T05 & 06 Extra PDF

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Tutorial 5 & Tutorial 6 Extra...

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Figure 1: Beam. The beam in Figure 1 is made from three boards nailed together. The moment acting on the cross section is M = 600 Nm. Determine: (a) The distance yc of the neutral axis (about which the bending moment acts) from the bottom edge of the cross-section. (b) The second moment of area IN of the cross-section about its neutral axis. (c) the maximum bending stress in the beam. Specify whether this maximum stress is tensile or compressive.

Question 2 (Problem A/2 from M and K – Engineering Mechanics and Statics)

Figure 2 Determine the moments of inertia of the rectangular area about the x-axis and y-axis shown in Figure 2. (Hint: Use parallel axes theorem) 1

Week 06

Tutorial Five – Centroids, Second Moment of Area and Bending

Question 3 (Problem A/6 from M and K – Engineering Mechanics and Statics)

Figure 3 The moments of inertia of the area A in Figure 3, about the parallel p- and p′ -axes differ by 15× 106 mm4 . Compute the cross-sectional area of A, which has its centroid at C. (Hint: Use parallel axes theorem)

Question 4 (Problem 12-2 from Hibbeler – Statics and Mechanics of Materials)

Figure 4: Wooden beam. For the wooden beam shown in Figure 4, determine: (a) The second moment of area about the axis that bending occurs. (b) The moment M that should be applied to the beam in order to create a compressive stress at point D of σ D = 30 MPa. (c) Sketch the stress distribution acting over the cross section and compute the maximum stess developed in the beam.

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Week 06

Tutorial Five – Centroids, Second Moment of Area and Bending

Question 5 (Problem 12-8 from Hibbeler – Statics and Mechanics of Materials)

Figure 5: Aluminium machine part. The aluminium machine part shown in Figure 5 is subjected to a moment M = 75 Nm. Given that the neutral axis is 0.0175 m from the top surface of the top flange, determine: (a) The second moment of area about the neutral axis. (b) The bending stress created at point B .

Question 6 (Problem 12-5 from Hibbeler – Statics and Mechanics of Materials)

Figure 6: Beam. The beam shown in Figure 6 is made up of multiple sections. The beam is subjected to a moment M = 4 kNm, and its second moment of area about the neutral axis is IN = 91.73 cm4 . Find: (a) The location of the neutral axis (measured from the top surface of the top flange). (b) The maximum tensile bending stress. (c) The maximum compressive bending stress.

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Week 06

Tutorial Five – Centroids, Second Moment of Area and Bending

Question 7 (Problem A/40 from M and K – Engineering Mechanics and Statics)

Figure 7 Determine the moment of inertia about the x-axis (Ixx ) in two different ways for the cross section in Figure 7. The wall thickness is 20 mm on all sides of the rectangle.

Part B Question 8 (Problem 12-46 from Hibbeler – Statics and Mechanics of Materials)

Figure 8: I-beam. Determine the maximum tensile and compressive bending stress in the I-beam (Figure 8) if it is subjected to a moment of M = 10 kNm.

Question 9 (Problem A/1 from M and K – Engineering Mechanics and Statics)

Figure 9 Use the differential element shown in Figure 9 to determine the moment of inertia of the triangular area about the x-axis and y-axis

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Week 06

Tutorial Five – Centroids, Second Moment of Area and Bending

Question 10 (Problem A/4 from M and K – Engineering Mechanics and Statics)

Figure 10 Determine the ratio b/h such that Ix = Iy for the area of the isosceles triangle in Figure 10.

Question 11 (Problem 12-24 and 12-26 from Hibbeler – Statics and Mechanics of Materials)

(a) Utility pole.

(b) Rod with distributed loads.

Figure 11

(a) The strut CD on the utility pole in Figure 11a supports the cable having a weight of 600 N. Determine the absolute maximum bending stress in the strut if A, B and C are assumed to be pinned. (b) The rod in Figure 11b is supported by smooth journal bearings at A and B that only exert vertical reactions on the shaft. If d = 90 mm, (i) determine the absolute maximum bending stress in the beam; and (ii) sketch the stress distribution acting over the cross section.

Question 12 (Problem 12-6 from Hibbeler – Statics and Mechanics of Materials) In Figure 6, given that M = 4 kNm, determine the resultant force that the bending stress produces on the horizontal top flange plate AB .

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Week 06

Tutorial Five – Centroids, Second Moment of Area and Bending

Question 13 (Problem 12-25 from Hibbeler – Statics and Mechanics of Materials)

(a) Man on diving board.

(b) Board cross-section.

Figure 12 The man in Figure 12a has a mass of 78 kg and stands motionless at the end of the diving board. If the board has the cross-section shown in Figure 12b, determine the maximum normal strain developed in the board. The modulus of elasticity for the material is E = 125 GPa. Assume A is a pin and B is a roller.

Question 14 (Problem 12-32 from Hibbeler – Statics and Mechanics of Materials)

Figure 13: Strut. If the internal moment on the cross section of the strut has magnitude of M = 800 Nm and is directed as shown in Figure 13, determine the bending stress at points A and B. The location z of the centroid C of the strut’s cross sectional area must be determined. Also, specify the orientation of the neutral axis.

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Week 06

Tutorial Five – Centroids, Second Moment of Area and Bending

Question 15 (Problem 12-38 from Hibbeler – Statics and Mechanics of Materials)

Figure 14: Shaft with pulleys. The 30 mm diameter shaft is subjected to the vertical and horizontal loadings of two pulleys as shown in Figure 14. It is supported on two journal bearings at A and B which offer no resistance to axial loading. Furthermore, the coupling to the motor at C can be assumed not to offer any support to the shaft. Determine the maximum bending stress developed in the shaft.

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