Consider the beam shown in (Figure 1). EI is constant. Part A Determine the expression for the elastic curve using the coordinate x1 for 0 < 1 ? Determine the expression for the elastic curve using the coordinate 2 for 0 < x2
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- Beam AB is made of three plates glued together and is subjected, in its plane of symmetry, to the loading shown. Knowing that the shear force is V=3.5kN and I=8.63*106 m“, determine the following: -100 mm 20 mm -Joint a 80 mm C 20 mm - 68.3 mm 20 mm 60 mm The value of Q is equal to in m3: The value of t for the Joint a is equal to in mm: The average shearing stress at Joint a is equal to in kPa:Three steel rods, each having a cross-sectional area of 500 mm2, are assembled in a symmetrical manner, ass shown in the igure. Assume that steek behaves as a linear elastic material with E= 200 GPa. Determine the deflection of joint A due to a downward force of P= 2MNQ2) A rectangular block of an elastic material is subjected to normal and shear loads. The deformed (distorted) shape of the block is shown by the dashed lines. Determine the shear strain Yxy at corners D and C. Also find the average normal strain that occurs along the diagonal's AC and DB. 4 mm 2 mm 4 mm 2 mm; 300 mm }2 mm D 500 mm- A 3 mm
- 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 rigid bar DEFis welded at point D to the uniform steel beam AB. For the loading shown in figure 5, determine (a) the equation of the elastic curve of the beam, (b) the deflection at the mid-point C of the beam by double integration method Use E=29x106 psi and I= 2000 in4 X=4740A beam having a tee-shaped cross section is subjected to equal (12 kN.m) bending moments, as shown in Figure. The centroid location (y-) is (110 mm) measured upward from bottom edge of stem, the moment of inertia about the z axis, is (Iz=18646000 mm4).Determine the bending stress at point H. State * .whether the normal stress at (H) is tension (T) or compression (C) 100 mm 25 mm 12 kN-m 175 mm 150 mm 12 kN-m 25 mm 70.8 MPа (С) О 50.8 MPa (T) O 25.7 MPа (С) С 70.8 MPa (T) O
- Problem 2: Deflection Calculation Determine the maximum deflection of the beam loaded as shown in the figure below using Conjugate beam method. Also draw the deflected shape of the beam. El is uniform throughout the beam. A is a roller support, and C is fixed support. There is an internal hinge/pin at B. The value of P must be calculated using your student ID and the following equation P(kN) = [(V218503042) – C]/4 C=14700 So, P= 20 kN 4P 2P 3 m 6 m 2 m 2 m Find 1. BMD of real beam 2. Conjugate beam+ loading 3. Reactions of conjugate beam 4. Location of maximum deflection 5. Maximum deflection & its direction 6. Deflected shape of the beamIn the figure, one end of a uniform beam of weight 270 N is hinged to a wall; the other end is supported by a v 27° with both wall and beam. Find (a) the tension in the wire and the (b) horizontal and (c) vertical componen on the beam. Hinge (a) Number i Units (b) Number i Units (c) Number i Units >. Consider the following wooden T-beam on its side. It consists of two wooden parts glued together. Assume the glue nas a perfect bond. The densities of the two wooden parts differ and are indicated on the figure. The figure is not to scale. y Pq = 900 kg/m %3D 17 mm P2 = 740 kg/m? 20 mm 150 тm Determine the a-coordinate I of the center of mass of the T-beam. 90 mm
- Problem 5.2 The rigid bar shown is pinned at A and supported by two steel rods, each having a diameter of 1 in. The system is subjected to a load P = 2 kip (note: kip refers to kilopound). If the bar is assumed to be rigid (meaning that it does not bend due to the loading) and is initially vertical, determine: A) The force in each bar when P is applied B) The displacement of end B when P is applied a = 1 ft, b= 1 ft D -b 2b B E AG Check your work: FEF = 1.26 kips a a a a PA rigid bar AB if of a length B = 66 in. is. hinged to a support at A and supported by two vertical wires attached at points C and D (see figure). Both wires have the same cross-sectional area (A= 0.0272 in2) and are made of the same material (modulus E = 30 X 106 psi). The wire at C has a length h = 18 in. and the wire at D has a length twice that amount. The horizontal distances are c = 20 in. and d = 50 in. (a) Determine the tensile stresses ac find aD in the wires due to the load P = 340 lb acting at end B of the bar. (b) Find the downward displacement 8B at end B of the bar.3. A force P is applied to the rigid lever arm ABC as shown. The arm rotates counterclockwise about pin A through an angle of 0.06°. Calculate the normal strain developed in wire BD. Answer: EnD = 0.0014 mm/ mm 300 mm B 400 mm