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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- The beam in the figure below is subjected to a load P= 3.9 kN at its end. Young's modulus is 210 GPa and the moment of inertia for the beam's cross-section is 5×106 mm². P A |×-| a B 1x₂. b If a 1.5 m and b= 1.3 m, determine: a) Reaction value at support A. Positive direction is considered upwards. Enter your answer in kN to 2 decimal places. Jvcarrow_forwardAT-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_forwardA rigid beam is supported by a pin at A and two metallic wires at Band C. Determine the force P that causes the point C to displace downward by 0.2 mm. Given: E (wire B) 70 Gpa, E (wire C) = 200 Gpa and both wires have a diameter D 5 mm. Consider a linear elastic behavior.arrow_forward
- 1. 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_forwardQuestion 2A rigid beam ABC is supported by pin at A and reinforced by a bar BD in order to sustain the uniform distributed load of 5 kN/m along the beam ABC in the direction shown in the Figure Q2.(a) Draw the free body diagram and determine the reaction forces at joint A(b) Determine the resultant force at joint A and its direction(c) Determine the internal loadings at section a--aarrow_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_forward
- 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 0.1 mm. Given: E (wire B) = 200 Gpa, E (wire C)70 Gpa and both wires have a diameterD =6 mm. Consider a linear elastic behavior.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 0.1 mm. Given: E (wire B) = 200 Gpa, E (wire C)70 Gpa and both wires have a diameterD =6 mm. Consider a linear elastic behavior.arrow_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_forwardThe beam shown in Figure Q.2 consists of a W610 x 140 structural steel wide-flange shape [E = 200 GPa; /= 1120 x 106 mm4]. If w=65 kN/m and P= 124 kN, determine: A AV, V 1.5 m B W 3.5 m P 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. a) Calculate the value of the deflection at point B due to uniformly distributed load win the form UB = numerator EI Note: E/will cancel out in further calculations. Enter the numerator in the answer box below in kNm³ to three decimal places. Assume the positive direction of deflection in the positive direction of v axis.arrow_forward
- 3. A 3-meter-long beam is used to support a heavy object. The object has a uniform distributed load of 6 kN/m on the entire beam. The Young’s modulus and moment of inertia of the beam are 200 GPa and 5×105 mm4, respectively. The beam is supported at three positions as shown below. (a) Label the element and node numbers (either on the figure or with a new simple sketch). (b) Determine the slopes at the three support positions of the beam.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_forwardThis course EHide blocks 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 B A 3 m 2 m 2 m Select one: OP= 573 N OP=130 Narrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning