QUESTIONS: 1-Answer the below questions as "true(T)"or "false (F)^ast and mention with one sentence why and for 1(a) fill right words in the empty spaces. [Each is 3 points. Total 30 points) (a) What two properties of lightweight sandwich materials possess to be used in aircraft structures? Good __ __ and good (b) The equations of compatibility of strains derived such as (partial ^2epsilon _(xx))/(partial y^2)+(partial ^2xyy)/(partial x^2)=(partial ^2Yxy)/(partial xpartial y) be applied. Following a similar procedure with Ea and a and then with Err and Ea These are the only three strain compatibility equation. __ (c) The Green shearing strains have twice the value of the corresponding engineering shearing strains. __ (d) The strain -displacement equations are a necessary part displacement formulation. __ (e) Superposition principle states that, for linearly elastic direction bear a fixed ratio to the strains in the other two orthogonal directions. __ (f) The product of the ultimate load factor to develop ultimate loads whose corresponding stresses are required to be less than the limit stresses. __ (g) The equations of equilibrium, which are derived for the shape, do not apply to a material undergoing plastic deformations. __ (h) Equilibrium equations are always sufficient to structural body in a state of plane stress but are not always sufficient to determine all the displacements in that same structure. __

(a) True. Lightweight sandwich materials possess good stiffness and good strength-to-weight ratio properties, which make them suitable for use in aircraft structures.<br /><br />(b) False. The given equation is not a correct strain compatibility equation. The correct strain compatibility equations are $\frac{\partial^2 \epsilon_{xx}}{\partial y^2} + \frac{\partial^2 \epsilon_{yy}}{\partial x^2} = \frac{\partial^2 \gamma_{xy}}{\partial x \partial y}$, $\frac{\partial^2 \epsilon_{yy}}{\partial x^2} + \frac{\partial^2 \epsilon_{xx}}{\partial y^2} = \frac{\partial^2 \gamma_{xy}}{\partial y \partial x}$, and $\frac{\partial^2 \epsilon_{xx}}{\partial x \partial y} + \frac{\partial^2 \epsilon_{yy}}{\partial x \partial y} = \frac{\partial^2 \gamma_{xy}}{\partial x^2} + \frac{\partial^2 \gamma_{xy}}{\partial y^2}$.<br /><br />(c) True. The Green shearing strains have twice the value of the corresponding engineering shearing strains.<br /><br />(d) True. The strain-displacement equations are a necessary part of the displacement formulation.<br /><br />(e) False. The superposition principle states that the total displacement of a point in a structure is the sum of the displacements caused by each load acting on the structure. It does not state anything about the ratio of strains in orthogonal directions.<br /><br />(f) False. The product of the ultimate load factor and the ultimate stress is equal to the ultimate load, not the limit stress.<br /><br />(g) False. The equations of equilibrium, which are derived for the shape, do apply to a material undergoing plastic deformations.<br /><br />(h) True. Equilibrium equations are always sufficient to determine the stresses and reactions in a structural body in a state of plane stress, but they are not always sufficient to determine all the displacements in that same structure.