Combination method of span division calculation

According to different components, different sections and different types of internal forces, the most unfavorable internal forces are combined.There are different live load arrangements (span x floor).In order to reduce the calculation workload, the most unfavorable distribution of roof live load can be considered as full distribution.　

2The most unfavorable load location method 

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

In order to find the most disadvantageous arrangement of the live load of the maximum positive moment MC of the mid span C section of a certain span beam AB, the influence line of MC can be drawn first, that is, the corresponding constraint is removed (C point is changed to hinge), and the positive binding force is replaced, so that the unit virtual displacement θ C = 1 is generated along the positive direction of the binding force, thus the virtual displacement diagram of the whole structure can be obtained.

According to the principle of virtual displacement, in order to find the maximum positive bending moment in the span of beam AB, the live load of the inter span structure with positive virtual displacement is arranged.In other words, in addition to the span must be arranged with live load, other spans should be arranged alternately, and at the same time, they should be arranged alternately in the vertical direction to form a chessboard layout.It can be seen that when the AB span reaches the maximum bending moment in the middle of the span, the most unfavorable arrangement of the live load is found, which also makes the mid span bending moment of other arrangements of live load span reach the maximum value.Therefore, as long as the second chessboard live load arrangement is carried out, the maximum positive bending moment of all beams in the whole frame can be obtained.

The most unfavorable arrangement of the live load of the maximum negative bending moment at the beam end or the maximum bending moment at the column end can also be obtained by the above method.

The most disadvantageous arrangement of the live load of the maximum axial force of the column is that the beam span adjacent to the column is full of live load in each layer above the column.　

3Layered combination method

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

(2) For the moment at the end of the column, 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, the case of full distribution of live load on the beam adjacent to the column in all layers above the floor is considered, but for the upper live load not adjacent to the column, only the transfer of axial force is considered, and the effect of bending moment is not considered.

4Full load method

When the internal force generated by live load is far less than that generated by dead load and horizontal force, the most unfavorable arrangement of live load can not be considered, and the live load can be applied to all frame beams at the same time. In this way, the internal force obtained at the support is very close to that obtained by the method of the most unfavorable load position, so the internal force combination can be carried out directly.However, the mid span bending moment is smaller than that calculated by the most unfavorable load location method. Therefore, the mid span bending moment should be multiplied by a coefficient of 1.1-1.2