Show that the stress function satisfies the boundary conditions for the simply supported beam subjected to a uniform pre

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Show that the stress function
satisfies the boundary conditions for the simply supported beam
subjected to a uniform pressure p shown below. Check the boundary
conditions in the week (Saint-Venant) sense on the short left and
right hand sides(for both normal and shear stress). Since normal
stress, sigma_x is not zero at the ends, but only its resultant,
check also that the moment is zero at each end.
(I checked other people's solution to this problem. However, the
scan quality was not clear, and it was difficult to
understand.)

Show That The Stress Function Satisfies The Boundary Conditions For The Simply Supported Beam Subjected To A Uniform Pre 1 (58.08 KiB) Viewed 11 times

Show That The Stress Function Satisfies The Boundary Conditions For The Simply Supported Beam Subjected To A Uniform Pre 2 (18.7 KiB) Viewed 11 times

E ? ?r X 7. Show that the stress function р [-20y?(– xº) – 4y– 15hºx’y+2h?y? – 5hºx?] 20h satisfies the boundary conditions for the simply supported beam subjected to a uniform pressure p shown below. Check the boundary conditions in the weak (Saint- Venant) sense on the shorter left and right hand sides (for both normal and shear stress). Since the normal stress og is not zero at the ends, but only its resultant, check also that the moment is zero at each end. XX 1 р Lp X Lp Is h L L
Note that the elementary beam theory predicts an approximate flexural stress but an exact shear stress: бр h2 y? h" h 4 6.2. y([° - x²) 0 - 0, -€ -) = X XX xy