Principles of mechanics, and their application to prime movers, naval architecture, iron bridges, water supply, etc; being an abstract of lectures ... the University of Glasgow, session 1872-73... - Softcover

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1874 Excerpt: ...be the supporting force, equal and opposite to the downward force at point of support; Si = stress on the bar 1, 2, or 3, 4; H, = horizontal thrust upon the bar 1, 4. Since the angle at 1 is an angle of 60, we have the following relations existing between the forces, F,: S1: Hx::-86:1:-5, F F-5 and therefore = S, and =, and if Fx = 1 ton, then we have Su or stress on bar 1,2, or 3, 4 = = 116 ton; and H, or hori-00 1X '5 zontal pull on the rod 1, 4 =--= 58 bo ton; tabulating these for the first frame, we have (1.) Fx = 1 ton = load at 2 or at 3. Sx =1-16 ton on bar 1, 2, or 3, 4. Hx = 0-58 ton on bar 1, 4, or 2, 3. Fig. 25. We have now to calculate the stresses on the bars of the second frame 5, 2, 3, 6 (Fig. 26); and since we have And by multiplying these values by the same ratios as in case 1, p. 63, we have for tbe inclined stresses, 2 90 tons = stress along 1, 2, or 3, 4. 1-74 ton = „ 2, 5, or 3, 6. 0-58 ton = „ 7, 5, or 7, 6. The horizontal stresses are found by finding the bending moments at the points 2, 5, 7, 6, and 3 (as explained at p. 54), and dividing the moments so found by the depth of the girder, thus:--Tons. Supporting force at 1 = 2-5 2 = 1-5 5 = 0-5 7 = 0-0 Bending Moments. Round 2 = 2 5 x-5 = 1-25 „ 5 = (1-25 + 1-5 x-5).. =2-00 „ 7 = (1-25 +-75 +-5 x-5) = 2-25 And the horizontal stresses are, 1 25 At 2 or 3, or their opposites = '= 1-45.-oo At 5 or 6, or their opposites =? = 2 32.-bo 2-25 At 7, or its opposite = = 2-61.-oo On comparison of the two methods it will be seen that the results are similar. FORMS OF GIRDERS. Plate Girders. Fig. 28 shows in section a wrought-iron plate girder; Fig. 29 shows part of same girder in elevation. A and B are the flanges of wrought-iron plates, suitably joined at their extremities...

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