A multi-platform installation-free stress analysis method and system

Abstract

The application discloses a multi-platform installation-free stress analysis method and system, comprising the following steps: constructing a standardized section database; performing multi-load beam analysis calculation; performing strength and deflection checking; and performing real-time visual output. Based on the static force balance and superposition principle, the application calculates the shearing force, bending moment and deflection point by point for multiple concentrated load conditions, adopts a segmented analysis formula for accurate solution, is high in calculation accuracy and fast in speed, and avoids finite element discrete error and modeling time consumption.

Description

Technical Field

[0001] This invention relates to the field of simply supported beams, specifically to a multi-platform, installation-free stress analysis method and system. Background Technology

[0002] Simply supported beams, as one of the most basic load-bearing components in engineering structures, are widely used in elevator frames, mechanical skeletons, building floors, and bridges. Their load-bearing performance directly affects the structural safety and reliability; therefore, the calculation of bending moment, shear force, deflection, and strength verification of beams are essential steps in engineering design.

[0003] Currently, beam calculations mainly rely on the following methods: first, manually consulting steel section handbooks to obtain section characteristic parameters and performing calculations manually or using Excel spreadsheets in conjunction with material mechanics formulas; second, using general-purpose finite element analysis software (such as ANSYS, ABAQUS, etc.) for modeling and analysis; and third, using some specialized calculation tools. These methods have the following problems:

[0004] Manual table lookup calculations are inefficient, requiring the consulting of manuals for section property parameters, making it impossible to directly obtain data for non-standard sections. Furthermore, calculations for multiple load superposition conditions are cumbersome and prone to errors. While general-purpose finite element software is powerful, it has a high learning curve, is time-consuming to model, and sometimes requires a dedicated workstation. For conventional structures like simply supported beams, this is also a waste of resources. Existing specialized tools are mostly PC-based software, which cannot be used for mobile calculations. They often only support table lookup for standard profiles or single-load calculations, and the material library is disconnected from the calculation of custom sections. This makes it difficult to handle multiple load conditions and lacks real-time visual feedback. As a result, designers have to switch repeatedly between multiple software programs or documents, data transfer is prone to errors, and overall efficiency is low.

[0005] Based on the above problems, the applicant proposes a multi-platform, installation-free stress analysis method and system. Summary of the Invention

[0006] The purpose of this invention is to provide a multi-platform, installation-free stress analysis method and system to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A multi-platform, installation-free stress analysis method includes: S1, construct a standardized profile database, store the moment of inertia, section bending modulus and cross-sectional area of ​​multiple types of channel steel, I-beam, H-beam, angle steel, rectangular tube, square tube, round tube and round steel, and can automatically traverse and fill in the section characteristic parameters; For non-standard cross-sections, the user-input geometric parameters are received, and the cross-sectional characteristic parameters are calculated in real time using the following methods: a. Applying the centerline method: For thin-walled sections, divide them into several straight elements along the centerline of the wall thickness. The length of each element is taken as the actual length of the centerline segment, and an equivalent cross-sectional area is assigned. This equivalent area is equal to the product of the element length and the wall thickness. Then, determine the cross-sectional characteristic parameters of each element relative to its own local centroidal axis. b. Apply the parallel axis theorem: Establish a global cross-sectional coordinate system, use the equivalent cross-sectional area of ​​each element as the weight, and determine the centroid position of the global cross-section by weighted summation; then, perform axis shifting conversion on the cross-sectional characteristic parameters of each element relative to its own local centroidal axis according to the position of the global centroidal axis, and synthesize the cross-sectional moment of inertia and cross-sectional bending modulus of the global cross-section by superimposing them segment by segment. S2, perform analytical calculation of multi-load beam: Based on the section characteristic parameters obtained in S1, configure the beam geometric parameters, material properties and multi-node concentrated loads, solve the support reaction force through static equilibrium, and calculate the shear force, bending moment and deflection distribution point by point along the beam length to obtain the mechanical calculation results, including the maximum shear force, maximum bending moment and maximum deflection; S3, Strength and Deflection Verification: Based on the mechanical calculation results obtained in S2, calculate the maximum shear stress, maximum bending stress, and combined stress. Then, compare the maximum bending stress, maximum shear stress, and combined stress with their corresponding allowable stresses, and compare the maximum deflection with the allowable deflection ratio. Finally, obtain the actual safety factor, classify and judge the structural safety, and output the verification conclusion. S4. Real-time visualization output: Finally, based on the mechanical calculation results of S2 and the verification conclusions of S3, draw the cross-sectional schematic diagram and load diagram using Canvas, draw the bending moment diagram, shear force diagram and deflection curve using ECharts, and output the summary data table.

[0008] Further, S2 includes: Receive beam length L, elastic modulus E, yield stress [σ], safety factor [n], allowable deflection ratio and impact coefficient K; Multiple node loads can be configured, and the first and last nodes are automatically identified as supports. Determining support reactions through static equilibrium: , , In the formula: R B R is the reaction force at the right support. A This is the reaction force at the left support; Discretize the beam along its length into N calculation points, and calculate each point individually: Shear force V(x) at a distance x from the left end: , Bending moment M(x) at a distance x from the left end: , Deflection f(x) at a distance x from the left end: Using the superposition method, for each individual concentrated load P i Let a = x i b=Lx i but: , , In the formula: P i This represents the concentrated load at the i-th node; x is the distance from any calculated point on the beam to the left end; x i For the i-th load P i The position of action, distance from the left end; 'a' represents the superposition method for a single load P. i The temporary position variable is taken, a=x i ; b represents the load P. i Distance from the right end, b=La=Lx i ; I is the moment of inertia of the cross section; Extract the maximum shear force V from the shear force distribution V(x). max Extract the maximum bending moment M from the bending moment distribution M(x) max Extract the maximum deflection f from the deflection distribution f(x) max The mechanical calculation results are obtained.

[0009] Further, S3 includes: The maximum bending moment M calculated based on S2 max Using the section modulus W obtained from S1, calculate the bending stress σ according to the bending stress formula: , The maximum shear force V calculated based on S2 max The cross-sectional area A obtained from S1 s The maximum shear stress τ is calculated using the shear stress formula: , Calculate the composite stress σ according to the third strength theory. eq : , The maximum bending stress σ, the maximum shear stress τ, and the combined stress σ eq The strength check conditions are obtained by comparing them with the allowable stress and introducing the design safety factor [n]. , , , Meanwhile, the maximum deflection f obtained based on S2 max Combining beam length L and allowable deflection ratio By determining the deflection limit, the stiffness check conditions are obtained: , The actual safety factor is deduced from the strength verification results: , In the above formula: Compare n with the input design safety factor [n], and output the structural safety status according to the ratio of the two, and output the verification conclusion.

[0010] Further, S4 includes: Draw a cross-sectional diagram using Canvas and label the parameter codes; A simplified beam load diagram is drawn using Canvas, dynamically displaying supports, force arrows, and position scale. It uses ECharts to draw bending moment diagrams, shear force diagrams, and deflection curves, and supports maximum / minimum value marking, zero line reference, and interactive prompts.

[0011] This invention also provides a multi-platform, installation-free stress analysis system for implementing the multi-platform, installation-free stress analysis method described above, comprising:

[0012] The section property parameter acquisition module is used to store the standardized profile database and receive the geometric parameters of non-standard sections input by the user. Based on the centerline method and the parallel axis theorem, it calculates the section property parameters in real time.

[0013] The multi-load beam analytical calculation module is used to receive beam length L, material elastic modulus E, yield stress, safety factor, allowable deflection ratio and impact coefficient, configure multiple nodal loads, automatically identify the first and last nodes as supports, calculate the support reaction force through static equilibrium, and discretize along the beam length into N calculation points to calculate shear force, bending moment and deflection based on the superposition principle point by point.

[0014] The strength-deflection verification module is used to calculate bending stress, deflection limit, and actual safety factor.

[0015] The real-time visualization module is used to draw cross-sectional schematic diagrams and load diagrams based on Canvas, and to draw bending moment diagrams, shear force diagrams and deflection curves based on ECharts. It also supports extreme value marking, zero line reference and interactive prompts.

[0016] Compared with the prior art, the beneficial effects of the present invention are:

[0017] (1) Cross-platform and installation-free: Based on pure HTML5 / JavaScript and browser interpretation and execution mechanism, it does not require installation and configuration. It can run consistently in browsers on all platforms including Windows, macOS, Linux desktops and iOS and Android mobile devices, achieving true plug-and-play functionality;

[0018] (2) Material library and custom section integration: Directly traverse the built-in standardized profile database, and at the same time provide real-time analysis of custom sections such as rectangular hollow tubes, round tubes, round steel, L-shaped angle steel, and C-shaped sheet metal using the centerline method and parallel axis theorem, covering all standard and non-standard scenarios, without the need for external table lookup or CAD assistance;

[0019] (3) Accurate analysis of multiple loads: Based on the principle of static equilibrium and superposition, the shear force, bending moment and deflection of multiple concentrated load conditions are calculated point by point. The piecewise analytical formula is used to solve the problem accurately, which has high calculation accuracy and fast speed, avoiding the discretization error of finite element and the time consumption of modeling.

[0020] (4) Dual control verification of strength and deflection: Simultaneously output the bending strength safety factor and deflection ratio to realize dual engineering control of stress and deformation, and provide graded early warning of structural safety status;

[0021] (5) Real-time visualization across the entire chain: The calculation engine and visualization module work together with zero latency. Canvas draws cross-sectional diagrams and load diagrams, and ECharts renders bending moment diagrams, shear force diagrams and deflection curves. Parameter modifications are recalculated and all outputs are updated immediately, improving the efficiency of iterative design. Attached Figure Description

[0022] Figure 1 This is a flowchart of a multi-platform, installation-free stress analysis method according to the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] Please see Figure 1 A multi-platform, installation-free stress analysis method, comprising:

[0025] S1, Obtain cross-sectional characteristic parameters. The system has a standardized profile database that stores the cross-sectional moment of inertia, section bending modulus, and cross-sectional area of ​​channel steel, I-beam, H-beam, angle steel, rectangular tube, square tube, round tube, round steel, etc. The cross-sectional characteristic parameters can be automatically traversed and filled in.

[0026] For non-standard cross-sections, the user-input geometric parameters are received, and the cross-sectional characteristic parameters are calculated in real time using the following methods:

[0027] a. Applying the centerline method: For thin-walled sections, divide them into several straight elements along the centerline of the wall thickness. The length of each element is taken as the actual length of the centerline segment, and an equivalent cross-sectional area is assigned. This equivalent area is equal to the product of the element length and the wall thickness. Then, determine the cross-sectional characteristic parameters of each element relative to its own local centroidal axis.

[0028] b. Apply the parallel axis theorem: Establish a global cross-sectional coordinate system, use the equivalent cross-sectional area of ​​each element as the weight, and determine the centroid position of the global cross-section by weighted summation; then, perform axis shifting conversion on the cross-sectional characteristic parameters of each element relative to its own local centroidal axis according to the position of the global centroidal axis, and synthesize the global cross-sectional moment of inertia and cross-sectional bending modulus by superimposing them segment by segment.

[0029] The system supports bidirectional switching between strong and weak axes. When the user selects different principal axis directions, the corresponding cross-sectional characteristic parameters are automatically recalculated and updated.

[0030] S2, performing analytical calculations of the beam under multiple loads: Based on the section characteristic parameters obtained in S1, the beam's geometric parameters, material properties, and multi-node concentrated loads are configured. Support reactions are solved through static equilibrium, and shear force, bending moment, and deflection distribution are calculated point-by-point along the beam length to obtain the mechanical calculation results, including maximum shear force, maximum bending moment, and maximum deflection. Specifically, this includes:

[0031] Receive beam length L, elastic modulus E, yield stress [σ], safety factor [n], allowable deflection ratio and impact coefficient K;

[0032] Multiple node loads can be configured, and the first and last nodes are automatically identified as supports.

[0033] Determining support reactions through static equilibrium:

[0034]

[0035]

[0036] In the formula: R B R is the reaction force at the right support. A This is the reaction force at the left support.

[0037] Discretize the beam along its length into N calculation points, and calculate each point individually:

[0038] Shear force V(x) at a distance x from the left end:

[0039]

[0040] Bending moment M(x) at a distance x from the left end:

[0041]

[0042] Deflection f(x) at a distance x from the left end: Using the superposition method, for each individual concentrated load P i (located at x) i (place), let a=x i b=Lx i ,but:

[0043]

[0044]

[0045] In the formula:

[0046] P i This represents the concentrated load at the i-th node;

[0047] x is the distance from any calculated point on the beam to the left end (traversal variable, 0≤x≤L);

[0048] x i For the i-th load P i The position of action, distance from the left end;

[0049] 'a' represents the superposition method for a single load P. i The temporary position variable is taken, a=x i ;

[0050] b represents the load P. i Distance from the right end, b=La=Lx i ;

[0051] I represents the moment of inertia of the cross section.

[0052] Extract the maximum shear force V from the shear force distribution V(x). max Extract the maximum bending moment M from the bending moment distribution M(x) max Extract the maximum deflection f from the deflection distribution f(x) max The mechanical calculation results are obtained.

[0053] S3, Strength and Deflection Verification: Based on the mechanical calculation results obtained in S2, calculate the maximum shear stress, bending stress, and combined stress. Then, compare the maximum bending stress, maximum shear stress, and combined stress with their corresponding allowable stresses, and compare the maximum deflection with the allowable deflection ratio. Finally, obtain the actual safety factor, classify and assess the structural safety, and output the verification conclusion. Specifically, this includes:

[0054] The maximum bending moment M calculated based on S2 max Using the section modulus W obtained from S1, calculate the bending stress σ according to the bending stress formula:

[0055]

[0056] The maximum shear force V calculated based on S2 max The cross-sectional area A obtained from S1 s The maximum shear stress τ is calculated using the shear stress formula:

[0057]

[0058] Calculate the composite stress (equivalent stress) according to the third strength theory (maximum shear stress theory):

[0059]

[0060] The maximum bending stress σ, the maximum shear stress τ, and the combined stress σ eq The strength check conditions are obtained by comparing them with the allowable stress and introducing the design safety factor [n].

[0061]

[0062]

[0063]

[0064] Meanwhile, the maximum deflection f obtained based on S2 max Combining beam length L and allowable deflection ratio By determining the deflection limit, the stiffness check conditions are obtained:

[0065]

[0066] The actual safety factor is deduced from the strength verification results:

[0067]

[0068] In the above formula:

[0069] W is the section bending modulus;

[0070] M max The maximum bending moment;

[0071] V max This is the maximum shear force;

[0072] f max Maximum deflection;

[0073] [σ] represents the allowable bending stress and the allowable combined stress;

[0074] [τ] is the allowable shear stress, taken as [τ] = 0.6 [σ].

[0075] [n] represents the allowable safety factor;

[0076] Allowable deflection ratio;

[0077] σ is the actual bending stress;

[0078] τ is the actual bending stress;

[0079] σ eq This represents the actual composite stress.

[0080] A s The cross-sectional area;

[0081] n is the actual safety factor.

[0082] For a typical slender beam (L / section height H>20), bending stress σ is absolutely dominant, and composite stress σ eq ≈σ; however, for short beams and near-support load conditions, the shear stress τ contributes significantly, so σ needs to be used as the approximation. eq Control design.

[0083] Compare n with the input design safety factor [n], and output the structural safety status according to the ratio of the two, and output the verification conclusion.

[0084] S4, Real-time Visualization Output: Finally, based on the mechanical calculation results of S2 and the verification conclusions of S3, a cross-sectional schematic diagram and load diagram are drawn using Canvas, and bending moment diagram, shear force diagram, and deflection curve are drawn using ECharts, and a summary data table is output. Specifically, this includes:

[0085] Draw a cross-sectional diagram using Canvas and label the parameter codes;

[0086] A simplified beam load diagram is drawn using Canvas, dynamically displaying supports, force arrows, and position scale.

[0087] Based on ECharts, it can draw bending moment diagrams (BMD), shear force diagrams (SFD), and deflection curves, and supports maximum / minimum value marking, zero line reference, and interactive prompts.

[0088] S5 runs on multiple platforms without installation, including:

[0089] The system is built on pure HTML5 / JavaScript and uses a browser-interpreted execution mechanism, ensuring cross-platform compatibility. Through user agent adaptive rendering, it runs consistently across all platforms, including Windows, macOS, Linux desktops, and iOS and Android mobile devices. The computing engine and visualization modules are all executed locally on the client side, requiring no server interaction or network dependencies.

[0090] This invention also provides a multi-platform, installation-free stress analysis system for implementing the multi-platform, installation-free stress analysis method described above, comprising:

[0091] Section property parameter acquisition module: This module stores a standardized profile database and receives geometric parameters of non-standard sections input by the user. Based on the centerline method and the parallel axis theorem, it calculates the section property parameters in real time. The section property parameter acquisition module is a computer program, and its specific implementation refers to S1 of the above analysis method.

[0092] Multi-load beam analytical calculation module: used to receive beam length L, material elastic modulus E, yield stress [σ], safety factor [n], and allowable deflection ratio. and impact coefficient, configured with multiple nodal loads (P) i ,x i )

[0093] The system automatically identifies the first and last nodes as supports, calculates the support reactions through static equilibrium, and discretizes the beam length into N calculation points to calculate shear force, bending moment, and deflection based on the superposition principle point by point. The multi-load beam analytical calculation module is a computer program, and its specific implementation refers to S2 of the above analysis method.

[0094] Strength-deflection verification module: Used to calculate bending stress, deflection limits, and actual safety factor. The strength-deflection verification module is a computer program, and its implementation is detailed in section S3 of the aforementioned analysis method.

[0095] Real-time visualization module: Used to draw cross-sectional schematics and load diagrams based on Canvas, and to draw bending moment diagrams, shear force diagrams, and deflection curves based on ECharts. It also supports extreme value marking, zero-line reference, and interactive prompts. The real-time visualization module is a computer program, and its specific implementation refers to S4 of the above analysis method.

[0096] Example 1 – Standard Channel Steel Selection Verification

[0097]

Substitute parameters

[0098] The component has a standard cross-section: 16a channel steel.

[0099] Beam length: L=2500 mm

[0100] Automatic traversal of the material property library for cross-sectional property parameters:

[0101] Moment of inertia of cross section: I x =866.2 cm 4 =8.662×10 6 mm 4

[0102] Section flexural modulus: W x =108.3cm 3 =1.083×10 5 mm 3

[0103] Cross-sectional area: A s =2195 mm 2

[0104] Material properties: Elastic modulus E = 206000 MPa

[0105] Yield stress [σ] = 235 MPa

[0106] Design safety factor: [n] = 2

[0107] Allowable deflection ratio:

[0108] Static load: P = 10000 N, impact coefficient k = 2, therefore the design load P d =P×2=20000 N acts at the mid-span x=1250 mm

[0109] Solution process

[0110] Calculate the support reactions, maximum bending moment, maximum shear force, bending stress, shear stress, combined stress, actual safety factor, maximum deflection and deflection ratio, and determine the structural safety status.

[0111] (1) Support reaction force

[0112]

[0113]

[0114] (2) Maximum bending moment (located at mid-span x=1250 mm)

[0115]

[0116] (3) Maximum bending stress

[0117]

[0118] (4) Maximum shear force (located inside the support)

[0119]

[0120] (5) Maximum shear stress

[0121]

[0122] (6) Composite stress (third strength theory)

[0123] (7) Strength verification

[0124] Allowable stress:

[0125] Allowable shear stress: ,

[0126]

[0127]

[0128] (critical)

[0129] (8) Actual safety factor

[0130]

[0131] (9) Maximum deflection (mid-span, x=1250 mm, b=Lx=1250 mm)

[0132] (10) Deflection check

[0133]

[0134]

in conclusion

[0135] (critical),

[0136] (critical), .

[0137] Both strength and deflection meet the requirements, and the result card shows "critical state (yellow)".

[0138] Example 2 – Selection and Verification of Non-Standard Cross-Section Components (Non-Standard Rectangular Tube)

[0139]

Substitute parameters

[0140] The component has a non-standard cross-section: a user-defined rectangular tube 80×60×4 (Q235), with inputs B=80 mm, H=60 mm, and t=4 mm.

[0141] Beam length: L=2500 mm

[0142] Moment of inertia of cross section:

[0143] Section flexural modulus:

[0144] Cross-sectional area: A s =1056 mm 2

[0145] Material properties: E = 206000 MPa, [σ] = 235 MPa

[0146] Design safety factor: [n] = 2

[0147] Allowable deflection ratio:

[0148] Static load: P = 10000 N, impact factor is taken as 2, design load P d =20000 N is applied at the mid-span x=1250mm

[0149] Solution process

[0150] Calculate all internal forces, stresses, safety factors, and deflections, and determine the structural safety status.

[0151] (1) Support reaction force

[0152]

[0153]

[0154] (2) Maximum bending moment

[0155]

[0156] (3) Maximum bending stress

[0157]

[0158] (4) Maximum shear force

[0159]

[0160] (5) Maximum shear stress

[0161]

[0162] (6) Composite stress

[0163]

[0164] (7) Strength verification

[0165]

[0166] (8) Actual safety factor

[0167]

[0168] (9) Maximum deflection

[0169] (10) Deflection check

[0170]

[0171]

in conclusion

[0172] ,

[0173] ,and .

[0174] Both strength and deflection are severely insufficient, and the result card shows "Insufficient Strength (red)".

[0175] Example 3 – Multi-load Condition

[0176]

Substitute parameters

[0177] Component type: Channel steel 14a

[0178] Beam length: L = 3000 mm

[0179] Automatic traversal of the material property library for cross-sectional property parameters:

[0180] Moment of inertia I of cross section x =564 cm 4 =5.64×10 6 mm 4

[0181] Section flexural modulus W x =80.5 cm 3 =8.05×10 4 mm 3

[0182] Cross-sectional area: A s =1851 mm 2

[0183] Material properties: E = 206000 MPa, [σ] = 235 MPa

[0184] Design safety factor: [n] = 2

[0185] Allowable deflection ratio:

[0186] Node configuration (3 nodes), static load and design load with an impact coefficient of 2:

[0187] Node 1: Static load 8000 N, design load P1 = 16000 N, x1 = 800 mm

[0188] Node 2: Static load 12000, design load P2=24000 N, x2=1800 mm

[0189] Node 3: Static load 8000, design load P3 = 16000 N, x2 = 2500 mm

[0190] Solution process

[0191] Calculate the support reactions, maximum bending moment, maximum shear force, bending stress, shear stress, combined stress, actual safety factor, maximum deflection and deflection ratio, and determine the structural safety status.

[0192] (1) Support reaction force

[0193]

[0194]

[0195]

[0196] (2) Maximum bending moment

[0197] Calculate the bending moment point by point:

[0198]

[0199] Therefore, the maximum bending moment is located at x2 = 1800 mm:

[0200]

[0201] (3) Maximum shear force (located inside the right support)

[0202]

[0203] (4) Maximum bending stress

[0204]

[0205] (5) Maximum shear stress

[0206]

[0207] (6) Combined stress

[0208]

[0209] (7) Strength check

[0210]

[0211] (8) Actual safety factor

[0212]

[0213] (9) Maximum deflection (superposition method, calculate the three loads separately and sum them at x≈1700 mm)

[0214] For P1=16000 N (a=800 mm, b1=2200 mm), use the right section formula at x=1700 mm (>a): For P2=24000 N (a=1800 mm, b2=1200 mm), use the left section formula at x=1700 mm (<a): For P3=16000 N (a=2500 mm, b3=500 mm), use the left section formula at x=1700 mm (<a):

[0215]

[0216] (10) Deflection check

[0217]

[0218] [Conclusion]

[0219]

[0220] , and .

[0221] Both strength and deflection are severely insufficient, and the result card displays "Insufficient Strength (Red)".

[0222] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A multi-platform, installation-free stress analysis method, characterized in that, include: S1, construct a standardized profile database, store the moment of inertia, section bending modulus and cross-sectional area of ​​multiple types of channel steel, I-beam, H-beam, angle steel, rectangular tube, square tube, round tube and round steel, and can automatically traverse and fill in the section characteristic parameters; For non-standard cross-sections, the user-input geometric parameters are received, and the cross-sectional characteristic parameters are calculated in real time using the following methods: a. Applying the centerline method: For thin-walled sections, divide them into several straight elements along the centerline of the wall thickness. The length of each element is taken as the actual length of the centerline segment, and an equivalent cross-sectional area is assigned. This equivalent area is equal to the product of the element length and the wall thickness. Then, determine the cross-sectional characteristic parameters of each element relative to its own local centroidal axis. b. Apply the parallel axis theorem: Establish a global cross-sectional coordinate system, use the equivalent cross-sectional area of ​​each element as the weight, and determine the centroid position of the global cross-section by weighted summation; then, perform axis shifting conversion on the cross-sectional characteristic parameters of each element relative to its own local centroidal axis according to the position of the global centroidal axis, and synthesize the cross-sectional moment of inertia and cross-sectional bending modulus of the global cross-section by superimposing them segment by segment. S2, perform analytical calculation of multi-load beam: Based on the section characteristic parameters obtained in S1, configure the beam geometric parameters, material properties and multi-node concentrated loads, solve the support reaction force through static equilibrium, and calculate the shear force, bending moment and deflection distribution point by point along the beam length to obtain the mechanical calculation results, including the maximum shear force, maximum bending moment and maximum deflection; S3, Strength and Deflection Verification: Based on the mechanical calculation results obtained in S2, calculate the maximum shear stress, maximum bending stress, and combined stress. Then, compare the maximum bending stress, maximum shear stress, and combined stress with their corresponding allowable stresses, and compare the maximum deflection with the allowable deflection ratio. Finally, obtain the actual safety factor, classify and judge the structural safety, and output the verification conclusion. S4. Real-time visualization output: Finally, based on the mechanical calculation results of S2 and the verification conclusions of S3, draw the cross-sectional schematic diagram and load diagram using Canvas, draw the bending moment diagram, shear force diagram and deflection curve using ECharts, and output the summary data table.

2. The multi-platform, installation-free stress analysis method according to claim 1, characterized in that, S2 includes: Receive beam length L, elastic modulus E, yield stress [σ], safety factor [n], allowable deflection ratio and impact coefficient K; Multiple node loads can be configured, and the first and last nodes are automatically identified as supports. Determining support reactions through static equilibrium: ， ， In the formula: R B R is the reaction force at the right support. A This is the reaction force at the left support; Discretize the beam along its length into N calculation points, and calculate each point individually: Shear force V(x) at a distance x from the left end: ， Bending moment M(x) at a distance x from the left end: ， Deflection f(x) at a distance x from the left end: Using the superposition method, for each individual concentrated load P i Let a = x i b=Lx i but: ， ， In the formula: P i This represents the concentrated load at the i-th node; x is the distance from any calculated point on the beam to the left end; x i For the i-th load P i The position of action, distance from the left end; 'a' represents the superposition method for a single load P. i The temporary position variable is taken, a=x i ; b represents the load P. i Distance from the right end, b=La=Lx i ; I is the moment of inertia of the cross section; Extract the maximum shear force V from the shear force distribution V(x). max Extract the maximum bending moment M from the bending moment distribution M(x) max Extract the maximum deflection f from the deflection distribution f(x) max The mechanical calculation results are obtained.

3. The multi-platform, installation-free stress analysis method according to claim 2, characterized in that, S3 includes: The maximum bending moment M calculated based on S2 max Using the section modulus W obtained from S1, calculate the bending stress σ according to the bending stress formula: ， The maximum shear force V calculated based on S2 max The cross-sectional area A obtained from S1 s The maximum shear stress τ is calculated using the shear stress formula: ， Calculate the composite stress σ according to the third strength theory. eq : ， The maximum bending stress σ, the maximum shear stress τ, and the combined stress σ eq The strength check conditions are obtained by comparing them with the allowable stress and introducing the design safety factor [n]. ， ， ， Meanwhile, the maximum deflection f obtained based on S2 max Combining beam length L and allowable deflection ratio By determining the deflection limit, the stiffness check conditions are obtained: ， The actual safety factor is deduced from the strength verification results: ， In the above formula: Compare n with the input design safety factor [n], and output the structural safety status according to the ratio of the two, and output the verification conclusion.

4. The multi-platform, installation-free stress analysis method according to claim 1, characterized in that, S4 includes: Draw a cross-sectional diagram using Canvas and label the parameter codes; A simplified beam load diagram is drawn using Canvas, dynamically displaying supports, force arrows, and position scale. It uses ECharts to draw bending moment diagrams, shear force diagrams, and deflection curves, and supports maximum / minimum value marking, zero line reference, and interactive prompts.

5. A multi-platform, installation-free stress analysis system, used to implement the multi-platform, installation-free stress analysis method as described in any one of claims 1-4, characterized in that, include: The section property parameter acquisition module is used to store the standardized profile database and receive the geometric parameters of non-standard sections input by the user. Based on the centerline method and the parallel axis theorem, it calculates the section property parameters in real time. The multi-load beam analytical calculation module is used to receive beam length L, material elastic modulus E, yield stress, safety factor, allowable deflection ratio and impact coefficient, configure multiple nodal loads, automatically identify the first and last nodes as supports, calculate the support reaction force through static equilibrium, and discretize along the beam length into N calculation points to calculate shear force, bending moment and deflection based on the superposition principle point by point. The strength-deflection verification module is used to calculate bending stress, deflection limit, and actual safety factor. The real-time visualization module is used to draw cross-sectional schematic diagrams and load diagrams based on Canvas, and to draw bending moment diagrams, shear force diagrams and deflection curves based on ECharts. It also supports extreme value marking, zero line reference and interactive prompts.

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