For the given frame below: a) Form the structural stiffness matrix [K] using the general stiffness method and the load vector {Q}. Consider the degrees of freedom indicated below (Note: Eliminate the degree of freedom 3 by using the modified stiffness relation for the member 2-3) b) Calculate the structural displacements [D]. c) Draw the internal force diagrams.

From the given figure Solve the following: Let P = 30 Find: Vertical reaction at CHorizontal reaction at CAxial force at member AB

tate of Stress Caused by Combined Loadings Learning Goal: To use the superposition principle to find the state of stress on a beam under multiple loadings. The beam shown below is subjected to a horizontal force P via the rope wound around the pulley. The state of stress at point A is to be determined. 100 mm 15 mm 20 mm 200 mm 150 mm f 20 mm The dimensions are di - 2.15 m. d₂ = 0.5 m. -0.85 m d-285 mm and r= 150 mm The applied force has magnitude P=4.5 kN Part A-Support Reactions and Internal Loading C₁, C₂=₁ N=, V = ₁ M = Determine the support reactions C, and C, and the internal normal force, shear force, and moment on the cross-section containing point A. Express your answers, separated by commas, to three significant figures. ► View Available Hint(s) Submit Part B- Properties of the Cross-Section A= I= Q = Submit VAX IT VOC JA=.TA= What are the cross-sectional area, moment of inertia with respect to the neutral axis, and first moment of the area with respect to point A for the…

The horizontal beam is supported by a pin at A and the pin-connected link BC. It has a uniformly distributed loading w = 2.6 kN/m as shown in the figure. All the pins are in double shear and have a diameter of 20 mm. Determine the max shear stress in the pin at C. Input your answer as a value only in MPa to one decimal place without +/- sign. W 1.5 m 2 m B 1m

Problem 2: For the beam given below: (a) Calculate all support reactions. (b) Draw the shear diagram. Show all important values of shear. Show the sign convention within each region. (c) Draw the moment diagram. Show all important values of moment. Show the sign conventions within each region (concavity: smiley face, sad face, etc.) (d) Sketch the deflected shape. Show supports in your sketch. For your solution, let w = 2 kips/ft and L = 20 ft. A L 22 B L W C

The beam is subjected to a shear of V= 2 kN. What is the average shear stress developed in each nail? if the nails are spaced 75 mm apart on each side of the beam. Each nail has a diameter of 4 mm. The N.A is located on 137.5 mm form the bottom of cross section. The second moment of inertia about N.A is 63.5417*10^(-6) m^4. 75 mm 50 mm 75 mm 200 mm 25 mm 200 mm 25 mm 442.62 MPa

For the one-dimensional 4-member truss-element system shown, determine the nodaldisplacements and reaction forces using the direct stiffness method.

For the truss in figure below, the cross-sectional area of the truss members is A=500 mm² and Young's modulus E= 200 GPa. Let P = 93.7 kN. 1 m √3 m B Ø D 1 m √3 m F Determine: a) Strain energy for truss AC. Enter your answer in Jto 2 decimal places. b) Strain energy for truss AB. Enter your answer in J to 2 decimal places. c) Strain energy for truss BC. Enter your answer in J to 2 decimal places. d) Strain energy for truss BD. Enter your answer in J to 2 decimal places. e) Strain energy for truss DC. Enter your answer in J to 2 decimal places. f) Strain energy for truss DF. Enter your answer in J to 2 decimal places. g) Strain energy for truss FC. Enter your answer in J to 2 decimal places. h) Strain energy for truss CE. Enter your answer in Jto 2 decimal places. i) The displacement at point A. Enter your answer in mm to 2 decimal places. A

Balancing the sums of the forces in the primed coordinate system yields two equations: 0x = 0x cos² +σy sin² 0 + Txy (2 sin 0 cos 0) Tx'y' = (σy — σx) sin 0 cos 0 + Txy (cos² 0 – sin² 0) - Using the trigonometric identities Figure Oy - 6 of 6 Part D - Clockwise Rotation of a Stress Element with No Shear Stress The state of stress at a point in a member is shown on the rectangular stress element in (Figure 6) where the magnitudes of the stresses are |σx | = 29 ksi and |σy| = 26 ksi. Determine the state of stress on an element rotated such that the +x' axis is 20° below the -x axis of the original stress element. Express your answers, separated by commas, to three significant figures. ▸ View Available Hint(s) σ =σy, Tx'y' = Submit ΜΕ ΑΣΦ ↓↑ vec ? ksi, ksi, ksi

1) Given the structure below, answer the following questions Determine the local stiff stiffness matrix "k" and global stiffness matrix "K" of each element b. Given the following local deformations on element 5, determine the axial force in the member a. [-0.5 0.5 in 0.75 i. u5 = [1.25 C. Given the following global deformations on element 5, determine the member end forces in the global coordinate frame. 0.5 i. v5 = in 0.25 EA = constant E = 10,000 ksi A = 8 in.? 12 ft 3 12 ft- 12 ft