A method for verifying the strength of deck beams

Abstract

This invention discloses a method for verifying the strength of a deck beam. The method involves: determining the working condition under which the beam experiences the target maximum bending moment based on the vehicle spacing 'a' and the span length 'l' of the deck beam, i.e., determining the number of wheel loads and the position of each wheel; calculating the target maximum bending moment by substituting the parameter 's' characterizing the wheel position into the corresponding formula; comparing the calculated target maximum bending moment with the beam's ultimate bending moment; if the calculated target maximum bending moment is less than the beam's ultimate bending moment, the beam strength meets the design requirements; if the calculated target maximum bending moment is greater than or equal to the beam's ultimate bending moment, the beam strength does not meet the design requirements. The beneficial effects of this invention are: it provides a method for verifying the strength of a deck beam, provides corresponding calculation formulas, and provides a method for determining wheel load working conditions.

Description

Technical Field

[0001] This invention belongs to the field of ship structural design technology, and specifically relates to a method for verifying the strength of deck beams. Background Technology

[0002] The increasing popularity of automobiles in my country has led to a booming market for "car transport by ship." For example, newly manufactured cars are transported by ship to coastal or riverside cities for sale; similarly, people traveling to and from Hainan Island for road trips need to use ships to transport their cars from Xuwen to Haikou, and back again. For these specialized car-carrying roll-on / roll-off ships or car ferries, the design must consider not only the overall strength of the hull but also the local strength caused by the weight of the cars. In the deck crossbeam system, the larger transverse members are called deck beams. Beams are crucial components of the ship's deck, and their local strength must be checked. A key parameter for checking the deck beams is the maximum bending moment of the beam. Based on the beam's cross-sectional parameters, the section modulus is easily calculated, and the allowable stress multiplied by the section modulus gives the ultimate bending moment of the beam. Once the maximum bending moment is determined, comparing the target maximum bending moment with the ultimate bending moment determines whether the beam's strength meets the design requirements.

[0003] When loading cars onto a ship, the spacing between them on the deck is often determined by the number of vehicles to maintain balance. More vehicles require smaller spacing, and fewer vehicles require larger spacing; in short, the cars should be evenly distributed across the entire cargo ship deck. This variation in placement causes changes in the bending moment on the deck beams. Furthermore, during loading, the movement of the cars on the beams to adjust the spacing between them also causes changes in the bending moment on the deck beams.

[0004] The span of the crossbeam ranges from accommodating one to three wheels. For ship design, it is necessary to find the arrangement of the car with the maximum bending moment and the corresponding bending moment under various different car placement methods; or, when the car is in motion, to find the position where the crossbeam experiences the maximum bending moment, i.e., the most unfavorable position and the most unfavorable load, in order to check the strength of the crossbeam. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for verifying the strength of a deck beam. The aim is to find a rapid method for calculating the maximum bending moment of the beam under wheel load, in order to verify the strength of the beam.

[0006] The technical solution adopted in this invention is: a method for verifying the strength of a deck beam; the method involves: determining the working condition under which the beam experiences the target maximum bending moment based on the vehicle spacing 'a' and the span length 'l' of the deck beam, i.e., determining the number of wheel loads and the position of each wheel. The target maximum bending moment is calculated by substituting the parameter 's' characterizing the wheel position into the corresponding formula. The calculated target maximum bending moment is compared with the ultimate bending moment of the beam. If the calculated target maximum bending moment is less than the ultimate bending moment of the deck beam, the beam strength meets the design requirements; if the calculated target maximum bending moment is greater than or equal to the ultimate bending moment of the deck beam, the beam strength does not meet the design requirements.

[0007] According to the above scheme, the calculation method for the target maximum bending moment of the deck beam under the following vehicle wheel load conditions is as follows:

[0008] S1. Two cars are parked on the deck beam at the same time. Calculate the target maximum bending moment generated by the three wheels on the deck beam under the load of three wheels:

[0009]

[0010] S2. A car is parked on a deck beam, with either its two front wheels or two rear wheels simultaneously located within the span of the beam. The maximum target bending moment generated by the two wheels on the deck beam in this situation is:

[0011]

[0012] S3. The target maximum bending moment generated when a single wheel is parked on the deck beam is:

[0013]

[0014] In formulas (1) to (3), m3(s) is the target maximum bending moment caused by the three wheel loads on the calculation beam, in N·m; m2(s) is the target maximum bending moment caused by the two wheel loads on the deck beam, in N·m; m1(s) is the target maximum bending moment caused by the single wheel load on the deck beam, in N·m; d is the distance between the left and right wheels of the car, in m; a is the distance between the wheels of two adjacent cars, in m; l is the span length of the beam, in m; s is the distance between the left front wheel or left rear wheel of the first car and the left support, in m; P is the concentrated load of a single wheel of the car, in N.

[0015] According to the above scheme, when a and l satisfy any one of S1(1), S1(2), and S1(3), the bending moment generated by all three wheels simultaneously resting on the calculation beam is greater than the bending moment generated by two wheels simultaneously resting, and also greater than the bending moment generated by a single wheel resting, which is the target maximum bending moment of the beam. At this time, the maximum bending moment is calculated using formula (1); S1(1), S1(2), and S1(3) are respectively:

[0016] S1(1): and

[0017] S1(2): and

[0018] S1(3) and

[0019] Under condition S1(1), the distance s3 between the left wheel of the first vehicle and the left support is:

[0020] s3=0................................................(4),

[0021] Under conditions S1(2) and S1(3), the distance s3 between the left wheel and the left support of the first vehicle is:

[0022]

[0023] According to the above scheme, when a and l satisfy any one of S2(1), S2(2), S2(3) and S2(4), the bending moment generated by two wheels simultaneously resting on the calculation beam is greater than the bending moment generated by three wheels simultaneously resting, and also greater than the bending moment generated by a single wheel resting, which is the target maximum bending moment of the beam. The maximum bending moment is calculated using formula (2); S2(1), S2(2), S2(3) and S2(4) are respectively:

[0024] S2(1): If but

[0025] S2(2): If but

[0026] S2(3): If but

[0027] S2(4): If but

[0028] When the maximum bending moment occurs under the four conditions S2(1), S2(2), S2(3), and S2(4), the distance s2 between the left wheel and the left support is always [value missing].

[0029]

[0030] According to the above scheme, when a and l satisfy either S3(1) or S3(2), the bending moment generated by a single wheel parked on the calculation beam is greater than the bending moment generated by two wheels parked at the same time, and also greater than the bending moment generated by three wheels parked at the same time. That is, the target maximum bending moment of the beam is calculated using formula (3); S3(1) and S3(2) are respectively:

[0031] S3(1): If but

[0032] S3(2): If

[0033] The maximum bending moment occurs under conditions S3(1) and S3(2), at which point the distance s1 between the left wheel and the left support is...

[0034]

[0035] According to the above scheme, the ultimate bending moment of the beam is calculated as follows:

[0036] M u =σW................................................(8).

[0037] M u σ is the ultimate bending moment of the beam, in N·m; σ is the allowable stress, in Pa; W is the section modulus of the deck beam, in m. 3 .

[0038] According to the above scheme, when a and l satisfy any one of conditions S1(1), S1(2), and S1(3), the corresponding target maximum bending moment m3(s3) is less than the ultimate bending moment M of the deck beam. u If the beam strength meets the design requirements, then the corresponding target maximum bending moment m3(s3) is greater than or equal to the ultimate bending moment M of the deck beam. u If so, the strength of the beam does not meet the design requirements;

[0039] When a and l satisfy any one of conditions S2(1), S2(2), S2(3), and S2(4), the corresponding target maximum bending moment m2(s2) is less than the ultimate bending moment M of the deck beam. uIf the beam strength meets the design requirements, then the corresponding target maximum bending moment m2(s2) is greater than or equal to the ultimate bending moment M of the deck beam. u If so, the strength of the beam does not meet the design requirements;

[0040] When a and l satisfy either condition S3(1) or S3(2), the corresponding target maximum bending moment m1(s1) is less than the ultimate bending moment M of the deck beam. u If the beam strength meets the design requirements, then the corresponding target maximum bending moment m1(s1) is greater than or equal to the ultimate bending moment M of the deck beam. u If the strength of the beam does not meet the design requirements, then the beam strength does not meet the design requirements.

[0041] The beneficial effects of this invention are as follows: This invention provides a method for calculating the target maximum bending moment of a deck beam, provides a corresponding calculation formula, and provides a method for determining wheel load conditions. Substituting the wheel position into the corresponding calculation formula allows for the rapid calculation of the target maximum bending moment. Comparing the calculated target maximum bending moment with the ultimate bending moment of the deck beam allows for verification of the deck beam's strength, enabling a rapid assessment of whether the deck strength meets design requirements. This method is simple, reliable, and highly efficient. This invention is applicable to the range of wheel spacing between adjacent vehicles where d / 2 ≤ a ≤ 2d, and the range of beam span length l where l ≤ 5d / 2, meaning that a maximum of two vehicles can be parked simultaneously within a single span of the deck beam. Attached Figure Description

[0042] Figure 1 This is a schematic diagram showing the forces acting on the three wheels simultaneously resting on the deck beam in this invention.

[0043] Figure 2 This is a schematic diagram showing the forces acting on two wheels simultaneously resting on the deck beam in this invention.

[0044] Figure 3 This is a schematic diagram of the forces acting on a single wheel resting on a deck beam in this invention. Detailed Implementation

[0045] To better understand the present invention, it will be further described below with reference to the accompanying drawings and specific embodiments.

[0046] A method for verifying the strength of a deck beam is provided. The method involves: determining the working condition under which the beam experiences its target maximum bending moment based on the vehicle spacing 'a' and the beam's span length 'l', i.e., determining the number of wheel loads and the position of each wheel; calculating the target maximum bending moment by substituting the parameter 's' representing the wheel position into the corresponding formula; comparing the calculated target maximum bending moment with the beam's maximum design bending moment; if the calculated target maximum bending moment is less than the beam's ultimate bending moment, the beam's strength meets the design requirements; if the calculated target maximum bending moment is greater than or equal to the beam's ultimate bending moment, the beam's strength does not meet the design requirements.

[0047] The crossbeam described in this invention is a single-span deck crossbeam. Currently, to maintain the strength of the crossbeam, the length of a single-span deck crossbeam in the industry is limited, allowing a maximum of two cars to be parked simultaneously. That is, the wheel distance between adjacent cars is in the range of d / 2 ≤ a ≤ 2d, and the span length l of the crossbeam is in the range of l ≤ 5d / 2. The mechanical model of a car parked on the deck crossbeam can be simplified to a simply supported beam subjected to multiple concentrated forces. Figure 1 This is a diagram showing three wheels parked simultaneously on the deck beam. Figure 2 This is a diagram showing two wheels parked simultaneously on the deck beam. Figure 3 A diagram showing a single wheel parked on a deck beam. Figure 1 , Figure 2 and Figure 3 Identical components are represented by the same numbers, and corresponding positions are represented by the same letters. The attached diagram is labeled as follows: 1-Deck beam, A-Left support point of the deck beam, F-Right support point of the deck beam, B-Left front wheel (or left rear wheel) of the first vehicle, C-Right front wheel (or right rear wheel) of the first vehicle, D-Left front wheel (or left rear wheel) of the second vehicle, s-Distance between the left front wheel (or left rear wheel) of the first vehicle and the left support, d-Distance between the left and right wheels of the vehicle, a-Distance between the wheels of two adjacent vehicles, i.e., the distance between the right wheel of the first vehicle and the left wheel of the second vehicle when the vehicles are parked side by side, l-Span length of the beam.

[0048] In this invention, the length of the deck beam, the wheel spacing of the vehicles, the wheel spacing between adjacent vehicles, and the vehicle weight are all known parameters. The wheel spacing d is a fixed value (in meters); the wheel spacing between adjacent vehicles is a (in meters), which can be adjusted appropriately according to the number of vehicles loaded, therefore a is a variable, with a range of d / 2 ≤ a ≤ 2d; the span length of the deck beam l ≤ 5d / 2 (in meters), meaning that a maximum of two vehicles can be parked on a single span of the deck beam simultaneously; the concentrated load on each wheel of the vehicle is approximately equal, with a magnitude of p; the distance from the left wheel to the left support is s (in meters), which means that different loading schemes result in different s values, or that s will also differ depending on the movement of the vehicle on the beam. The following descriptions all calculate the length of s starting from the left support; due to symmetry, a similar calculation method applies when starting from the right support.

[0049] The target maximum bending moment of the deck beam is directly related to the vehicle wheel load conditions, and the calculation methods differ. The deck beam under vehicle wheel loads can be categorized into three cases:

[0050] S1. Two cars are parked simultaneously on a deck beam. Calculate the load on the beam from three wheels. The first car has both front (or rear) wheels within the beam's span, while the second car has one front (or rear) wheel within the beam's span and the other front (or rear) wheel outside the span. The maximum target bending moment generated by these three wheels on the beam is:

[0051]

[0052] In the above formula, m3(s) is the target maximum bending moment caused by the three wheels on the deck beam. It is a function of s and its unit is N·m.

[0053] S2. A car is parked on a deck beam, with both front wheels (or both rear wheels) simultaneously located within the span of the beam. This means both wheels are resting on the beam, and the beam bears the load of both wheels. The maximum target bending moment generated by the two wheels on the beam under these conditions is:

[0054]

[0055] In the above formula, m2(s) is the target maximum bending moment caused by the two wheels on the deck beam. It is a function of s and its unit is N·m.

[0056] S3. Single wheel resting on the deck beam: If only the left front wheel (or left rear wheel) of the car is within the calculated span of the beam, and no other wheels are placed within the beam span, then it is considered that a single wheel is resting on the deck beam. In this case, the maximum target bending moment generated by a single wheel on the deck beam is:

[0057]

[0058] In the above formula, m1(s) is the target maximum bending moment caused by a single wheel on the deck beam. It is a function of s and its unit is N·m.

[0059] In ship design, the target maximum bending moment of the beam is of utmost concern. Once the specific values ​​of the wheel spacing 'a' between adjacent vehicles and the beam span 'l' are determined, the maximum bending moment of the beam can be determined according to the following formula.

[0060] When a and l satisfy any one of S1(1), S1(2), and S1(3), the bending moment generated by all three wheels stopping simultaneously is greater than the bending moment generated by two wheels stopping simultaneously, and also greater than the bending moment generated by a single wheel stopping, which is the target maximum bending moment of the crossbeam. At this time, the maximum bending moment is calculated using formula (1). S1(1), S1(2), and S1(3) are respectively:

[0061] S1(1): and

[0062] S1(2): and

[0063] S1(3) and

[0064] Under condition S1(1), the distance s3 between the left wheel of the first vehicle and the left support is

[0065] s3=0................................................(4),

[0066] The target maximum bending moment m3 is:

[0067]

[0068] Under conditions S1(2) and S1(3), the distance s3 between the left wheel and the left support of the first vehicle is always...

[0069]

[0070] At this point, the target maximum bending moment m3 is

[0071]

[0072] If a and l satisfy any of the conditions S1(1), S1(2), and S1(3), then the bending moment generated by the three wheels is the maximum. The wheel parking position corresponding to the maximum bending moment is calculated according to formula (4) or formula (6), and the target maximum bending moment is calculated according to formula (5) or formula (7). The target maximum bending moment can also be calculated by substituting formula (4) or formula (6) into formula (1). In this case, it is not necessary to calculate the bending moment generated by two wheels parking at the same time and the bending moment generated by a single wheel parking.

[0073] When a and l satisfy any one of S2(1), S2(2), S2(3), and S2(4), the bending moment generated by two wheels simultaneously resting on the deck beam is greater than the bending moment generated by three wheels simultaneously resting, and also greater than the bending moment generated by a single wheel resting, which is the target maximum bending moment of the beam. The maximum bending moment is calculated using formula (2). S2(1), S2(2), S2(3), and S2(4) are respectively:

[0074] S2(1): but

[0075] S2(2): If but

[0076] S2(3): If but

[0077] S2(4): If but

[0078] When the target maximum bending moment occurs under the four conditions S2(1), S2(2), S2(3), and S2(4), the distance s2 between the left wheel and the left support is always...

[0079]

[0080] The target maximum bending moment m2 is

[0081]

[0082] When a and l satisfy any one of S2(1), S2(2), S2(3) and S2(4) above, the bending moment generated by two wheels parked at the same time is the largest. The parking position is calculated according to formula (8), and the target maximum bending moment is calculated according to formula (9). The target maximum bending moment can also be calculated by substituting formula (8) into formula (2). At this time, it is not necessary to calculate the bending moment generated by three wheels parked at the same time and the bending moment generated by a single wheel parked.

[0083] When a and l satisfy either S3(1) or S3(2), the bending moment generated by a single wheel resting on the deck beam is greater than the bending moment generated by two wheels resting simultaneously, and also greater than the bending moment generated by three wheels resting simultaneously; at this time, the single wheel generates the maximum bending moment on the deck beam, which is calculated using formula (3). S3(1) and S3(2) are respectively:

[0084] S3(1): If but

[0085] S3(2): If

[0086] The maximum bending moment occurs under conditions S3(1) and S3(2), at which point the distance s1 between the left wheel and the left support is...

[0087]

[0088] The target maximum bending moment m1 is

[0089]

[0090] When a and l satisfy S3(1) or S3(2), the bending moment generated by parking a single wheel simultaneously is the largest. The parking position is calculated according to formula (10), and the target maximum bending moment is calculated according to formula (11). The target maximum bending moment can also be calculated by substituting formula (10) into formula (3). There is no need to calculate the bending moment generated by parking three wheels simultaneously or parking two wheels simultaneously.

[0091] The ultimate bending moment of the deck beam is

[0092] M u =σW ........................................................ (8)

[0093] M u σ is the ultimate bending moment of the beam, in N·m; σ is the allowable stress, in Pa; W is the section modulus of the deck beam, in m. 3 .

[0094] When a and l satisfy condition S1(1), if the target maximum bending moment is less than the ultimate bending moment of the deck beam, i.e. The strength of the beam meets the design requirements; if the target maximum bending moment is greater than or equal to the ultimate bending moment of the deck beam, that is... The strength of the beam does not meet the design requirements.

[0095] When a and l satisfy any one of conditions S1(2) and S1(3), if the target maximum bending moment is less than the ultimate bending moment of the deck beam, that is... The strength of the beam meets the design requirements; if the target maximum bending moment is greater than or equal to the ultimate bending moment of the deck beam, that is... The strength of the beam does not meet the design requirements.

[0096] When a and l satisfy any one of conditions S2(1), S2(2), S2(3), and S2(4), if the target maximum bending moment is less than the ultimate bending moment of the deck beam, i.e. The strength of the beam meets the design requirements; if the target maximum bending moment is greater than or equal to the ultimate bending moment of the deck beam, that is... The strength of the beam does not meet the design requirements.

[0097] When a and l satisfy either condition S3(1) or S3(2), if the target maximum bending moment is less than the ultimate bending moment of the deck beam, i.e. The strength of the beam meets the design requirements; if the target maximum bending moment is greater than or equal to the ultimate bending moment of the deck beam, that is... The strength of the beam does not meet the design requirements.

[0098] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0099] Finally, it should be noted that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. However, any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for verifying the strength of a deck beam, characterized in that, The method is as follows: based on the distance between vehicles a and the span of the deck beam l The size of the beam is used to determine the working condition in which the target maximum bending moment occurs, that is, to determine the number of wheel loads and the position of each wheel. The parameters characterizing the wheel position s Substitute the values ​​into the corresponding formula to calculate the target maximum bending moment; compare the calculated target maximum bending moment with the ultimate bending moment of the beam. If the calculated target maximum bending moment is less than the ultimate bending moment of the beam, the beam strength meets the design requirements; if the calculated target maximum bending moment is greater than or equal to the ultimate bending moment of the beam, the beam strength does not meet the design requirements. The method for calculating the target maximum bending moment of the deck beam under the following vehicle wheel load conditions is as follows: S1. Two cars are parked on the deck beam at the same time. Calculate the target maximum bending moment generated by the three wheels on the deck beam under the load of three wheels: .............................（1）， S2. A car is parked on a deck beam, with either its two front wheels or two rear wheels simultaneously located within the span of the beam. The maximum target bending moment generated by the two wheels on the deck beam in this situation is: ....................................（2）， S3. The target maximum bending moment generated when a single wheel is parked on the deck beam is: ....................................（3）， In formulas (1)~(3), m 3( s The target maximum bending moment caused by the three wheel loads on the calculation beam is N•m; m 2( s The target maximum bending moment caused by the loads of the two wheels on the deck beam is expressed in N•m. m 1( s The maximum target bending moment caused by a single wheel load on the deck beam is expressed in N•m. d This refers to the distance between the left and right wheels of a car, in meters (m). a The distance between the wheels of two adjacent cars, in meters (m). l Let be the span length of the beam, in meters (m). s The distance between the left front wheel or left rear wheel of the first vehicle and the left support, in meters; P This represents the concentrated load on a single wheel of a car, measured in N.

2. The method for verifying the strength of deck beams as described in claim 1, characterized in that, when a and l When any one of S1(1), S1(2), and S1(3) is satisfied, the bending moment generated when all three wheels are simultaneously parked on the calculation beam is greater than the bending moment generated when two wheels are simultaneously parked, and also greater than the bending moment generated when a single wheel is parked. This is the target maximum bending moment of the beam. At this time, the maximum bending moment is calculated using formula (1). S1(1), S1(2), and S1(3) are respectively: S1(1): ,and ; S1(2): ,and ; S1(3): ,and ; Under condition S1(1), the distance between the left wheel of the first vehicle and the left support. s 3 is: ....................................（4）， Under conditions S1(2) and S1(3), the distance between the left wheel of the first vehicle and the left support. s All 3 are: ....................................（5）。 3. The method for verifying the strength of deck beams as described in claim 2, characterized in that, when a and l When any one of S2(1), S2(2), S2(3), and S2(4) is satisfied, the bending moment generated when two wheels are simultaneously parked on the calculation beam is greater than the bending moment generated when three wheels are simultaneously parked, and also greater than the bending moment generated when a single wheel is parked. This is the target maximum bending moment of the beam, which is calculated using formula (2). S2(1), S2(2), S2(3), and S2(4) are respectively: S2(1): ,and ; S2(2): ,and ; S2(3): ,and ; S2(4): ,and ; When the maximum bending moment occurs under the four conditions S2(1), S2(2), S2(3), and S2(4), the distance between the left wheel and the left support is... s Both are: ....................................（6）。 4. The method for verifying the strength of deck beams as described in claim 3, characterized in that, when a and l When either S3(1) or S3(2) is satisfied, the bending moment generated by a single wheel resting on the calculation beam is greater than the bending moment generated by two wheels resting simultaneously, and also greater than the bending moment generated by three wheels resting simultaneously. That is, the target maximum bending moment of the beam is calculated using formula (3); S3(1) and S3(2) are respectively: S3(1): ,and ; S3(2): ,and ; The maximum bending moment occurs under conditions S3(1) and S3(2), at which point the distance between the left wheel and the left support is... s 1 is: ....................................（7）。 5. The method for verifying the strength of deck beams as described in claim 4, characterized in that, The ultimate bending moment of the deck beam is ....................................（8）， M u σ is the ultimate bending moment of the beam, in N•m; σ is the allowable stress, in Pa. W The section modulus of the deck beam, in meters. 3 .

6. The method for verifying the strength of deck beams as described in claim 5, characterized in that, when a and l When any one of conditions S1(1), S1(2), and S1(3) is satisfied, the corresponding target maximum bending moment m 3( s 3) Less than the ultimate bending moment M u If the beam strength meets the design requirements, then the corresponding target maximum bending moment... m 3( s 3) Greater than or equal to the ultimate bending moment M u If so, the strength of the beam does not meet the design requirements; when a and l When any one of conditions S2(1), S2(2), S2(3), and S2(4) is satisfied, the corresponding target maximum bending moment m 2( s 2) Less than the ultimate bending moment M u If the beam strength meets the design requirements, then the corresponding target maximum bending moment... m 2( s 2) Greater than or equal to the ultimate bending moment M u If so, the strength of the beam does not meet the design requirements; when a and l When either condition S3(1) or S3(2) is satisfied, the corresponding target maximum bending moment m 1( s 1) Less than the ultimate bending moment M u If the beam strength meets the design requirements, then the corresponding target maximum bending moment... m 1( s 1) Greater than or equal to the ultimate bending moment M u If so, the strength of the beam does not meet the design requirements.

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