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
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Old questions for practice
Transcribed Image Text: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
Transcribed Image Text: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
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