Stiffeners used simply to prevent buckling from the shear, need not be fitted to either flange. Sometimes stiffeners used for this latter purpose are not carried over the flange angles, but stop clear so as to avoid the necessity of fillers, as indicated by Fig. 247. It is better practice, and more generally followed, to carry these angles over the flange angles, as shown by Fig. 248.
1. Determine by the method previously described the bottom flange section of a girder 28 inches deep between centers of gravity of flanges, and having a bending moment of 3,500,000 inch-pounds. The flange is to be proportioned to carry the whole bending moment. Use fiber stresses given for building.
2. In the above problem, if the top flange is unsupported later ally for 20 feet, determine the section of top flange required, using the formula given for reducing allowable compression stress.
3. Given a girder 35 feet long between centers of bearings, and carrying a uniformly distributed load of 2,000 pounds per linear foot. Assume a web 36 inches deep and 34 inches between centers of gravity of flanges. Determine bottom flange section without making any allowance for the portion of bending moment carried by the web.
4. In the above girder, redesign bottom section on the basis that the web is not spliced and that it bears a portion of the bending mo ment.
5. Determine the thickness of web required in above girder.
6. If the girder was 40 feet long, 42 inches deep, and loaded with 4,000 pounds per linear foot, determine the thickness of web if no stiffeners are to be used. Assume flange angles are 6 inches by 6 inches by inch.
7. Determine thickness of web in above girder which could be used with stiffeners, and determine spacing of stiffeners required.
Solution. In this case the shear at end is 80,000 pounds. From the diagram for spacing of stiffeners, it will be seen that any thickness of web from i inch up could be used. Where stiffeners are used to prevent buckling of web, it is more economical to use a web than a ,-inch. If the girder was 60 inches deep, probably it would not be well to use less than web, even with stiffeners. In this case assume a -A, by 42-inch web. Area is therefore 13.12 square inches, and fiber stress is 6,150 pounds.
From the diagram it is seen that a web with this stress per square inch requires stiffeners about 163 inches back to back.
This then determines the space of first stiffener from those over the bearing plate. Assume two spaces the same as this, and then deter mine shear at point say 3 feet 6 inches from the end bearing. This is found to be S0,000 — (4,000 X 3.5) = 66,000 pounds. The stress here is about 5,075 pounds per square inch of web. From the diagram, this is seen to require stiffeners 20 inches apart. Assume two more spaces at 20 inches, and calculate shear, which is found to be 52,600 pounds. This gives a fiber stress of 4,050 pounds per square inch of web, and requires stiffeners 24 inches apart. Take three spaces at this distance, and calculate shear, which is found at this point to be 2S,600. This gives a stress of 2,200 pounds per square inch of web. From the diagram the spacing of stiffeners for this fiber stress, in a web, is found to be 36 inches. This distance, however, is greater than the clear distance between flange angles, which is 30 inches, and indicates, therefore, that at this point the web is strong enough without being stiffened by angles.
If it is desired to see whether or not two spaces at 24 inches, in stead of three a-s above taken, would have been sufficient, the shear at this point can be calculated. This is found to be 36,600 pounds, or 2,800 pounds per square inch of web. This is seen to require stiffeners 31 inches apart. This is greater than the distance between flange and indicates that the last stiffener could be omitted. How ever, it is better to carry the stiffeners a little beyond the actual point where the diagram would indicate that they could be dropped; so that it would be better to use the last stiffener, as originally determined. The spacing of stiffeners at each end of girder is of course made the same where the load is uniformly distributed.
Size of Stiffeners, Stiffeners for concentrated loads and for reac tions should have sufficient area to take the whole load or reaction at this point. Stiffeners used to prevent buckling are not generally calculated, but are made either 3 x 3 x inch or 4 x 3 x a inch. When stiffeners are fitted to the flanges, the outstanding leg should be made large enough to come nearly out to the edge of the flange angle. If the flange angle is 6 by 6, the stiffener would be perhaps 5 by 31.