Homework Answers
calculation of bending tensile stress is done by using equation
of pure bending.For calculation of shear stresses due to torsion
equation of pure torsion is used.
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Question 4: (25 marks) A hollow rectangular cross-section (Figure 4) is subject to the combined effect...
Question 4: (25 marks) A hollow rectangular cross-section (Figure 4) is subject to the combined effect...
Question 4: (25 marks) A hollow rectangular cross-section (Figure 4) is subject to the combined effect of A torque T (causing downward shear stress in the right wall and upward shear stress in the left wall): T= 60 kNm. A negative bending moment M about the horizontal centroidal x-axis (causing tension in the top part of the cross-section): M= 100 kNm. Given t 15 mm: i. Determine the maximum tensile stress at A on the x-axis on the left wall...
A rectangular cross section at a location along a beam in bending is
(a). A rectangular cross section at a location along a beam in bending is acted upon by a bending moment and a shear force. The cross section is \(120 \mathrm{~mm}\) wide, \(300 \mathrm{~mm}\) deep and is orientated such that it is in bending about its major axis of bending. The magnitudes of the bending moment and shear force are \(315 \mathrm{kNm}\) and \(240 \mathrm{kN}\) respectively. Determine the maximum bending and shear stresses on the cross section. Plot the bending and...
The hollow steel construction auger in Figure 4 has an outer diameter d2 = 140 mm...
The hollow steel construction auger in Figure 4 has an outer diameter d2 = 140 mm and thickness of t = 8 mm. The steel has a shear modulus of elasticity E = 200 GPa and v = 0.3. For an applied torque of 35 kN m, determine the following quantities: a) Shear stress at the mid-center of the thickness t of the shaft. [2] b) Shear stress on the outer surface. [1] c) Shear stress in the inner surface,...
3. A beam with a hollow circular cross section of outer diameter D and inner diameter...
3. A beam with a hollow circular cross section of outer diameter D and inner diameter d. The length Lis fixed at a wall. Consider the following loading conditions, all applied to the beam at the midpoint of length L. For each loading scheme state determine the magnitude of that stress in terms of the variables given in the problem). (5 points) i. ii. iii. iv. V. Normal stress due to axial load F Shear stress due to torque T...
4. (30%) For a beam with a T-section as shown, the cross-sectional dimensions of 12 mm....
4. (30%) For a beam with a T-section as shown, the cross-sectional dimensions of 12 mm. The centroid is 75 mm, h = 90 mm, t the beam are b 60 mm, h, at C and c 30 mm. At a certain section of the beam, the bending moment is M 5.4 kN m and the vertical shear force is V= 30 kN. (a) Show that the moment of inertia of the cross-section about the z axis (the neutral axis)...
Figure Q3 shows a simply supported beam carrying a point load. The beam hasa rectangular hollow...
Figure Q3 shows a simply supported beam carrying a point load. The beam hasa rectangular hollow steel section as shown in Figure Q3. a. Calculate the second moment of area of the section about the horizontal (10 marks) centroidal axis. Calculate the maximum allowable value of the point load Wif the elastic bending (15 marks) b. stress in the beam is to be limited to 250 MPa. c. Calculate the maximum shear stress at q-q in the beam when the...
A beam whose cross-section is shown in the figure is subjected to a bending moment M...
A beam whose cross-section is shown in the figure is subjected to a bending moment M inclined at 0 = 70° from the z axis. a) Locate the orientation of the neutral axis B and draw this axis on the figure b) Calculate the maximum flexural tensile stress Omax,T and the maximum flexural compressive stress Omax.c in the beam and indicate at which points in the section these occur. M= 2 Nm D e Z 20 mm A B 60...
Figure 1 shows the cross section of a lipped channel. The cross section carries a shear force of ...
Figure 1 shows the cross section of a lipped channel. The cross section carries a shear force of 250 kN acting at 45° below the major principal axis (as shown) and through the shear centre. Determine the (Ans: 134.1 MPa) maximum shear stress. (Use line of mid-thickness properties) た45 S.c 4250 N たA 100 Figure 1
Figure 1 shows the cross section of a lipped channel. The cross section carries a shear force of 250 kN acting at 45° below...
Figure 1 shows the cross section of a lipped channel. The cross section carries a shear...
Figure 1 shows the cross section of a lipped channel. The cross section carries a shear force of 250 kN acting at 45° below the major principal axis (as shown) and through the shear centre. Determine the Ans: 134.1 MPa) maximum shear stress. (Use line of mid-thickness properties) t 45 34 S.C 250 N たA 100 Figure
A beam of rectangular cross section 200 mm deep and 100 mm wide. If the beam...
A beam of rectangular cross section 200 mm deep and 100 mm wide. If the beam is 3m long, simply supported at either end and carries point loads as shown in FIGURE 2 (on page 4). 2. SAN 1OAN R, FR 100mm FIG.2 (a) Calculate the maximum bending moment (b) Calculate the maximum stress in the beam (c) At the point of maximum stress sketch a graph of the stress distribution through the thickness of the beam, indicating which are...
Question 4: (25 marks) A hollow rectangular cross-section (Figure 4) is subject to the combined effect of A torque T (causing downward shear stress in the right wall and upward shear stress in the left wall): T= 60 kNm. A negative bending moment M about the horizontal centroidal x-axis (causing tension in the top part of the cross-section): M= 100 kNm. Given t 15 mm: i. Determine the maximum tensile stress at A on the x-axis on the left wall...
The hollow steel construction auger in Figure 4 has an outer diameter d2 = 140 mm and thickness of t = 8 mm. The steel has a shear modulus of elasticity E = 200 GPa and v = 0.3. For an applied torque of 35 kN m, determine the following quantities: a) Shear stress at the mid-center of the thickness t of the shaft. [2] b) Shear stress on the outer surface. [1] c) Shear stress in the inner surface,...
3. A beam with a hollow circular cross section of outer diameter D and inner diameter d. The length Lis fixed at a wall. Consider the following loading conditions, all applied to the beam at the midpoint of length L. For each loading scheme state determine the magnitude of that stress in terms of the variables given in the problem). (5 points) i. ii. iii. iv. V. Normal stress due to axial load F Shear stress due to torque T...
4. (30%) For a beam with a T-section as shown, the cross-sectional dimensions of 12 mm. The centroid is 75 mm, h = 90 mm, t the beam are b 60 mm, h, at C and c 30 mm. At a certain section of the beam, the bending moment is M 5.4 kN m and the vertical shear force is V= 30 kN. (a) Show that the moment of inertia of the cross-section about the z axis (the neutral axis)...
Figure Q3 shows a simply supported beam carrying a point load. The beam hasa rectangular hollow steel section as shown in Figure Q3. a. Calculate the second moment of area of the section about the horizontal (10 marks) centroidal axis. Calculate the maximum allowable value of the point load Wif the elastic bending (15 marks) b. stress in the beam is to be limited to 250 MPa. c. Calculate the maximum shear stress at q-q in the beam when the...
A beam whose cross-section is shown in the figure is subjected to a bending moment M inclined at 0 = 70° from the z axis. a) Locate the orientation of the neutral axis B and draw this axis on the figure b) Calculate the maximum flexural tensile stress Omax,T and the maximum flexural compressive stress Omax.c in the beam and indicate at which points in the section these occur. M= 2 Nm D e Z 20 mm A B 60...
Figure 1 shows the cross section of a lipped channel. The cross section carries a shear force of 250 kN acting at 45° below the major principal axis (as shown) and through the shear centre. Determine the (Ans: 134.1 MPa) maximum shear stress. (Use line of mid-thickness properties) た45 S.c 4250 N たA 100 Figure 1
Figure 1 shows the cross section of a lipped channel. The cross section carries a shear force of 250 kN acting at 45° below...
Figure 1 shows the cross section of a lipped channel. The cross section carries a shear force of 250 kN acting at 45° below the major principal axis (as shown) and through the shear centre. Determine the Ans: 134.1 MPa) maximum shear stress. (Use line of mid-thickness properties) t 45 34 S.C 250 N たA 100 Figure
A beam of rectangular cross section 200 mm deep and 100 mm wide. If the beam is 3m long, simply supported at either end and carries point loads as shown in FIGURE 2 (on page 4). 2. SAN 1OAN R, FR 100mm FIG.2 (a) Calculate the maximum bending moment (b) Calculate the maximum stress in the beam (c) At the point of maximum stress sketch a graph of the stress distribution through the thickness of the beam, indicating which are...
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