A method for calculating the strength and stability of a statically indeterminate tripod structure

Abstract

The present invention discloses a method for calculating the strength and stability forces of a statically indeterminate tripod structure, including: assuming that the cantilever beam in the cantilever steel structure of the tripod is fixed at point A, and the hinge points of the diagonal braces are points B and C; determining that the load applied to the cantilever steel structure of the tripod is P; measuring the angle α between the diagonal brace BC and the horizontal direction, the horizontal distance L1 between point A and point C, and the horizontal distance L2 between point C and point D; calculating the load F borne by the diagonal brace BC according to the load P applied to the cantilever steel structure of the tripod, the angle α between the diagonal brace BC and the horizontal direction, the horizontal distance L1 between point A and point C, and the horizontal distance L2 between point C and point D BC , and this method can calculate the load borne by the diagonal brace in the cantilever steel structure of the tripod relatively accurately.

Description

Technical Field

[0001] The invention relates to a force calculation method, in particular to a force calculation method for the strength and stability of an over-statically indeterminate tripod structure. Background Art

[0002] There are a large number of tripod cantilever steel structures in engineering construction, which play the role of bearing the weight of suspended equipment. Usually, the strength and stability checks of this kind of structure are mostly based on empirical formulas and computer simulation calculations, which have problems such as excessive safety margins, overly complex professional software, and long modeling calculation cycles. In addition, due to the differences in the level of calculation personnel and the differences in on-site structures, empirical formulas and calculation simulations are also difficult to ensure the applicability of tripod cantilever steel structures for analysis, and therefore cannot accurately calculate the load borne by the diagonal brace. Summary of the invention

[0003] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a method for calculating the strength and stability of an over-statically indeterminate tripod structure. The method can more accurately calculate the load borne by the diagonal brace in the tripod cantilever steel structure.

[0004] To achieve the above-mentioned purpose, the method for calculating the strength and stability of a hyperstatic tripod structure according to the present invention includes:

[0005] Assume that the cantilever beam in the tripod cantilever steel structure is fixed at point A, and the hinge points of the diagonal brace are points B and C;

[0006] Determine the load on the tripod cantilever steel structure as P;

[0007] Measure the angle α between the diagonal brace BC and the horizontal direction, the horizontal distance L1 between point A and point C, and the horizontal distance L2 between point C and point D;

[0008] According to the load P on the tripod cantilever steel structure, the angle α between the diagonal brace BC and the horizontal direction, the horizontal distance L1 between point A and point C, and the horizontal distance L2 between point C and point D, calculate the load F borne by the diagonal brace BC BC .

[0009] The load F borne by the diagonal brace BC BC for:

[0010]

[0011] The maximum load F that the brace BC can bear BCmax for:

[0012] F BCmax =Aσ s (2)

[0013] Among them, A is the cross-sectional area of ​​the steel section, σ s is the allowable stress of steel.

[0014] Also includes:

[0015] The load F borne by the diagonal brace BC BC The maximum load F that the brace BC can bear BCmax For comparison, when F BC ≤F BCmax When , it means that the diagonal brace BC is in a safe state.

[0016] The present invention has the following beneficial effects:

[0017] The method for calculating the strength and stability of a hyperstatic tripod structure according to the present invention only needs to measure the parameters of the tripod cantilever steel structure during specific operation, and the load borne by the diagonal brace BC can be calculated according to the load P borne by the tripod cantilever steel structure and the parameters of the tripod cantilever steel structure. The calculation complexity is low and the method is not affected by the differences in the calculation personnel's level and the differences in the on-site structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is the force analysis model diagram of the tripod cantilever steel structure;

[0019] Figure 2 The deflection analysis diagram of the deformation coordination condition of the tripod cantilever steel structure. DETAILED DESCRIPTION

[0020] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only an embodiment of a part of the present invention, not all embodiments, and is not intended to limit the scope of the present invention. In addition, in the following description, the description of well-known structures and technologies is omitted to avoid unnecessary confusion of the concepts disclosed in the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work should fall within the scope of protection of the present invention.

[0021] The accompanying drawings show schematic diagrams of structures according to embodiments disclosed in the present invention. These figures are not drawn to scale, and some details are magnified and some details may be omitted for the purpose of clear expression. The shapes of various regions and layers shown in the figures and the relative sizes and positional relationships therebetween are only exemplary, and may deviate in practice due to manufacturing tolerances or technical limitations, and those skilled in the art may additionally design regions / layers with different shapes, sizes, and relative positions according to actual needs.

[0022] refer to Figure 1 The method for calculating the strength and stability of a hyperstatic tripod structure according to the present invention comprises the following steps:

[0023] Assuming that the cantilever beam in the tripod cantilever steel structure is fixed at point A, and the hinge points of the diagonal brace are points B and C, the purpose of the present invention is to solve the force and moment at point A and the force of the diagonal brace BC, and to analyze the relationship between the load and the failure of the diagonal brace BC.

[0024] Among them, the force on the diagonal brace BC is F BC , the load on the tripod cantilever steel structure is P.

[0025] The tripod cantilever steel structure is a primary hyperstatic structure, and a deformation coordination equation needs to be added. Ignoring the compression of the diagonal brace BC and the deformation of the rigid part CE, the vertical displacement of point E is 0. From material mechanics, when there is no diagonal brace BC, the load P causes point E of the cantilever beam AD to move downward, such as Figure 2 shown.

[0026] Only force F BC When acting, point E is equivalent to the force F BC and a moment M E , force F BC The moment causes the upward displacement of point E of the cantilever beam AD by δ PE for:

[0027]

[0028]

[0029] The deformation coordination equation, force and moment balance equations are:

[0030]

[0031] ∑F X =0 F AX -F BC Cosα=0

[0032] ∑F Y =0 F BC Sinα+F AY -P=0

[0033] ∑M C =0 PL2+L1F AY +M A -aF AX =0

[0034] The load F borne by the diagonal brace BC is BC for:

[0035]

[0036] Among them, α is the angle between the diagonal brace BC and the horizontal direction, L1 is the horizontal distance between point A and point C, L2 is the horizontal distance between point C and point D, and P is the load on the tripod cantilever steel structure.

[0037] The above is the stress condition of the diagonal brace BC. We continue to use the material yield condition of Hooke's law to evaluate the safety of the diagonal brace.

[0038] The maximum load F that the brace BC can bear BCmax for:

[0039] F BCmax =Aσ s (2)

[0040] Among them, A is the cross-sectional area of ​​the steel section, σ s is the allowable stress of steel.

[0041] The load F borne by the diagonal brace BC BC The maximum load F that the diagonal brace BC can bear BCmax For comparison, when F BC ≤F BCmax When , it means that the diagonal brace BC is in a safe state.

Claims

1. A method for calculating the strength and stability of a statically indeterminate tripod structure, characterized in that: include: Assume that the cantilever beam in the tripod cantilever steel structure is fixed at point A, and the hinge points of the diagonal brace are points B and C; Determine the load on the tripod cantilever steel structure as P; Measure the angle α between the diagonal brace BC and the horizontal direction, the horizontal distance L1 between point A and point C, and the horizontal distance L2 between point C and point D; According to the load P on the tripod cantilever steel structure, the angle α between the diagonal brace BC and the horizontal direction, the horizontal distance L1 between point A and point C, and the horizontal distance L2 between point C and point D, calculate the load F borne by the diagonal brace BC BC ; The load F borne by the diagonal brace BC BC for: The maximum load F that the brace BC can bear BCmax for: F BCmax =Aσ s (2) Among them, A is the cross-sectional area of ​​the steel section, σ s is the allowable stress of steel, and a is the vertical distance from point C to point D.

2. The method for calculating the strength and stability of a statically indeterminate tripod structure according to claim 1, characterized in that: Also includes: According to the load F borne by the diagonal brace BC BC The maximum load F that the brace BC can bear BCmax Determine whether the diagonal brace BC is in a safe state.

3. The method for calculating the strength and stability of a statically indeterminate tripod structure according to claim 2, characterized in that: When F BC ≤F BCmax When , it means that the diagonal brace BC is in a safe state.

4. The method for calculating the strength and stability of a statically indeterminate tripod structure according to claim 2, characterized in that: When F BC Greater than F BCmax , it means that the diagonal brace BC is not in a safe state.

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