810 



APPLIED MECHANICS. 



[TRANSVERSE BTKESOTH. 



the breadth may be diminished at a distance from 

 the poiut of support; because the strength of a beam 

 lit its breadth, and the leverage of the weight being 

 lessened as we recede from the breaking-point, the breadth 

 may be lessened in like proportion. Sometimes it is 

 convenient to vary the depth and breadth also, and thus 

 maintain a similar section throughout the whole length ; 

 that is, a section of like figure, but of varying dimen- 

 sions. 



In the case of beams supported at both ends, and 

 loadfl in tln> middle (Fig. 83), the same principle is ap- 

 plied ; the dimensions, in respect of depth and breadth, 

 being made greatest in the middle, and diminished gra- 

 dually towards the ends. This economy of material is 

 easily effected in cast-iron girders, by making the pattern 

 from which the casting is moulded of the requisite form. 



Fig. 86. 



When timber beams are used, the increased depth to- 

 wards the middle is attained by piling several beams on 

 one another (Fig. 86). As the lower side of a beam 

 resting at both ends i subject to a tensive strain, great 

 additional transverse strength may be secured by strain- 

 ing a rod or chain B B (Fig. 87) from end to end of the 



Fig. 87. 



beam, and blocking it off from the lower surface by means 

 of one or more wooden or iron struts A or C C. By 

 this arrangement the wooden beam, when loaded between 

 the supports, is subjected to a compressive strain only, 

 the whole of the tensive strain being thrown upon the 

 rod or chain. 



Again, by fixing a strut, or king-post, C (Fig. 88), 

 Fig. 88. 



upon the upper side of the beam A A, and connecting it 

 by pieces B B to the ends, the compresHive strain is 

 thrown on B B, and the tensive strain only on A A. In- 

 deed, there is no limit to the contrivances by means of 

 which the direction and amount of the strain can bo 

 varied so as to economise material and secure stability. 

 We have only instanced a few as examples of arrange- 

 *, a complete account of which would fill many 



OLATION OF TRANSVERSE STRENGTH. 

 The table of transverse strengths gives the load which 

 may be safely placed on the middle of beams of different 

 materials supported at both ends. The table applies 

 to beams 1 foot long between the points of support. 

 The weights are those for beams the transverse section 

 of which in the middle is 1 inch square, or 1 inch broad 



and 1 inch deep ; and these apply to all beams of rec- 

 tangular section. The weights for beams of circular 

 section, may be taken at two-thirds of those for square 

 section. The following are the rules for computing the 

 strengths of beams of various dimensions, according to 

 the data furnished by the table : 



Table of transverse strengths of beams, 1 foot long between 

 sitp/Hirts, lyiiy loose at both ends, loaded in the middle, 

 having a tection 1 inch square. 



Name of Permanent 



material. load. 



Ok (Engli.h) 190 Ibi. 



Pitch pine 190 



Teak 270 



Iron (cat) 850 



Iron (wrought) 1300 



Name of Permanent 



material. 1. ..1. 



Ah 250 Ibs. 



Betch I/O 



Deal 130 



Elm 120 



Oak (African) 230 



I. For beams supported at both ends and loaded in 

 the middle. Given the length, breadth, and depth, to 

 find the load. 



Rule. Multiply the number in the table by the 

 breadth (in inches), twice by the depth (in inches), and 

 divide by the length (in feet). 



Example 1. Required the transverse strength of a 

 beam of teak 8 inches broad, 12 inches deep, and 14 feet 

 between bearings. 



Number from table opposite teak . . 270 Ibs. 



Multiply by breadth 8 ins. 



Multiply by depth 



21CO 

 12 ins. 



25920 

 12 ins. 



14)311040 



Again by depth ..... 

 Divide by length 



22217 Ibs. 



Very nearly 10 tons, or 22,400 Ibs. 



Example 2. Required the transverse strength of a 

 wrought-iron bar 1$ inch broad, 4 inches deep, and 6 

 feet long. 



1300X1|X4X4 = 52()0 lbg ^ ne&rly46i ^ 



For bars of circular section. 



Rule. Multiply the number in the table three times 

 by the diameter (in inches), divide by the length (in 

 feet), and deduct one-third of the result from itself. 



Example 3. Required the transverse strength of a 

 beech roller, 2 inches diameter, and 4 feet long. 



170 X 2 X 2 X 2 , 



j = J40 



Deduct one-third = 113 



227 Ibs., about 2 cwt. 



II. When the beam is fixed down at its ends. 



Rule. Find the strength as before (I.), and add to it 

 its half. 



Example 4. Required the strength of a cast-iron bar 

 2 inches broad, 6 inches deep, 9 feet long, fixed at both 

 ends. 



850 X 2 X 6 X 6 



=6800 Ibs., about 3 tons. 



And one-half 3400 



IJton. 



10200 4i tons. 



III. When the beam is supported lixisoly at both 

 ends, and has the load uniformly distributed over its 

 length. 



Rule. Find the strength as before (I.), and double it. 



Example 5. Required the strength of a deal rafter ;i 

 inches broad, 11 inches deep, 10 feet long, loaded uni- 

 formly throughout its length. 



130x3xllXll v9 _ Q ^a lbs.,*bout 4} ton.. 



