How to calculate the axial force of frame structure
Publish: 2021-05-19 22:12:42
1. 1. If you don't use calculation software, you have to do it by hand
2. Manual calculation steps: firstly, the plane frame calculation diagram to be calculated is extracted from the structural system. Because the space system needs to be transformed into a plane according to the mechanical principle in manual calculation, and the horizontal frame and vertical frame are calculated respectively, it is almost impossible to calculate the structural space system directly; The calculation diagram includes span, number of spans, column height, load, beam column stiffness, etc; ② In the calculation diagram, use the iterative method to calculate the internal force. After the calculation, you can get the axial force and bending moment of the column, including the internal force of the beam.
2. Manual calculation steps: firstly, the plane frame calculation diagram to be calculated is extracted from the structural system. Because the space system needs to be transformed into a plane according to the mechanical principle in manual calculation, and the horizontal frame and vertical frame are calculated respectively, it is almost impossible to calculate the structural space system directly; The calculation diagram includes span, number of spans, column height, load, beam column stiffness, etc; ② In the calculation diagram, use the iterative method to calculate the internal force. After the calculation, you can get the axial force and bending moment of the column, including the internal force of the beam.
2. Multi story frame is a high-order statically indeterminate structure. It is very difficult or even impossible to calculate its internal force and displacement by hand according to the accurate method. Therefore, approximate analysis method is usually used in engineering structure calculation. Next, we will introce several common approximate methods, that is, the reverse bending point method and D-value method under horizontal load, and the secondary distribution method of bending moment under vertical load< Calculation of internal force and displacement of frame under horizontal load
internal force calculation
1. Reverse bending point method
under horizontal load, the joint will proce rotation and lateral displacement at the same time. According to the analysis, when the ratio of the linear stiffness of the beam to that of the column is greater than 3, the rotation angle of the joint will decrease θ It has little influence on the internal force of the frame. Therefore, in order to simplify the calculation, it is usually ignored, that is, assumed θ= 0 In fact, this is equivalent to simplifying the frame beam into a rigid beam with linear stiffness KB = ∞. In this way, the calculation can be greatly simplified, and the error is generally less than 5%
with the above assumption, the section bending moment is zero at 1 / 2 of the column height. The elastic curve of the column changes the concave convex direction at this place, so this place is called the reverse bending point, and the distance from the reverse bending point to the bottom of the column is called the height of the reverse bending point
after the reverse bending point of the column is determined, if the shear force of the column is obtained, the bending moment diagram of the frame can be drawn
2. Improved reverse bending point method - D value method
the above reverse bending point method is only applicable to the case that the linear stiffness ratio of beam to column is greater than 3. If this condition is not satisfied, the lateral stiffness and the position of the reverse bending point of the column will change with the small angle of the frame joint. At this time, using the reverse bending point method to calculate the internal force of the frame will proce large errors
the improved reverse bending point method is introced below. This method approximately considers the influence of the rotation of the frame joints on the lateral stiffness and the height of the anti bending point. The improved reverse bending point method is a simple and accurate approximate method for analyzing the internal forces of frames. Therefore, it is widely used in residential engineering
the lateral stiffness of the column can be obtained by the improved reverse bending point method, which is expressed by D in engineering, so the improved reverse bending point method is also called & quot; D-value method & quot< br />
internal force calculation
1. Reverse bending point method
under horizontal load, the joint will proce rotation and lateral displacement at the same time. According to the analysis, when the ratio of the linear stiffness of the beam to that of the column is greater than 3, the rotation angle of the joint will decrease θ It has little influence on the internal force of the frame. Therefore, in order to simplify the calculation, it is usually ignored, that is, assumed θ= 0 In fact, this is equivalent to simplifying the frame beam into a rigid beam with linear stiffness KB = ∞. In this way, the calculation can be greatly simplified, and the error is generally less than 5%
with the above assumption, the section bending moment is zero at 1 / 2 of the column height. The elastic curve of the column changes the concave convex direction at this place, so this place is called the reverse bending point, and the distance from the reverse bending point to the bottom of the column is called the height of the reverse bending point
after the reverse bending point of the column is determined, if the shear force of the column is obtained, the bending moment diagram of the frame can be drawn
2. Improved reverse bending point method - D value method
the above reverse bending point method is only applicable to the case that the linear stiffness ratio of beam to column is greater than 3. If this condition is not satisfied, the lateral stiffness and the position of the reverse bending point of the column will change with the small angle of the frame joint. At this time, using the reverse bending point method to calculate the internal force of the frame will proce large errors
the improved reverse bending point method is introced below. This method approximately considers the influence of the rotation of the frame joints on the lateral stiffness and the height of the anti bending point. The improved reverse bending point method is a simple and accurate approximate method for analyzing the internal forces of frames. Therefore, it is widely used in residential engineering
the lateral stiffness of the column can be obtained by the improved reverse bending point method, which is expressed by D in engineering, so the improved reverse bending point method is also called & quot; D-value method & quot< br />
3. Under pressure and torsion
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5. If you only calculate the axial force of the column under static force, you can use the above method, but pay attention to the combination coefficient. If we calculate the axial force under wind or earthquake, we have to use the moment distribution.
6. There is no 7.6 in the axis
set the concentrated wind load on the top floor as h, H × Top floor height ÷ AC＝2.9 Here AC is the distance between a and C.
set the concentrated wind load on the top floor as h, H × Top floor height ÷ AC＝2.9 Here AC is the distance between a and C.
7.
After controlling the bending moment M of the section, the M diagram is made first; Then, the member is intercepted from the M diagram. Considering the bending moment M at the end of the member (M acts on the end of the member according to the actual direction) and the external load on the member, the shear force FQ is calculated by using the member balance, and the FQ diagram is drawn; Then, the node is intercepted from the FQ diagram. Considering the FQ (FQ is drawn according to the actual direction) and the node load, the axial force FN is calculated by using the node balance, and the axial force FN diagram is drawn
The relationship betweenbending moment MFZ, external force ty and shear force py is as follows: &; Mfz/∂ x=-Ty, ∂ Ty/∂ x=-py So the relationship between bending moment and shear force is & 8706; 2Mfz/∂ x2=py
extended data:
in the no load area, when the shear diagram is parallel to the X axis, the bending moment diagram is an oblique line. When the shear diagram is positive, the bending moment diagram slants downward to the right; When the shear diagram is negative, the bending moment diagram slants upward to the right. Under the action of uniform load, the law is: load downward, shear force downward to the right, bending moment concave upward
at the action of concentrated force, the shear diagram changes suddenly, and the absolute value of the change is equal to the size of concentrated force; The bending moment diagram changes. There is a sudden change in the moment diagram of the concentrated couple, and the absolute value of the sudden change is equal to the moment of the concentrated couple; There is no change in shear diagram. There is an extreme value of bending moment at zero shear force
8. Best answer: after controlling the bending moment M of the section, make the M diagram first; Then, the member is intercepted from the M diagram. Considering the bending moment M at the end of the member (M acts on the end of the member according to the actual direction) and the external load on the member, the shear force FQ is calculated by using the member balance, and the FQ diagram is drawn; And then by
9. After calculating the bending moment M of each control section, the M diagram is drawn first; Then, the member is intercepted from the M diagram. Considering the bending moment M at the end of the member (M acts on the end of the member according to the actual direction) and the external load on the member, the shear force FQ is calculated by using the member balance, and the FQ diagram is drawn; Then, the node is intercepted from the FQ diagram. Considering the FQ (FQ is drawn according to the actual direction) and the node load, the axial force FN is calculated by using the node balance, and the axial force FN diagram is drawn.
10. The internal force of frame structure under vertical load can be approximately calculated by the layered method. In the internal force analysis under the vertical load, it can be assumed that: (1) the vertical load acting on the frame beam of one floor has no effect on the frame beam of other floors, but only the frame beam of this floor and the frame column connected with the frame beam of this floor proce bending moment and shear force 2) Under the vertical load, the lateral displacement of the frame is not considered. The calculation process can be as follows: (1) delamination: the upper and lower ends of the columns in the layered frame are assumed to be fixed end supports; (2) calculation of each independent rigid frame element: the moment distribution method or iterative method is used to calculate each independent rigid frame element.. The internal force of each layer of beam calculated by layer is the internal force of the corresponding layer of beam in the original frame structure 3) Superposition: after the structural internal forces of each independent frame are obtained, the internal forces of columns with the same floor and column number in two adjacent independent frames can be superimposed as the internal forces of columns in the original frame structure. Since the bending moment at the column joint of the frame is the sum of the upper and lower layers of the column, the bending moment diagram after superposition is often unbalanced at the frame joint. This is e to the error caused by the difference between the layered computing unit and the actual structure. In order to improve the accuracy, the unbalanced bending moment of the joints, especially the side joints, can be redistributed and corrected.
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