Section B 1. Calculate the internal normal force, shear force, torque and bending moment at A. (5p) 1 m 0.75 m 0.5 n 450 N 0.75 m 750 N 1300 N 2. A beam is supported and loaded as presented in picture below. The cross-section of the beam is shown on the right (all dimensions are millimeters). a) Draw the shear and moment diagrams for the beam. (4p) b) Calculate the greatest normal stress acting in the beam. Specify also the location of this greatest normal stress. (4p) c) Calculate the greatest shear stress acting in the beam. Specify also the location of this greatest shear stress. (2p) 20 kN 8 kN/m 20 kN 100 I 100 220 14 14 4 m 6 m B 4 m 4. A piece of pipe is subjected to a force of F = 800 N as shown in picture. a) Determine the force in vector form. (3p) A B 45° 4 m b) Determine the moment of this force subject to point A (in vector form). (3p) 4 m F 6 m C 6 m 5. There is an eye bar link at point (0,0,0). Connected to this eye bar link there are three ropes: rope 1 that goes to point (3,5,2), rope 2 that goes to point (1,2,5) and rope 3 that goes to point (4,-2,3). The tension forces in ropes are 500, 800 and 350 newtons, respectively. a) Calculate the rope forces in vector form. (3p) b) Calculate the resultant force that affects the eye bar link (in vector form) and the magnitude of it. (4p) 6. A 250-kg cylinder is to be supported by the cord which wraps over the pipe. The coefficient of friction between the cord and the pipe is 0.2. a) What is the smallest vertical force F needed to support the load, if the cord passes over the pipe twice (as pictured)? (3p) b) What is the smallest vertical force F needed to hoist the cylinder upwards, if the cord passes over the pipe three times (i.e. one full rotation more than in the picture)? (3p) 7. The stress state in one point of our structure is as pictured on the stress element on the right. 60 MPa a) Calculate the principal stresses (only stress values; direction angles are not needed). (3p) b) The yield strength of our material is 80 MPa. Does yielding occur, if we use Von Mises yield criterion? (3p) 30 MPa 45 MPa

Section B 1. Calculate the internal normal force, shear force, torque and bending moment at A. (5p) 1 m 0.75 m 0.5 n 450 N 0.75 m 750 N 1300 N 2. A beam is supported and loaded as presented in picture below. The cross-section of the beam is shown on the right (all dimensions are millimeters). a) Draw the shear and moment diagrams for the beam. (4p) b) Calculate the greatest normal stress acting in the beam. Specify also the location of this greatest normal stress. (4p) c) Calculate the greatest shear stress acting in the beam. Specify also the location of this greatest shear stress. (2p) 20 kN 8 kN/m 20 kN 100 I 100 220 14 14 4 m 6 m B 4 m 4. A piece of pipe is subjected to a force of F = 800 N as shown in picture. a) Determine the force in vector form. (3p) A B 45° 4 m b) Determine the moment of this force subject to point A (in vector form). (3p) 4 m F 6 m C 6 m 5. There is an eye bar link at point (0,0,0). Connected to this eye bar link there are three ropes: rope 1 that goes to point (3,5,2), rope 2 that goes to point (1,2,5) and rope 3 that goes to point (4,-2,3). The tension forces in ropes are 500, 800 and 350 newtons, respectively. a) Calculate the rope forces in vector form. (3p) b) Calculate the resultant force that affects the eye bar link (in vector form) and the magnitude of it. (4p) 6. A 250-kg cylinder is to be supported by the cord which wraps over the pipe. The coefficient of friction between the cord and the pipe is 0.2. a) What is the smallest vertical force F needed to support the load, if the cord passes over the pipe twice (as pictured)? (3p) b) What is the smallest vertical force F needed to hoist the cylinder upwards, if the cord passes over the pipe three times (i.e. one full rotation more than in the picture)? (3p) 7. The stress state in one point of our structure is as pictured on the stress element on the right. 60 MPa a) Calculate the principal stresses (only stress values; direction angles are not needed). (3p) b) The yield strength of our material is 80 MPa. Does yielding occur, if we use Von Mises yield criterion? (3p) 30 MPa 45 MPa

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter10: Statically Indeterminate Beams

Section: Chapter Questions

Problem 10.4.32P: Two identical, simply supported beams AB and CD are placed so that they cross each other at their...

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