The strength of bolts in resisting shear and bending may be analyzed similarly to rivets and pins. When bolts or round bars threaded at the end are subjected to tensile stress, they tend to break at the weakest section, which is at the root of the screw thread. In order to make the threaded part equal in strength to that of the body of the rod, the end is sometimes upset, so that the diameter at the root of the thread will equal that of the body. Upsetting, however, requires more smithwork, the cost of which will likely be more than that of the additional material required to increase the size enough to make upset ends unnecessary.

The following table (XXXI) gives the principal dimensions for U. S. standard screw threads and nuts, and the area at the root of thread of any usual size rod. The strength of any tension rod may be found by multiplying this area by the tensile strength of the material.

### Example

Required, the size of a threaded round tension rod, to sustain a stress of 13,350 lb., the safe working tensile stress of the material being 15,000 lb. per sq. in.

### Solution

The area required is 13,350 lb. / 15,0001b. = .890 sq. in. at the root of the thread; from the table, it will be found that a rod 1 1/4 in. in diameter will suffice.

In designing tension bars it would be well to observe the following: Proportion the heads of eyebars so that the bar will break in the body instead of in the eye; the pin hole should be 1/50 of an inch larger than the pin; all rivet holes in eyebars should be drilled and the wire edge cut off; bars should be thoroughly annealed after forging, and no smith-work should be done at a blue heat; small tension rods up to, say, 1 3/4 in. square are preferably, either simple loop or clevis rods; the eyes of loop rods should be bored to fit the pin; upset screw ends should have a net section at root of thread 15 per cent, greater than the body of the bar; steel rods may be used for upset screw ends, but should be tested in full size section, and thoroughly annealed after forging; clevises, twinbuckles, and sleeve nuts should be of standard approved pattern.

## Table XXXI. Bolts And Nuts

 Bolts. U. S. Standard Screw Thread. Nuts. Manufacturers' Standard. Diam. of Bolt. In. No. of Threads per Inch. Diam. at Root of Thread. Inches. Area of Body of Bolt. Sq. In. Area at Root of Thread. Sq. In. Hexagon. Square. Short Diam. Inches. Long Diam. Inches. Side of Square. (In.) Diagonal. Inches. 1/4 20 .185 .049 .027 1 .58 1 .71 5/16 18 .240 .077 .045 | .72 5/8 .88 I 16 .294 .110 .068 3/4 .87 3/4 1.06 7/16 14 .344 .150 .093 7/8 1.01 7/8 1.24 1 13 .400 .196 .126 1 1.15 1 1.41 9/16 12 .454 .249 .162 1 1/8 1.30 1 1/8 1.59 5/8 11 .507 .307 .201 1 1/4 1.44 1 1/4 1.77 3/4 10 .620 .442 .302 1 3/8 1.59 1 1/2 2.12 7/8 9 .731 .601 .419 1 5/8 1.88 1 3/4 2.47 1 8 .837 .785 .550 1 3/4 2.02 2 2.83 1 1/8 7 .940 .994 .694 2 2.31 2 1/4 3.18 1 1/4 7 1.060 1.230 .890 2 1/4 2.60 21 3.54 1 3/8 6 1.160 1.480 1.060 2 1/2 2.89 2 3/4 3.89 1 1/2 6 1.280 1.770 1.290 2 3/4 3.18 3 4.24 1 5/8 51 1.390 2.070 1.510 3 3.46 3 1/4 4.60 1 3/4 5 1.490 2.400 1.740 3 1/4 3.75 3 1/2 4.95 1 7/8 5 1.610 2.760 2.050 3 1/2 4.04 3 3/4 5.30 2 41 1.710 3.140 2.300 31 4.04 4 5.66 2k 4 1/2 1.960 3.980 3.020 3 3/4 4.33 4 1/4 6.01 21 4 2.170 4.910 3.710 4 1/4 4.91 41 6.36 2 3/4 4 2.420 5.940 4.620 41 5.20 4 3/4 6.72 3 3 1/2 2.630 7.070 5.430 4 3/4 5.48 5 7.07 3 1/4 3 1/2 2.880 8.300 6.510 5 5.77 51 7.78 3 1/2 3 1/4 3.100 9.620 7.550 5 1/4 6.06 5 3/4 8.13 3 3/4 3 3.320 11.040 8.640 6 6.93 6 1/2 9.19 4 3 3.570 12.570 10.000 61 7.51 7 9.90 4 1/2 2 3/4 4.030 15.900 12.740 7 1/2 8.58 8 11.31

The thickness of rough bolt heads, either hexagonal or square, is one-half the short diameter or side of square respectively; for rough nuts, it is equal to the diameter of the bolt. Finished heads and nuts have a thickness equal to the diameter of bolt less 1/16 in.