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7.5 (A/B). Fig. 7.18 shows the cross-section of a beam which carries a shear force of 20 kN. Plot a graph to scale hich shows the distribution of shear stress due to bending across the cross-section.

7.5 (A/B). Fig. 7.18 shows the cross-section of a beam which carries a shear force of 20 kN. Plot a graph to scale hich shows the distribution of shear stress due to bending across the cross-section.

Elements Of Electromagnetics
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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7.5 (A/B). Fig. 7.18 shows the cross-section of a beam which carries a shear force of 20 kN. Plot a graph to scale which shows the distribution of shear stress due to bending across the cross-section. [I.Mech.E.] [21.7, 5.2, 5.23 MN/m?] 12 mm 75 mm 40 mm 50mm- Fig. 7.18. 7.6 (B). Show that the difference between the maximum and mean shear stress in the web of an I-section beam is where Q is the shear force on the cross-section, h is the depth of the web and I is the second moment of area of the 241 cross-section about the neutral axis of bending. Assume the I-section to be built of rectangular sections, the flanges having width B and thickness t and the web a thickness b. Fillet radii are to be ignored. [I.Mech.E.] 7.7 (B). Deduce an expression for the shearing stress at any point in a section of a beam owing to the shearing force at that section. State the assumptions made. A simply supported beam carries a central load W. The cross-section of the beam is rectangular of depth d. At what distance from the neutral axis will the shearing stress be equal to the mean shearing stress on the section? [U.L.C.I.] [d//12.] 7.8 (B). A steel bar rolled to the section shown in Fig. 7.19 is subjected to a shearing force of 200 kN applied in the direction YY. Making the usual assumptions, determine the average shearing stress at the sections A, B, C and D, and find the ratio of the maximum to the mean shearing stress in the section. Draw to scale a diagram to show the variation of the average shearing stress across the section. [U.L.] [Clue: treat as equivalent section similar to that of Example 7.3.] [7.2, 12.3, 33.6, 43.8 MN/m2, 3.93.] 120 mm. lY A 20 mm 20 mm B 20 mm 160 mm C 20 mm Fig. 7.19.
Transcribed Image Text:7.5 (A/B). Fig. 7.18 shows the cross-section of a beam which carries a shear force of 20 kN. Plot a graph to scale which shows the distribution of shear stress due to bending across the cross-section. [I.Mech.E.] [21.7, 5.2, 5.23 MN/m?] 12 mm 75 mm 40 mm 50mm- Fig. 7.18. 7.6 (B). Show that the difference between the maximum and mean shear stress in the web of an I-section beam is where Q is the shear force on the cross-section, h is the depth of the web and I is the second moment of area of the 241 cross-section about the neutral axis of bending. Assume the I-section to be built of rectangular sections, the flanges having width B and thickness t and the web a thickness b. Fillet radii are to be ignored. [I.Mech.E.] 7.7 (B). Deduce an expression for the shearing stress at any point in a section of a beam owing to the shearing force at that section. State the assumptions made. A simply supported beam carries a central load W. The cross-section of the beam is rectangular of depth d. At what distance from the neutral axis will the shearing stress be equal to the mean shearing stress on the section? [U.L.C.I.] [d//12.] 7.8 (B). A steel bar rolled to the section shown in Fig. 7.19 is subjected to a shearing force of 200 kN applied in the direction YY. Making the usual assumptions, determine the average shearing stress at the sections A, B, C and D, and find the ratio of the maximum to the mean shearing stress in the section. Draw to scale a diagram to show the variation of the average shearing stress across the section. [U.L.] [Clue: treat as equivalent section similar to that of Example 7.3.] [7.2, 12.3, 33.6, 43.8 MN/m2, 3.93.] 120 mm. lY A 20 mm 20 mm B 20 mm 160 mm C 20 mm Fig. 7.19.
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