Concept explainers
A cable CD of a length H is attached to the third point of a simple beam AB of a length L (see figure). The moment of inertia of the beam is I, and the effective cross-sectional area of the cable is A. The cable is initially taut but without any initial tension,
(a)
Obtain a formula for the tensile force S in the
cable when the temperature drops uniformly by
(b)
Repeat part (a), assuming a wood beam and
steel cable.
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Chapter 10 Solutions
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- AT-shape beam is a load-bearing structure. The top of the T-shape cross section serves as a flange or compression member in resisting compressive stresses. In a building construction, the T-Shape beam which made of an elastic perfectly plastic material was used and its dimension is shown in Figure 3.2. For the beam indicated, determine the fully plastic moment and shape factor of the beam if the value of E = 200 GPa and o, = 250 MPa. (Use moment inertia for the cross section, I = 2600 x 10° m*) 60 mm 20 mm 60 mm 20 mm Figure 3.2 Beam cross-sectionarrow_forwardFigure Q2 shows the free body diagram of a 10 m long beam AD of uniform cross-section, simply supported at locations A and C. A uniformly distributed load of 10 kN/m is applied on the part AB of the beam together with a concentrated load of 20 kN at the end D. 10KN/m 20kN 4m 4m 2m X Fig.Q2: Structural Beam (a) Draw a free body diagram and find the reaction forces at the supports A and C. (b) Draw the shear force diagram (SFD) for the beam and show the values at A, B, C and D. (c) Draw the bending moment diagram (BMD) and show the values at A, B, C and D. 4. (d) From the SFD drawn in (b), find the distance from point A to the position between points A and B where there is no shear and determine the bending moment at that position. 5. (e) Write the mathematical expression for shear force V at section X-X between the points B and C which is at distance x measured from support A.arrow_forward1. Below on the left you can see a cantilever beam (of structural steel, E = 210 GPa), which is fixed to a wall at C and loaded by a force F=6kN at an angle a=45°. The magnitude and angle of the force as well as dimensions a=2.5m and d=4m. On the right side of the beam picture you can see its cross-section, which has been parametrized by height h=130mm, width b=160mm and thicknesses t₁ =9mm and tw = 5mm(flange and web, respectively). Six points E, F, G, H, I and K have also been marked in the cross-section - starting alphabetically from the top. a) Calculate the support reactions at C and draw normal force-, shear- and moment diagrams. b) Calculate the displacement of D in horizontal direction. In the following sections, feel free to take advantage of symmetry as much as you can! please collate your results for each section in a table. c) Calculate axial stresses for all points E...K in the cross-section at C. d) Calculate bending stresses for all points E...K in the cross-section at…arrow_forward
- Example The beam ABC is loaded via a 500 N.m couple and a 600 N force as shown. The beam is connected to the rest of the system by a pin joint at B and a roller support at C. Determine the magnitude of the reaction forces on the beam at the supports. 600 N 500N.m 400 300 500 Ans. RC=1700 N RBx=1597.5 N Dimensions in mm 20 RBy=1181.4 Narrow_forwardThe beam shown in Figure Q.2 consists of a W610 x 140 structural steel wide-flange shape [E= 200 GPa; /= 1120 x 106 mm²]. If w= 65 kN/m and P= 124 kN, determine: AY, V 1.5 m B W 3.5 m P C 2.5 m D Figure Q.2 Part A: The reactions at A, B, and D. Choose the reaction force at B as the redundant; therefore, the released beam is simply supported between A and D. Part B. The magnitude of the maximum bending stress in the beam. f) Find the maximum bending moment in the beam. Enter your answer in kNm to two decimal places. g) Calculate the magnitude of the maximum bending stress in the beam. Enter your answer in MPa to two decimal placesarrow_forwardFigure Q2 shows the free body diagram of a 10 m long beam AD of uniform cross-section, simply supported at locations A and C. A uniformly distributed load of 10 kN/m is applied on the part AB of the beam together with a concentrated load of 20 kN at the end D. 10kN/m 20kN AV 4m 4m 2m Fig.Q2: Structural Beam Draw a free body diagram and find the reaction forces at the supports A and C. (a) (b) Draw the shear force diagram (SFD) for the beam and show the values at А, В, С and D. (c) Draw the bending moment diagram (BMD) and show the values at A, B, C and D.arrow_forward
- 3. A spring wire with diameter of 6 mm in a circular arc shape was initially set on the horizontal plane. One end is fixed at point B and the other end A is free. The radius of the arc R-80 mm and the center angle of the arc 0=60°. The wire is made of a steel with modulus of elasticity: 200 GPa and Poisson's ratio: 0.29. Considering that F=25 N which is applied vertically downward at A, find the total deflection at A. Hint: I = π (64)/64 = 63.62 mmª. 0 R BX A Farrow_forwardEHide block This course A rigid beam is supported by a pin at A and two metallic wires at B and C. Determine the force P that causes the point C to displace downward by 0.6 mm. Given: E (wire B) = 70 Gpa, E (wire C) = 200 Gpa and both wires have a diameter D = 2 mm. Consider a linear elastic behavior. 2 m 1.5 m A 3 m 2 m 2 m Select one: O P = 573 N P = 537 N P = 597 N 420 N.arrow_forward2. In a laboratory test of a beam loaded by end couples, the fibers at layer AB in Figure below are found to increase 60 x 10-3 mm whereas those at CD decrease 100 x 10-3 mm in the 200-mm-gage length. Using E=70 GPa, determine the flexural stress in the top and bottom fibers. 200 mm 30 mm | 120 mm 30 mm Please solve according to the exporters of a typical solution. 4. Stress in Beams The beam in figure (1) shows two section EF, -0 * fo. •da = o (ab) and (cd) that separate by distance (dx). le Neuteal fece dA-o Figure (2) show the deflected shape of the beam. Since the (vtA) is the moment of the differential area (A4) about the neutral axis, the integral 6 = hk = ydÐ Fig.1 Fig 3 f ydA ) is the total moment of area Ay' -o yd0 ef ef pd0 hence : Strain = %3D only (y) can be equal zero, Le. the neutral axis must contain the centroid of the cross-sectional area . EF, -0 that leads to the shear stress formula (V, = |t, *dA) Neutral surface yde EF,-0 That leads to the formula of shear (t.dA=0)…arrow_forward
- 1- The two uniform linearly elastic rods shown below are welded together at B, and the resulting two-segment rod is attached to rigid supports at A and C. Rod (1) has a modulus E = 135 GPa, cross-sectional area A = 520 mm“, length LI coefficient of thermal expansion a = 7.5 x 10/°C. Rod (2) has a modulus E2 = 85 GPa, cross-sectional area A2 = 950 mm2, length L2 = 90 mm, and coefficient of thermal expansion a2 = 12.5 x 10/°C. Determine the axial stresses in the rods if the temperature of both is raised by 60 °C. b) Determine whether joint B moves to the right or left and by how much? %3D 120 mm, and %3D %3D Rigid support Rigid support В (1) (2)arrow_forwardA rectangular steel block is 4 inches long in the x-direction, 6 inches long in the y-direction, and 3 inches long in the z-direction. The block is subjected to a tri-axial loading of three uniform distributed forces as follows: 55 kips compression in the x direction, 62 kips tension in the y direction, and 24 kips tension in the z direction. If the Poisson’s ration is 0.26 and E = 29 x 106 psi, determine the single uniform distributed load in the y direction that would produce the same deformation in the x direction as the original loading.arrow_forwardA 5.15-N beam of uniform density is 1.70 m long. The beam is supported at an angle of 35.0° by a cable attached to one end. There is a pin through the other end of the beam (see figure below). Use the values given in the figure to find the tension in the cable. (Assume L = 1.70 m and d = 0.390 m.) Note: The answer is 2.51 N per the text. I would just like someone to help/show me how to get there. Thank you.arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning