329 Calculation Of Reactions In Statically Determinate Systems

For statically determinate systems, reactions can be determined from equilibrium equations [Eq. (3.11) or (3.12)]. For example, in the planar system shown in Fig. 3.66, reactions R1, H1, and R2 can be calculated from the three equilibrium equations. The beam with overhang carries a uniform load of 3 kips/ft over its 40-ft horizontal length, a vertical 60-kip concentrated load at C, and a horizontal 10-kip concentrated load at D. Support A is hinged; it can resist vertical and horizontal forces. Support B, 30 ft away, is on rollers; it can resist only vertical force. Dimensions of the member cross sections are assumed to be small relative to the spans.

Only support A can resist horizontal loads. Since the sum of the horizontal forces must equal zero and there is a 10-kip horizontal load at D, the horizontal component of the reaction at A is H1 = 10 kips.

The vertical reaction at A can be computed by setting the sum of the moments of all forces about B equal to zero:

from which R1 = 68 kips. Similarly, the reaction at B can be found by setting the sum of the moments about A of all forces equal to zero:

from which R2 = 112 kips. Alternatively, equilibrium of vertical forces can be used to obtain R2, given R1 = 68:

R2 + R1 - 3 x 40 - 60 = 0 Solution of this equation also yields R2 = 112 kips.

Renewable Energy 101

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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