What are the most unfavorable arrangements for vertical loads in frame design?

1. Crossover combination method

The active load is applied to the structure layer by layer, and the internal forces of the whole structure are calculated separately. The most unfavorable internal force is composed according to different components, different sections and different internal forces. In order to reduce the computational workload, consider taking into account the live load of the roof.

2. The most unfavorable load position method

In order to find the most unfavorable internal force of a given section, the live load arrangement that produces the most unfavorable internal force can be directly determined according to the influence line method.

If you want the most unfavorable arrangement of the live load of the maximum positive bending moment MC of the cross-section C of a span beam AB, you can first make the influence line of the MC, that is, release the corresponding constraint (change the point C to the hinge) and replace it with the positive constraint. The force causes the structure to generate a unit virtual displacement θc=1 along the positive direction of the binding force, thereby obtaining a virtual displacement map of the entire structure.

According to the principle of virtual displacement, in order to find the maximum positive bending moment of the beam AB span, the cross-interfacial structure that produces the positive virtual displacement is arranged. That is to say, in addition to the fact that the span must be arranged with live loads, the other spans are arranged at the same time, and at the same time, they are also arranged vertically, forming a checkerboard spacing arrangement. It can be seen that the most unfavorable arrangement of the live load when the AB span reaches the maximum mid-span bending moment is also such that the mid-span bending moment of the other disposed live load span reaches a maximum. Therefore, as long as the second checkerboard live load arrangement is performed, the maximum positive bending moment among the spans of all the beams in the entire frame can be obtained.

The most unfavorable arrangement of the live load of the maximum axial force of the column is that in each layer above the column, the beam span adjacent to the column is covered with a live load.

3. layered combination method

(1) For the beam, only the unfavorable arrangement of the live load of the layer is considered, and the influence of the live load of other layers is not considered. Therefore, the arrangement method is the same as the most unfavorable arrangement method of the live load of the continuous beam.

(2) For the bending moment of the column end, only the influence of the live load of the adjacent upper and lower layers of the column is considered, and the influence of the live load of other layers is not considered.

(3) For the maximum axial force of the column, consider the case where the beam adjacent to the column is full of live loads in all layers above the layer, but for the upper layer live load not adjacent to the column, only the axial direction is considered. The transmission of force does not take into account the role of its bending moment.

4. full load method

When the internal force generated by the live load is much smaller than the internal force generated by the constant load and the horizontal force, the live load can be applied to all the frame beams simultaneously without considering the most unfavorable arrangement of the live load, so that the internal force is obtained at the support. It is very similar to the internal force obtained by the most unfavorable load position method, and the internal force combination can be directly performed. However, the calculated mid-span bending moment of the beam is smaller than that of the most unfavorable load position method. Therefore, the bending moment of the beam span should be multiplied by a factor of 1.1 to 1.2.