Use the graphical method to construct the shear-force diagram and identify the magnitude of the largest shear force (consider both positive and negative). The ground reactions are provided. P = 58 kN w=14 kN/m L=3m A₂ = 45.67 kN Dy=54.33 kN L B L W L
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- A sign of weight W is supported at its base by four bolls anchored in a concrete footing. Wind pressure P acts normal to the surface of the sign; the resultant of the uniform wind pressure is force fat the center of pressure (C.P). The wind force is assumed to create equal shear forces F/4 in the y direction at each boll (see figure parts a and c). The overturning effect of the wind force also causes an uplift force R at bolts A and C and a downward force (— R) al bolts B and D (see figure part b). The resulting effects of the wind and the associated ultimate stresses for each stress condition are normal stress in each boll (h — 60 ksi); shear through the base plate (th = 17 ksi); horizontal shear and bearing on each bolt ( tfur = 25 ksi and cr^ = 75 ksi): and bearing on the bottom washer at B (or D) (abor = 50 ksi).Solve the preceding problem if the diameter is 480 mm, the pressure is 20 MPa, the yield stress in tension is 975 MPa, the yield stress in shear is 460 MPa, the factor of safety is 2,75, the modulus of elasticity is 210 GPa, Poissorfs ratio is 0.28, and the normal strain must not exceed 1190 x 10" . For part (b), assume that the tank thickness is 8 mm and the measured normal strain is 990 x 10~ .The strains for an element of material in plane strain (see figure) are as follows: x = 480 ×10-6. y = 140 × l0-6, and xy = —350 x 10”. Determine the principals strains and maximum shear strains, and show these strains on sketches of properly oriented elements.
- Use the graphical method to construct the shear-force diagram and identify the magnitude of the largest shear force (consider both positive and negative). The ground reactions at the wall of the cantilever are provided. L₁= 14.75 ft L₂ = 7.75 ft Vc = 91.50 kips Mc = 706.4375 kip-ft 20 kips 6 kips/ft L₁ 103.50 kips 68.50 kips 91.50 kips O 79.50 kips O 114.50 kips 70 kips BO 12 kips/ft L2 O Vc McUse the graphical method to construct the shear-force diagram and identify the magnitude of the largest shear force (consider both positive and negative). The ground reactions at the wall of the cantilever are provided. L₁= 14.00 ft L2= 7.75 ft Vc = 87.00 kips Mc = 621.875 kip-ft 20 kips 6 kips/ft L₁ 64.00 kips 99.00 kips 110.00 kips 87.00 kips O 75.00 kips 70 kips B 12 kips/ft L2 Vc McAnswer p1 and Part 2: Determine the shear force acting at each of the following locations:(a) x = 11.0- ft (i.e., just to the left of point B)(b) x = 11.0+ ft (i.e., just to the right of point B)(c) x = 28.5 ftNote that x = 0 at support A. When entering your answers, use the shear-force sign convention detailed in Section 7.2.Answers: a) V = ____ kips b) V = ____ kips c) V = ____ kips Part 3: Determine the bending moment acting at each of the following locations:(a) x = 11.0 ft (i.e., at point B)(b) x = 28.5 ftNote that x = 0 at support A. When entering your answers, use the bending-moment sign convention detailed in Section 7.2. Answers: a) M = ____ kips-ft b) M = ____ kips-ft Part 4: Use your shear-force and bending-moment diagrams to determine the maximum bending moment, Mmax, and its location, xmax. Use the bending-moment sign convention detailed in Section 7.2.Answers: Mmax = ____ kips-ft xmax = ____ ft
- Figure below shows the bar with three equal elements. Use the finite element method and calculate: 2.1 the global stiffness matrix 2.2 the displacement on node 2, 3, 4 2.3 the Strain in each element 2.4 the stresses in each element using Hook's law and compare with theoretical stresses (o=F/A) (1) (2) (3) -50 N 10 mm 10 mm 10 mm A1=50 mm? A2=20 mm? A:=10 mm? E=200 GPaThe state of strain at the point has components of €g = 180(10 6). €y = -100(10 6) Submit Previous Answers and All attempts used; correct answer displayed Yay = -200(10-6). Part B Figure < 1 of 1 Specify the orientation of the element. Enter your answers numerically separated by a comma. Hν ΑΣφ It vec (6,)1, (0,)2 = Submit Request Answer Part CA very thick structure is subjected to certain traction boundary conditions on its surface. The cross-section and the applied load do not vary with the z-coordinate. The following stress function is proposed for this problem: -y p(x,y) = Sin (x) (A x²e + B e") (i) use the biharmonic equation to find restrictions, if any, on values of A and B (ii) calculate all stress components (iii) calculate all strain components in terms of A, B, and C as well as the Young modulus and Poisson's ratio E and y, respectively. (iv) check that the equilibrium equations are satisfied (v) determine the traction boundary conditions at x =± a and y=+b
- Question 3 Show that the following function o may be used as an Airy stress function $ = Ax? + Ba²y+ Cry Evaluate A, B and C for the rectangle shown in Figure Q3: (1) there are no external loads for any kind applied along KN; (2) along KL there is a uniform normal load p; (3) and along MN there is no normal load; (4) along KL, LM and MN there are shear stresses (but none along KN). Make a neat sketch of the stresses along the boundary KLMN. y N M Thickness=1 b p per unit length aA square post which is made up of two parts is glued atplane ABCD with the angle α = 30° with the vertical.Allowable compressive stress @ glue = 5.2 MPaAllowable shearing stress = 3.5 MPaP = 36 kN. 1. What is the minimum post dimension, w (mm), withoutexceeding the allowable shearing stress at the glue? 2. What is the minimum post dimension, w (mm), withoutexceeding the allowable compressive stress at the glue? 3. What angle, α, will give the maximum shearing stress? with brief explanation each partProblem 3. As shown in the Figure below, please determine the internal force in the middle of AB, with the given data: OA-15 cm, OB-30 cm, OC-60 cm. W=40N, Wo=60N. F=1214N, B-10°, FM=1236 N, and 8=15%. Fj B FM W Wo 4