Cantilever Beam Is Fixed At The End X L And Occupies The Region 0 X Land H X H The Beam Is Under Uni 1 (61.62 KiB) Viewed 51 times

3. A cantilever beam is fixed at the end x₁ = L and occupies the region 0 ≤ x₁ ≤ Land -H ≤ X₂ ≤ H. The beam is under uniform loading from above, as shown in the figure below. H Ф= where q is a constant. H L The beam can be modelled using the Airy stress function 3 q 19x² 1 q 8H3 8H =x²x₂ + a) Demonstrate that is a valid Airy stress function 1 (x²x² − }{x{ ) + 1 q x² 20 H X1 (10 Marks) b) Calculate the components T₁1, T12, T21 and T22 of the two-dimensional stress tensor acting throughout the body (5 Marks) c) Calculate the resultant force acting on the surfaces i) x₁ = 0, ii) x₁ = L, and iii) x₂ = H (20 Marks)