## 20

Since T + Q = 15 + 3.51 = 18.5 kips < 31.0 kips, the bolts are OK. The tee flange, however, should be checked independently. This can be done as follows.

Assume that the prying force Q = 3.51 acts at a distance a from the bolt line. The moment at the bolt line then is

Mb = 3.51 X 1.777 = 6.24 kip-in and that at the toe of the fillet, with T + Q = 18.5 kips, is

Mf = 3.51 X (1.777 + 1.1875) - 18.5 X 1.1875 = -11.6 kip-in

The maximum moment in the flange is thus 11.6 kip-in, and the bending stress in the flange is fb =

5.25.4 Welded Butt Joints

A hanger also may be connected with a simple welded butt joint (Fig. 5.27). The allowable stress for the complete-penetration groove weld is the same as for the base metal used.

Examples—AISC ASD. A bar hanger carries a 60-kip load and is supported through a complete-penetration groove weld at the edge of a tee stub.

For A36 steel with allowable tensile stress of 22 ksi, the bar should have an area of 6%2 = 2.73 in2. A bar 5V2 X V2 with an area of 2.75 in2 could be used. The weld strength is equal to that of the base metal. Hence no allowance need be made for its presence.

Example—AASHTO ASD. Suppose, however, that the hanger is to be used in a highway bridge and the load will range from 30 kips in compression (minus) to 60 kips in tension (plus). The design then will be governed by the allowable stresses in fatigue. These depend on the stress range and the number of cycles of load the structure will be subjected to. Design is to be based on 100,000 cycles. Assuming a redundant load path and the detail of Fig. 5.27, load category C applies with an allowable stress range SR = 35.5 ksi, according

FIGURE 5.27 Groove weld for hanger connection.

FIGURE 5.28 Recommended taper for unequal-width plates at groove-welded splice.

FIGURE 5.27 Groove weld for hanger connection.

FIGURE 5.28 Recommended taper for unequal-width plates at groove-welded splice.

to AASHTO. For A36 steel, the maximum tensile stress is 20 ksi. At 60-kip tension, the area required is 60/20 = 3 in2. A bar 5 x 5/s could be tried. It has an area of 3.125 in2. Then the maximum tensile stress is 60/3.125 = 19.2 ksi, and the maximum compressive stress is 30/3.125 = 9.6 ksi. Thus the stress range is 19.2 - (-9.6) = 28.8 ksi < 35.5 ksi—OK. The 5 x y8 bar is satisfactory.

As another example, consider the preceding case subjected to 2 million cycles. The allowable stress range is now 13 ksi. The required area is [60 - (-30)]/13 = 6.92 in2. Try a bar 5 x 1V2 with area 7.5 in2. The maximum tensile stress is 60/7.5 = 8.0 ksi (<20 ksi), and the maximum compressive stress is 30/7.5 = 4.0 ksi. Thus the actual stress range is 8.0 - (-4.0) = 12.0 ksi < 13.0 ksi—OK. The 5 x 11/2 bar is satisfactory.

## Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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