6. For the stress function ф 2x4 3x2y2 - y4. find the following 1.The stress components...
5. Find where the function f(x) = 2x4 - 4x?- 5 is increasing and decreasing, and find the relative extrema. 6 6. Find the absolute extrema of the function f(x) + over the interval (1,6]. I
(i) Determine whether ф defines a hornom Orphism. (ii) Find ker ф :-0€ G | ф(G) e} and in ф ф(G). (ii) Draw Cayley diagrams of the domain and codomain, and arrange them so one can "visually see" the cosets of ker ф in G. Draw dotted lines around these cosets. (iv) Is the quotient G/kero a group? If so, what is it isomorphic to? Z, defined by ф(n) n (mod 3). Here is an example of Step (iii) for...
3. (a) For the following stress function to be a valid Airy stress function, what should be the relationship between B and D? $ = Bx?y* – Dy6 (8 marks) (6) A thin plate of thickness t fixed along one edge is loaded by a shear force P on the opposite edge as shown in Figure Q3. The assumed Airy function is: 0 = A(a - x)(2 – 3bºy) (i) Show that this is a valid Airy stress function. (6...
Question 19 Find the partial fraction decomposition of the rational function. x5 – 2x4 + x3 + 3x + 6 x3 – 2x2 + x - 2
For an isotropic material, (a) Calculate the components of the strain tensor and the stress tensor for the following set of given displacements for an isotropic material: Uj = - X1 , U2 = -V – X2, U3 = -V – X3 , E E E where o is a constant. (b) Check the equilibrium equations to see if they are satisfied for zero body forces. (c) Show the edge tractions on a diagram of the body0 S XL SL,0...
The cantilever beam shown in the figure is subjected to a distributed shear stress oon the upper face. The following Airy stress function is proposed for this problem Determine the constants c and find the stress distribution in the beam. Use resultant force boundary conditions at the ends. (Answer: C1-ToC/12/, С2-Tp/201.c3- -to/24cl,...) TOXI Suggested process is as follows: (a) Write out the boundary conditions using St. Venant's principle for the semi-inverse (b) Write the stress field corresponding to the Airy...
Question 1: The stress-strain diagram for a material is shown in figure. Find the following properties of the material. (a) Yield load if the diameter of specimen at yielding is 13mm. (b) Modulus of resilience (c) Elastic Strain Stress (MPa) CS Scanned with CamScanner 0.001 0.003 Strain
Figure 4 shows an element experiencing several stress components. Determine the following: 1. The stress components Oxvxr. Oysy, and T xuy, acting on the element oriented at a counter clockwise angle = 40° from the horizontal x axis 2. The principal stresses, the maximum shear stress and their associated angles For each of the stress state calculated in parts 1 and 2, show all results on sketches of properly oriented elements. Note: Solutions MUST be obtained using Mohr's circle ONLY....
The state of strain at the point on the bracket has components ϵ
x= -130(10-6), ϵ y= 280(10-6), and
γ x y= 75(10-6).
Determine the principal stress, σ 1 in MPa at the point.
Determine the principal stress, σ 2 in MPa at the point.
Assume E = 200 GPa, and ν= 0.3.
1 х
Page l2 Q110 A uniform edge load of p, 6000 Ib/in and P, 4500 lb/in is applied to the specimen. If the specimen is originally rectangle and has dimensions ofa 5 in.,b-3 in. and a thickness off 0.25 in.. After the load is applied, determine pr 1) 2) 3) 4) the stress components in the specimen: ση σ' rry. the strain components: ε, ε" rry,e- the change in volume of the specimen. the reading of a strain gauge placed at...