1. Consider a rectangular plate with sides a and b of thickness t, as showen in...
1. Consider a rectangular plate with sides a and b of thickness t, as showen in Fig. P1, for the stress function 0 = px?y, where p is a constant, what will be the resultant normal bounday force Py allong the edge of the plate y = b? (a) 3pabt, (b) pat, (c) 2pabt, (d) 0, (e) none of above YA 3 4 6 4 25 6 51 MPa X a Fig. P1 Fig. P2
62 (1%) Consider a rectangular plate with sides a and b and thickness t, as shown in the figure at left below. a. Biharmonic equation. If we assume an Airy's stress function: Ф(x,y)-p(x'-y'), where p is a constant, will the biharmonic equation be satisfied? Ignore the body forces. b. Stresses. Determine the stresses (σ.σ..). c. Resultant forces & moment. Apply the Saint-Venant's Principle to find the resultant normal and shearing boundary forces as well as resuitant bending moment along all...
2. A rectangular plate with sides 6 m and 4 m of thickness l 12 mm (Fig. 1) is subjected to the stresses σο Ơy and Fry. An Airy stress function is proposed to be φ = 12x3y. (a) Is φ a possible valid Airy stress function? Prove your answer by a calculation. (b) If φ is valid, determine the values of stresses (Ox, σ, and τ, at point (xy,z) which satisfy the stress function. (c) Draw a sketch showing...
Consider a rectangular plate with sides a and b and thickness t, as shown in the figure at left below. a. Resultant forces & moment, Apply the Saint-Venant's Principle to find the resultant normal and shearing boundary forces as well as resultant bending moment along the left (x-0,0sysb) and right (x-a0sysb) edges of the plate. The respective sense of each resultant is defined in the figure at right below. b Plane stress vs plane strain. The solutions to the above...
Problem 1 (40%) A thin rectangular plate is 6 meters long and 0.8 meter wide. The plate is submerged (both sides) and held stationary in a stream of water (T = 10°C) that has a velocity of 0.5 meters/second. a) (5%) What is the boundary layer thickness at a distance x = 0.5m downstream of the leading edge? b) (5%) What is the shear stress on the plate at the same point? c) (10%) What is the friction drag on...
Problem 1 (40%) A thin rectangular plate is 6 meters long and 0.8 meter wide. The plate is submerged (both sides) and held stationary in a stream of water (7 = 10"C) that has a velocity of 0.5 meters/second. a) (5%) What is the boundary layer thickness at a distance x = 0.5m downstream of the leading edge? b) (5%) What is the shear stress on the plate at the same point? c) (10%) What is the friction drag on...
A triangular plate of narrow rectangular cross-section and uniform thickness is loaded uniformly along its top edge as shown in the following figure. Verify that the Airy stress function º = zip.cotoo | - tan a + xy + (x2 + y2)(a - tan-+ %) solves this plane problem. For the particular case of a = 10°, explicitly calculate the normal and shear stress distribution over a typical cross-section AB. We were unable to transcribe this image
5. Consider a rectangular plate with one of the sides of length a lying along the y axis and one of the sides of length b lying along the r axis. The interior of the plate is depleted of electric charge. Only the side lying along the line x = 0 is charged so that the electric potential on that side is held constant at Vo, for 0 < y <a, while the other sides of the plate are kept...
minimum of 3 significsnt figures please A thin rectangular plate is 6 meters long and 0.8 meter wide. The plate is submerged (both sides) and held stationary in a stream of water (T = 10°C) that has a velocity of 0.5 meters/second. a) (5%) What is the boundary layer thickness at a distance x = 0.5m downstream of the leading edge? b) (5%) What is the shear stress on the plate at the same point? c) (10%) What is the...
A rectangular plate in plane stress is subjected to normal stresses Ox =50 MPa, Oy = 25 MPa, and shear stress Txy = -12.5 MPa. The ratio of the magnitudes of the principal stresses (01/02) is approximately: (A) 3.5 (B) 2 (C) 2.8 (0)4