B 4

_4PL_2Mc 3

_4PL_2Mc 3

MD = Mp

FIGURE 3.97 (a) Two-span continuous beam with concentrated loads. (b) Moment diagrams for positive and negative moments. (c) Combination of moment diagrams in (b). (d) Valid solution for ultimate load is obtained with plastic moments at peaks at C and D, and Mp is not exceeded anywhere. (e) Invalid solution results when plastic moment is assumed to occur at B and Mp is exceeded at D.

FIGURE 3.97 (a) Two-span continuous beam with concentrated loads. (b) Moment diagrams for positive and negative moments. (c) Combination of moment diagrams in (b). (d) Valid solution for ultimate load is obtained with plastic moments at peaks at C and D, and Mp is not exceeded anywhere. (e) Invalid solution results when plastic moment is assumed to occur at B and Mp is exceeded at D.

The peak moment at B should be checked to ensure that MB < Mp. For the ultimate load Pu and equilibrium in span AC,

This indicates that at the limit load, a plastic hinge will not form in the center of span AC.

If the combined moment diagram had been adjusted so that span AC becomes a mechanism with the peak moments at B and C equaling Mp (Fig. 3.97e), this would not be a statically admissible mode of failure. Equilibrium of span AC requires

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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