Computer mechanics analysis method for single-side bolted connection joint of fabricated component

Abstract

The application discloses a computer mechanical analysis method for single-side bolt connection joint of fabricated component, which comprises the following steps: 1, inputting parameters in the computer; 2, judging the joint bending moment M and joint axial force N, and initially calculating the height x of the outer edge of the compression zone to the neutral axis, the joint section rotation angle θ, the bolt tension T and the outer edge stress σ0 of the compression zone of the component; if the joint axial force N is a compression force, the initial calculation result is output; 4, under the condition that N is a compression force, comparing x and h, if x < h and T > 0 are obtained through the initial calculation, the initial calculation result is correct, and the initial calculation result is output; if not, x, θ, T and / or σ0 are modified; 5, outputting the modified data. The application can quickly and effectively analyze the stress state of the connection joint and the bolt through the computer, can liberate the designers from the mechanical checking calculation and further improves the design efficiency.

Description

Technical Field

[0001] This invention relates to the field of computer-aided design technology, and in particular to a computer-based mechanical analysis method for single-sided bolted joints of prefabricated components. Background Technology

[0002] Many existing prefabricated components use single-sided bolts for connection between components, such as bolts connecting shield tunnel segments on the inside of the segments. However, the stress state analysis of the connection joints and bolts is rarely mentioned. In design calculations and structural analysis, there is a lack of a convenient and quick method.

[0003] With the continuous development of computer technology, mechanical analysis of various complex situations can be performed quickly using computer software.

[0004] Therefore, how to use computers to quickly and effectively analyze the stress state of joints and bolts has become a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of the above-mentioned deficiencies of the prior art, the present invention provides a computer mechanical analysis method for single-sided bolted joints of prefabricated components. The purpose is to provide a method for quickly and effectively analyzing the stress state of the joints and bolts using a computer, thus filling the gap in the prior art.

[0006] To achieve the above objectives, this invention discloses a computer-based mechanical analysis method for single-sided bolted joints in prefabricated components, comprising the following steps:

[0007] Step 1: Input parameters into the computer, specifically including: joint bending moment M, joint axial force N, bolt preload T0, component cross-sectional width b, component cross-sectional height h, and distance a from the bolt to the tension zone or the edge with less compression. s E, the elastic modulus of concrete c Bolt elastic modulus E s And the tensile stiffness K of the bolt t ;

[0008] Step 2: Determine whether the joint bending moment M and the joint axial force N are compression or tension, and whether the joint bending moment M causes the bolt side section to be under tension or compression, respectively calculate the height x from the outer edge of the compression zone to the neutral axis, the joint section rotation angle θ, the bolt tension T, and the stress σ0 at the outer edge of the component compression zone.

[0009] If the axial force N at the joint is a tensile force, the initial calculation result will be output to complete the execution process;

[0010] Step 3. When the joint axial force N is compressive, compare the calculated height x from the outer edge of the compression zone to the neutral axis with the member cross-section height h. If x < h and T > 0 obtained through preliminary calculation, it indicates that the preliminary calculation result is correct. Output the preliminary calculation result to complete the execution process.

[0011] If not, correct the height x from the outer edge of the compression zone to the neutral axis, the joint cross-section rotation angle θ, the bolt tension T, and / or the stress σ0 at the outer edge of the member compression zone.

[0012] Step 4. Output the corrected data.

[0013] Preferably, the tensile stiffness K of the bolt t = E s A s / L s ; where A s is the bolt cross-sectional area; L s is the bolt length.

[0014] Preferably, in Step 2, when the joint axial force N is compressive and the joint bending moment M acts to cause tension in the bolt side cross-section, the calculation formulas for preliminarily calculating the height x from the outer edge of the compression zone to the neutral axis, the joint cross-section rotation angle θ, the bolt tension T, and the stress σ0 at the outer edge of the member compression zone are as follows:

[0015]

[0016]

[0017] T = T0 + (h0 - x)θk t ;

[0018]

[0019] where h0 is the distance from the bolt to the larger compression edge;

[0020] A1 is a process parameter, and the calculation formula is

[0021] B1 is a process parameter, and the calculation formula is

[0022] D1 is a process parameter, and the calculation formula is

[0023] l is the compression influence depth in the case where the joint axial force N is compressive and the joint bending moment M acts to cause tension in the bolt side cross-section;

[0024] N1” is a process parameter, and the calculation formula is N1' = N + T0;

[0025] M1' is a process parameter, and its calculation formula is

[0026] More preferably, in step 3, when the joint axial force N is compressive and the joint bending moment M acts to cause the bolt side cross-section to be in tension, when x < h and T ≯ 0, it indicates that the stress state of the joint at this time is that the bolts are loose and part of the cross-section is in compression. The height x from the outer edge of the compression zone to the neutral axis and the joint cross-section rotation angle θ are corrected. The specific formulas are as follows:

[0027]

[0028]

[0029] More preferably, in step 3, when the joint axial force N is compressive and the joint bending moment M acts to cause the bolt side cross-section to be in tension, when x ≮ h, it indicates that the entire contact surface of the segment joint is in compression. First, the joint cross-section rotation angle θ and the bolt tension T are corrected. The specific formulas are as follows:

[0030]

[0031]

[0032] After completion, if the corrected bolt tension T > 0, it indicates that the bolts are still in the tension state. Then, the stress σ0 at the outer edge of the compression zone of the member is corrected and the result is output. The specific formula is as follows:

[0033]

[0034]

[0035] If the corrected bolt tension T ≯ 0, it indicates that the bolts are in the loose state. The joint cross-section rotation angle θ and the stress σ0 at the outer edge of the compression zone of the member are corrected again and the result is output. The specific formulas are as follows:

[0036]

[0037]

[0038] Where, σ1 is the outer edge stress on the other side of the trapezoidal compression zone of the member opposite to the outer edge stress σ0 on one side.

[0039] Preferably, in step 2, when the joint axial force N is compressive and the joint bending moment M acts to cause the bolt side cross-section to be in compression, the calculation formulas for initially calculating the height x from the outer edge of the compression zone to the neutral axis, the joint cross-section rotation angle θ, the bolt tension T, and the stress σ0 at the outer edge of the compression zone of the member are as follows:

[0040]

[0041]

[0042] T = T0 - θ·(x - a s )k t ;

[0043]

[0044] Among them, h0 is the distance from the bolt to the edge with larger compression;

[0045] A2 is a process parameter, and its calculation formula is

[0046] B2 is a process parameter, and its calculation formula is

[0047] D2 is a process parameter, and its calculation formula is

[0048] More preferably, in step 3, when the joint axial force N is a pressure and the joint bending moment M acts to compress the bolt side section, when x < h and T ≯ 0, it indicates that the stress state of the joint at this time is bolt relaxation and partial section compression. The height x from the outer edge of the compression zone to the neutral axis and the joint section rotation angle θ are corrected, and the specific formulas are as follows:

[0049]

[0050]

[0051] More preferably, in step 3, when the joint axial force N is a pressure and the joint bending moment M acts to compress the bolt side section, when x ≮ h, it indicates that the entire contact surface of the segment joint is under compression. First, the joint section rotation angle θ and the bolt tension T are corrected, and the specific formulas are as follows:

[0052]

[0053]

[0054] Among them,

[0055]

[0056] A4 is a process parameter, and its calculation formula is

[0057] B4 is a process parameter, and its calculation formula is

[0058] C4 is a process parameter, calculated using the following formula:

[0059] D4 is a process parameter, calculated using the following formula:

[0060] E4 is a process parameter, calculated using the following formula:

[0061] I4 is a process parameter, and the calculation formula is I4 = N + T0;

[0062] Once completed, if the corrected bolt tension T > 0, it indicates that the bolt is still in the tensioned state. Output the result to complete all processes.

[0063] If the corrected bolt tension T≯0, it indicates bolt loosening. The joint section rotation angle θ and the outer edge stress σ0 of the component compression zone are then corrected again, and the results are output. The specific formula is as follows:

[0064]

[0065]

[0066] Wherein, σ1 is the outer edge stress on the other side of the trapezoidal compression zone of the component, opposite to the outer edge stress σ0 on one side.

[0067] Preferably, in step 2, when the axial force N of the joint is tensile, the initial calculation formulas for the height x from the outer edge of the compression zone to the neutral axis, the rotation angle θ of the joint section, the bolt tension T1, the tensile force T2 of the outer steel plate, and the stress σ0 at the outer edge of the compression zone of the component are as follows:

[0068]

[0069]

[0070] T1=-θ(xa s )k t +T0;

[0071] T2=(hx)θk s ;

[0072]

[0073] Where h0 is the distance from the bolt to the edge under greater pressure;

[0074] A3 is a process parameter, and the calculation formula is as follows:

[0075] B3 is a process parameter, and the calculation formula is as follows:

[0076] C3 is a process parameter, and its calculation formula is as follows:

[0077]

[0078] D3 is a process parameter, and its calculation formula is D3 = β / α;

[0079] E3 is a process parameter, calculated using the following formula:

[0080] α is a process parameter, and the calculation formula is:

[0081] β is a process parameter, and its calculation formula is β = hk s +a s k t ;

[0082] γ is a process parameter, and the calculation formula is:

[0083] The beneficial effects of this invention are:

[0084] This invention aims to quickly and effectively analyze the stress state of joints and bolts using a computer, freeing designers from mechanical verification calculations and further improving design efficiency.

[0085] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0086] Figure 1 This invention illustrates the execution flow under the condition that the joint axial force N is a compressive force and the joint bending moment M causes the bolt side section to be under tension, in one embodiment of the invention.

[0087] Figure 2 This invention illustrates the execution flow under the condition that the joint axial force N is pressure and the joint bending moment M causes the bolt side section to be compressed, in one embodiment of the invention.

[0088] Figure 3 This illustrates the execution flow of a tensile force N in the joint axial force according to an embodiment of the present invention.

[0089] Figure 4 This diagram illustrates the stress state of a bolt in one embodiment of the present invention, where the axial force is pressure, the bending moment causes the bolt side section to be under tension, and the section is under compression and the bolt is under tension.

[0090] Figure 5This diagram illustrates the stress at the joint location in an embodiment of the present invention, where the axial force is compressive, the bending moment causes the bolt side section to be under tension, and the section is partially under compression while the bolt is under tension.

[0091] Figure 6 This diagram illustrates the stress state of a bolt in one embodiment of the present invention, where the axial force is pressure, the bending moment causes the bolt side section to be under tension, and the section is under compression, resulting in a bolt in a relaxed state.

[0092] Figure 7 This diagram illustrates the stress at a joint location where the axial force is compressive, the bending moment causes the bolt side section to be under tension, and the section is under compression, resulting in a relaxed bolt state.

[0093] Figure 8 This diagram illustrates the bolt stress state in one embodiment of the present invention, where the axial force is pressure, the bending moment causes the bolt side section to be under tension, and the entire cross section is under compression and the bolt is under tension.

[0094] Figure 9 This diagram illustrates the stress at the joint location in an embodiment of the present invention, where the axial force is compressive, the bending moment causes the bolt side section to be under tension, and the entire cross section is under compression and the bolt is under tension.

[0095] Figure 10 This diagram illustrates the stress state of a bolt in one embodiment of the present invention, where the axial force is pressure, the bending moment causes the bolt's side section to be under tension, the entire section is under compression, and the bolt is in a relaxed state.

[0096] Figure 11 This diagram illustrates the stress state of a bolt in one embodiment of the present invention, where the axial force is pressure and the bending moment causes the bolt's side section to be compressed, and the section is partially compressed while the bolt is under tension.

[0097] Figure 12 This diagram illustrates the stress at the joint location in an embodiment of the present invention, where the axial force is pressure and the bending moment causes the bolt side section to be compressed, and the section is partially compressed while the bolt is under tension.

[0098] Figure 13 This diagram illustrates the bolt stress state in an embodiment of the present invention, where the axial force is pressure, the bending moment causes the bolt side section to be compressed, and the section is partially compressed while the bolt is in a relaxed state.

[0099] Figure 14 This diagram illustrates the stress state of a bolt when the axial force is compressive and the bending moment causes the bolt's side section to be compressed, and the entire section is compressed while the bolt is under tension, according to an embodiment of the present invention.

[0100] Figure 15 This diagram illustrates the stress at the joint when the axial force is compressive and the bending moment causes the bolt's side section to be compressed, and the entire section is compressed while the bolt is under tension, according to an embodiment of the present invention.

[0101] Figure 16 Schematic diagram of the stress state of a bolt where the axial force is a compressive force and the bending moment causes the side cross-section of the bolt to be compressed, and the entire cross-section is compressed and the bolt is in a relaxed state, in an embodiment of the present invention.

[0102] Figure 17 Schematic diagram of the stress state of a bolt when the axial force is in a tensile state in an embodiment of the present invention.

[0103] Figure 18 Schematic diagram of the stress at the joint position when the axial force is in a tensile state in an embodiment of the present invention. Detailed implementation manners

[0104] Embodiment

[0105] As Figures 1 to 3 shown, a computer-aided mechanical analysis method for the single-sided bolt connection joint of prefabricated components includes the following steps:

[0106] Step 1: Input parameters into the computer, specifically including: joint bending moment M, joint axial force N, bolt pre-tightening force T0, width b of the component cross-section, height h of the component cross-section, distance a from the bolt to the tensile zone or the edge with less compression s , elastic modulus E of concrete c , elastic modulus E of the bolt s and tensile stiffness K of the bolt t ;

[0107] Step 2: Judge the joint bending moment M and the joint axial force N. According to whether the joint axial force N is a compressive force or a tensile force, and whether the joint bending moment M causes the side cross-section of the bolt to be in tension or compression, initially calculate the height x from the outer edge of the compression zone to the neutral axis, joint cross-section rotation angle θ, bolt tension T, and stress σ0 at the outer edge of the component compression zone respectively;

[0108] If the joint axial force N is a tensile force, output the initially calculated result and complete the execution process;

[0109] Step 3: In the case where the joint axial force N is a compressive force, compare the calculated height x from the outer edge of the compression zone to the neutral axis with the height h of the component cross-section. If x < h and T > 0 are obtained through initial calculation, it indicates that the initially calculated result is correct, output the initially calculated result, and complete the execution process;

[0110] If not, correct the height x from the outer edge of the compression zone to the neutral axis, the joint cross-section rotation angle θ, the bolt tension T, and / or the stress σ0 at the outer edge of the component compression zone;

[0111] Step 4: Output the corrected data.

[0112] In some embodiments, the tensile stiffness K of the boltt =E s A s / L s Among them, A s L is the cross-sectional area of ​​the bolt. s This refers to the bolt length.

[0113] This invention is based on the assumption that the deformation at the bolted joint on one side of the prefabricated component conforms to the plane section assumption, and at the same time, it is assumed that the concrete at the joint is in an elastic working state and conforms to the linear stress-strain relationship.

[0114] Based on the direction of the axial force and bending moment on the joint, there are two cases. These are further subdivided into nine stress states based on the cross-sectional compression distribution and bolt stress state, as follows:

[0115] 1. When the axial force is compressive and the bending moment causes tension on the bolt's side section,

[0116] (1-1) Section under compression and bolt under tension

[0117] (1-2) Section under compression but with loose bolts

[0118] (1-3) The entire cross-section is under compression and the bolts are under tension.

[0119] (1-4) Full cross-section under compression and bolts loosened;

[0120] 2. When the axial force is compressive and the bending moment causes the bolt's side section to be compressed,

[0121] (2-1) Section under compression and bolt under tension

[0122] (2-2) Sectional part under compression but bolts loosened

[0123] (2-3) The entire cross-section is under compression and the bolts are under tension.

[0124] (2-4) Full cross-section under compression and bolts loosened;

[0125] 3. The axial force is in a tensile state.

[0126] In some embodiments, in step 2, when the axial force N at the joint is compressive and the bending moment M at the joint causes tension on the bolt side section, the initial calculation formulas for the height x from the outer edge of the compression zone to the neutral axis, the rotation angle θ of the joint section, the bolt tension T, and the stress σ0 at the outer edge of the compression zone of the component are as follows:

[0127]

[0128]

[0129] T = T0 + (h0 - x)θk t ;

[0130]

[0131] Where, h0 is the distance from the bolt to the edge with larger compression;

[0132] A1 is a process parameter, and its calculation formula is

[0133] B1 is a process parameter, and its calculation formula is

[0134] D1 is a process parameter, and its calculation formula is

[0135] l is the depth of the compression influence area under the condition that the axial force N of the joint is pressure and the joint bending moment M acts to make the bolt side section in tension;

[0136] N1” is a process parameter, and its calculation formula is N1' = N + T0;

[0137] M1' is a process parameter, and its calculation formula is

[0138] In some embodiments, in step 3, when the axial force N of the joint is pressure and the joint bending moment M acts to make the bolt side section in tension, when x < h and T ≯ 0, it indicates that the stress state of the joint at this time is bolt relaxation and partial section compression, and the height x from the outer edge of the compression area to the neutral axis and the joint section rotation angle θ are corrected. The specific formulas are as follows:

[0139]

[0140]

[0141] In some embodiments, in step 3, when the axial force N of the joint is pressure and the joint bending moment M acts to make the bolt side section in tension, when x ≮ h, it indicates that the entire contact surface of the segment joint is in compression. First, the joint section rotation angle θ and the bolt tension T are corrected. The specific formulas are as follows:

[0142]

[0143]

[0144] After completion, if the corrected bolt tension T > 0, it indicates that the bolt is still in the tension state. Then, the stress σ0 at the outer edge of the compression area of the component is corrected and the result is output. The specific formula is as follows:

[0145]

[0146]

[0147] If the corrected bolt tension T ≤ 0, it indicates that the bolt is in a relaxed state. Then, the joint section rotation angle θ and the stress σ0 at the outer edge of the compression zone of the member are corrected again, and the results are output. The specific formulas are as follows:

[0148]

[0149]

[0150] Where, σ1 is the stress at the outer edge on the other side of the trapezoidal compression zone of the member that is opposite to the stress σ0 at one outer edge.

[0151] In some embodiments, in step 2, when the joint axial force N is compressive and the joint bending moment M acts to compress the bolt side section, the calculation formulas for initially calculating the height x from the outer edge of the compression zone to the neutral axis, the joint section rotation angle θ, the bolt tension T, and the stress σ0 at the outer edge of the member compression zone are as follows:

[0152]

[0153]

[0154] T = T0 - θ·(x - a s )k t ;

[0155]

[0156] Where, h0 is the distance from the bolt to the larger compression edge;

[0157] A2 is a process parameter, and its calculation formula is

[0158] B2 is a process parameter, and its calculation formula is

[0159] D2 is a process parameter, and its calculation formula is

[0160] In some embodiments, in step 3, when the joint axial force N is compressive and the joint bending moment M acts to compress the bolt side section, when x < h and T ≤ 0, it indicates that the stress state of the joint at this time is that the bolt is relaxed and part of the section is compressed. The height x from the outer edge of the compression zone to the neutral axis and the joint section rotation angle θ are corrected. The specific formulas are as follows:

[0161]

[0162]

[0163] In some embodiments, in step 3, when the joint axial force N is compressive and the joint bending moment M causes the bolt side section to be compressed, when x ≮ h, it indicates that the entire contact surface of the segment joint is under compression. The joint section rotation angle θ and the bolt tension T are then corrected using the following formula:

[0164]

[0165]

[0166] in,

[0167]

[0168] A4 is the process parameter, and the calculation formula is as follows:

[0169] B4 is a process parameter, and the calculation formula is as follows:

[0170] C4 is a process parameter, calculated using the following formula:

[0171] D4 is a process parameter, calculated using the following formula:

[0172] E4 is a process parameter, calculated using the following formula:

[0173] I4 is a process parameter, and the calculation formula is I4 = N + T0;

[0174] Once completed, if the corrected bolt tension T > 0, it indicates that the bolt is still in the tensioned state. Output the result to complete all processes.

[0175] If the corrected bolt tension T≯0, it indicates bolt loosening. The joint section rotation angle θ and the outer edge stress σ0 of the component compression zone are then corrected again, and the results are output. The specific formula is as follows:

[0176]

[0177]

[0178] Wherein, σ1 is the outer edge stress on the other side of the trapezoidal compression zone of the component, opposite to the outer edge stress σ0 on one side.

[0179] In some embodiments, in step 2, when the axial force N of the joint is tensile, the initial calculation formulas for the height x from the outer edge of the compression zone to the neutral axis, the rotation angle θ of the joint section, the bolt tension T1, the tensile force T2 of the outer steel plate, and the stress σ0 at the outer edge of the compression zone of the component are as follows:

[0180]

[0181]

[0182] T1=-θ(xa s )k t +T0;

[0183] T2=(hx)θk s ;

[0184]

[0185] Where h0 is the distance from the bolt to the edge under greater pressure;

[0186] A3 is a process parameter, and the calculation formula is as follows:

[0187] B3 is a process parameter, and the calculation formula is as follows:

[0188] C3 is a process parameter, and its calculation formula is as follows:

[0189]

[0190] D3 is a process parameter, and its calculation formula is D3 = β / α;

[0191] E3 is a process parameter, calculated using the following formula:

[0192] α is a process parameter, and the calculation formula is:

[0193] β is a process parameter, and its calculation formula is β = hk s +a s k t ;

[0194] γ is a process parameter, and the calculation formula is:

[0195] The fundamental principle of this invention is as follows:

[0196] like Figure 4 and Figure 5 As shown, when the axial force is compressive and the bending moment causes the bolt side section to be under tension, and the section is partially under compression and the bolt is under tension, the simplified mechanical model diagram is as follows (x < h, T > 0):

[0197]

[0198]

[0199] T-T0=(h0-x)θk t (a-3)

[0200] FT = N(a-4)

[0201]

[0202] Based on the assumption that the maximum influence depth of the compression zone is equal to the height of the compression zone, we can obtain:

[0203] l = x(a - 6)

[0204] Combining equations (a-1) to (a-1), we can obtain:

[0205] A1x 2 +B1x+D1=0(a-7)

[0206] In the formula:

[0207]

[0208]

[0209]

[0210] In the formula: N1' and M1' are calculated as follows:

[0211] N1' = N + T0(a-11)

[0212]

[0213] Seek;

[0214]

[0215]

[0216] T = T0 + (h0 - x)θk t (a-15)

[0217]

[0218] like Figure 6 and Figure 7 As shown, the axial force is the result of pressure and bending moment causing tension on the bolt's side section, while the section is partially under compression and the bolt is in a relaxed state. The simplified mechanical model diagram is as follows (x>h, T≤0):

[0219] Based on the aforementioned analysis, if x < h and T < 0, it indicates that the joint stress state is characterized by bolt relaxation and partial section compression. Figure 6 , Figure 7 The calculation model analysis shown is based on the deformation compatibility conditions, mechanical equilibrium conditions, and stress-strain relationship conditions at the joint location:

[0220]

[0221]

[0222] F = N(b-3)

[0223]

[0224] l = x(b-5)

[0225] Solving equations (b-1) to (b-5) simultaneously, we get:

[0226]

[0227]

[0228]

[0229] like Figure 8 and Figure 9 As shown, the axial force is the result of compression and bending moment causing tension on the bolt's side section, and the entire cross section is under compression while the bolt is under tension. The simplified mechanical model diagram is as follows (x≥h, T>0):

[0230] Based on the foregoing analysis, when x ≥ h, it indicates that the entire contact surface of the segment joint is under pressure. Assuming the bolts are still under tension at this point, then according to... Figure 8 , Figure 9 The calculation model analysis shown is based on the deformation compatibility conditions, mechanical equilibrium conditions, and stress-strain relationship conditions at the joint location:

[0231]

[0232] F1=bhσ1(c-2)

[0233]

[0234] F1 + F2 - T = N(c - 4)

[0235]

[0236]

[0237] l0 = l1 = h(c-7)

[0238] Solving equations (c-1) to (c-7) simultaneously, we get:

[0239]

[0240]

[0241]

[0242]

[0243] like Figure 10 As shown, when the axial force is compressive, the bending moment causes the bolt's side section to be under tension, and the entire section is under compression, and the bolt is in a relaxed state, the simplified mechanical model diagram is as follows (x≥h, T≤0):

[0244] As analyzed above, a T≤0 indicates that the bolt is loose and needs to be adjusted accordingly. Figure 10 The calculation model shown is re-analyzed based on the deformation compatibility conditions, mechanical equilibrium conditions, and stress-strain relationship conditions at the joint location:

[0245]

[0246]

[0247]

[0248] l0 = l1 = h(d-4)

[0249] By solving the four equations (d-1) to (d-4) simultaneously, we can obtain:

[0250]

[0251]

[0252] like Figure 11 and Figure 12 As shown, when the axial force is compressive and the bending moment causes the bolt side section to be under compression, and the section is partially under compression while the bolt is under tension, the simplified mechanical model diagram is as follows (x < h, T > 0):

[0253] Based on the deformation compatibility conditions, mechanical equilibrium conditions, and stress-strain relationship conditions at the joint location:

[0254] N+T=F(e-1)

[0255]

[0256]

[0257]

[0258] l0 = x(e-5)

[0259] -θ·(xa s )k t =T-T0(e-6)

[0260] By combining equations (e-1) to (e-6), we can obtain:

[0261] A2x 2 +B²x + D² = 0(e-7)

[0262] In the formula:

[0263]

[0264]

[0265]

[0266] Seek;

[0267]

[0268]

[0269]

[0270] T = T0 - θ·(xa) s )k t (e-14).

[0271] like Figure 13 As shown, when the axial force is compressive and the bending moment causes the bolt side section to be compressed, and the section is partially compressed while the bolt is in a relaxed state, the simplified mechanical model is as follows (x < h, T ≤ 0):

[0272] Based on the aforementioned analysis, if x < h and T < 0, it indicates that the joint stress state is characterized by bolt relaxation and partial section compression. Figure 6 Analysis of the computational model shown yields the following results:

[0273] N = F(f-1)

[0274]

[0275]

[0276] By combining equations (f-1) to (f-3), we can obtain:

[0277]

[0278]

[0279]

[0280] like Figure 14 and Figure 15 As shown, when the axial force is compressive and the bending moment causes the bolt's side section to be under compression, and the entire section is under compression and the bolt is under tension, the simplified mechanical model diagram is as follows (x≥h, T>0):

[0281] Based on the aforementioned analysis, when x ≥ h, it indicates that the entire contact surface of the segment joint is under pressure. Assuming the bolts are still under tension at this time, then according to... Figure 14 , Figure 15 Analysis of the computational model shown yields the following results:

[0282] N+T=F1+F2(g-1)

[0283]

[0284]

[0285] l0 = l1 = h(g-4)

[0286] F1=bhσ1(g-5)

[0287]

[0288]

[0289] From equations (g-1) to (g-7), we get:

[0290] A4σ0 + B4σ1 = C4(g-8)

[0291] D4σ0+E4σ1=I4(g-9)

[0292] In the formula:

[0293]

[0294]

[0295]

[0296]

[0297]

[0298] I4 = N + T0(g - 15)

[0299] Combining equations (g-8) and (g-9), we get:

[0300]

[0301]

[0302]

[0303]

[0304] like Figure 16 As shown, when the axial force is compressive and the bending moment causes the bolt's side section to be compressed, and the entire section is compressed while the bolt is in a relaxed state, the simplified mechanical model is as follows (x≥h, T≤0):

[0305] Based on the aforementioned analysis, the calculated T≤0 indicates that the bolt is loose and needs to be adjusted accordingly. Figure 16 The computational model shown is re-analyzed, and the corresponding equations are as follows:

[0306] N = F1 + F2(h-1)

[0307]

[0308]

[0309] F1=bhσ1(g-5)

[0310] (g-6)

[0311] (h-4)

[0312]

[0313]

[0314] Combining equations (h-1) to (h-6), we get:

[0315]

[0316]

[0317]

[0318] like Figure 17 and Figure 18 As shown, when the axial force is in a tensile state, the simplified mechanical model is as follows (to ensure that the joint maintains rotational stiffness, a welded steel plate connection or a measure to bear the tensile force is provided on the outside of the joint):

[0319] When the axial force N is under tension, the joint's ability to transmit rotational stiffness is relatively weak. Therefore, a welded steel plate needs to be installed on the outside of the joint as a measure to bear the tensile force.

[0320] The stress state is that the entire cross-section is under tension, or part of the cross-section is under compression, the bolt is under tension force T1 and the outer steel plate is under tension force T2, according to Figure 17, Figure 18 Analysis of the computational model shown yields the following results:

[0321] N+T=F1+F2(i-1)

[0322]

[0323]

[0324]

[0325] -θ(xa s )k t =T1-T0(i-5)

[0326] (hx)θk s =T2(i-6)

[0327] From equations (i-1) to (i-6), we get:

[0328]

[0329] In the formula:

[0330]

[0331]

[0332]

[0333] D3=β / α(i-11)

[0334]

[0335]

[0336] β=hk s +a s k t (i-14)

[0337]

[0338] Find:

[0339]

[0340]

[0341]

[0342] T1=-θ(xa s )k t +T0(i-19)

[0343] T2=(hx)θk s (i-20).

[0344] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A computer-aided mechanical analysis method for single-sided bolted joints in prefabricated components; characterized in that, It includes the following steps: Step 1: Input parameters into the computer, specifically including: joint bending moment M, joint axial force N, bolt preload T0, component cross-sectional width b, component cross-sectional height h, and distance a from the bolt to the tension zone or the edge with less compression. s E, the elastic modulus of concrete c Bolt elastic modulus E s And the tensile stiffness K of the bolt t ; Step 2: Judge the joint bending moment M and the joint axial force N. According to whether the joint axial force N is compressive or tensile, and whether the bolt side cross-section is in tension or compression under the action of the joint bending moment M, initially calculate the height x from the outer edge of the compression zone to the neutral axis, the joint cross-section rotation angle θ, the bolt tension T, and the stress σ0 at the outer edge of the member compression zone respectively; If the joint axial force N is tensile, output the initial calculation result and complete the execution process; Step 3: In the case where the joint axial force N is compressive, compare the calculated height x from the outer edge of the compression zone to the neutral axis with the member cross-section height h. If x < h and T > 0 are obtained through initial calculation, it means the initial calculation result is correct. Output the initial calculation result and complete the execution process; If not, correct the height x from the outer edge of the compression zone to the neutral axis, the joint cross-section rotation angle θ, the bolt tension T, and / or the stress σ0 at the outer edge of the member compression zone; Step 4: Output the corrected data.

2. The computer-based mechanical analysis method for single-sided bolted joints of prefabricated components according to claim 1, characterized in that, The tensile stiffness K of the bolt t =E s A s / L s ; Among them, A s L is the cross-sectional area of ​​the bolt. s This refers to the bolt length.

3. The computer-based mechanical analysis method for single-sided bolted joints of prefabricated components according to claim 1, characterized in that, In Step 2, in the case where the joint axial force N is compressive and the bolt side cross-section is in tension under the action of the joint bending moment M, the calculation formulas for initially calculating the height x from the outer edge of the compression zone to the neutral axis, the joint cross-section rotation angle θ, the bolt tension T, and the stress σ0 at the outer edge of the member compression zone are as follows: T=T0+(h0-x)θk t ; Where, h0 is the distance from the bolt to the larger compression edge; A1 is a process parameter, and the calculation formula is as follows: B1 is a process parameter, and the calculation formula is as follows: D1 is a process parameter, and the calculation formula is as follows: l is the compression influence depth of the compression zone in the case where the joint axial force N is compressive and the bolt side cross-section is in tension under the action of the joint bending moment M; N’1’ is a process parameter, and the calculation formula is N’1 = N + T0; M'1 is a process parameter, and the calculation formula is as follows:

4. The computer-based mechanical analysis method for single-sided bolted joints of prefabricated components according to claim 3, characterized in that, In Step 3, in the case where the joint axial force N is compressive and the bolt side cross-section is in tension under the action of the joint bending moment M, when x < h and T ≯ 0, it indicates that the stress state of the joint at this time is bolt relaxation and partial cross-section compression. Correct the height x from the outer edge of the compression zone to the neutral axis and the joint cross-section rotation angle θ. The specific formulas are as follows:

5. The computer-based mechanical analysis method for single-sided bolted joints of prefabricated components according to claim 3, characterized in that, In Step 3, in the case where the joint axial force N is compressive and the bolt side cross-section is in tension under the action of the joint bending moment M, when x ≮ h, it indicates that the entire contact surface of the segment joint is in compression. First, correct the joint cross-section rotation angle θ and the bolt tension T. The specific formulas are as follows: After completion, if the corrected bolt tension T > 0, it indicates that the bolt is still in the tension state. Then correct the stress σ0 at the outer edge of the member compression zone and output the result; The specific formula is as follows: If the corrected bolt tension T ≯ 0, it indicates that the bolt is in the relaxation state. Again, correct the joint cross-section rotation angle θ and the stress σ0 at the outer edge of the member compression zone and output the result; The specific formula is as follows: Where, σ1 is the outer edge stress on the other side of the trapezoidal member compression zone opposite to the outer edge stress σ0 on one side.

6. The computer-based mechanical analysis method for single-sided bolted joints of prefabricated components according to claim 1, characterized in that, In Step 2, in the case where the joint axial force N is compressive and the bolt side cross-section is in compression under the action of the joint bending moment M, the calculation formulas for initially calculating the height x from the outer edge of the compression zone to the neutral axis, the joint cross-section rotation angle θ, the bolt tension T, and the stress σ0 at the outer edge of the member compression zone are as follows: T=T0-θ·(x-a s )k t ; Where, h0 is the distance from the bolt to the larger compression edge; A2 is a process parameter, and the calculation formula is as follows: B2 is a process parameter, and the calculation formula is as follows: D2 is a process parameter, and the calculation formula is as follows:

7. The computer-based mechanical analysis method for single-sided bolted joints of prefabricated components according to claim 6, characterized in that, In step 3, when the joint axial force N is compressive and the joint bending moment M acts to compress the bolt-side cross-section, when x < h and T ≯ 0, it indicates that the stress state of the joint at this time is bolt relaxation and partial cross-section compression. The height x from the outer edge of the compression zone to the neutral axis and the joint cross-section rotation angle θ are corrected. The specific formulas are as follows:

8. The computer-based mechanical analysis method for single-sided bolted joints of prefabricated components according to claim 6, characterized in that, In step 3, when the joint axial force N is compressive and the joint bending moment M acts to compress the bolt-side cross-section, when x ≮ h, it indicates that the entire contact surface of the segment joint is under compression. First, the joint cross-section rotation angle θ and the bolt tension T are corrected. The specific formulas are as follows: in, A4 is the process parameter, and the calculation formula is as follows: B4 is a process parameter, and the calculation formula is as follows: C4 is a process parameter, calculated using the following formula: D4 is a process parameter, calculated using the following formula: E4 is a process parameter, calculated using the following formula: I4 is a process parameter, and the calculation formula is I4 = N + T0; After completion, if the corrected bolt tension T > 0, it indicates that the bolt is still in the tension state, and the result is output to complete all processes; If the corrected bolt tension T ≯ 0, it indicates bolt relaxation. The joint cross-section rotation angle θ and the stress σ0 at the outer edge of the compression zone of the member are corrected again, and the result is output. The specific formulas are as follows: Where σ1 is the stress at the outer edge on the other side of the trapezoidal compression zone of the member opposite to the outer edge stress σ0 on one side.

9. The computer-based mechanical analysis method for single-sided bolted joints of prefabricated components according to claim 1, characterized in that, In step 2, when the joint axial force N is tensile, the calculation formulas for initially calculating the height x from the outer edge of the compression zone to the neutral axis, the joint cross-section rotation angle θ, the bolt tension T1, the tension T2 on the outer steel plate, and the stress σ0 at the outer edge of the compression zone of the member are as follows: T1=-θ(x-a s )k t +T0; T2=(h-x)θk s ; Where h0 is the distance from the bolt to the edge with larger compression; A3 is a process parameter, and the calculation formula is as follows: B3 is a process parameter, and the calculation formula is as follows: C3 is a process parameter, and the calculation formula is as follows: D3 is a process parameter, and the calculation formula is D3 = β / α; E3 is a process parameter, calculated using the following formula: α is a process parameter, and the calculation formula is: β is a process parameter, and its calculation formula is β = hk s +a s k t ; γ is a process parameter, and the calculation formula is:

Images