How to calculate the square of the bending moment of the span of a simply supported beam with a bend

y 0 obtains that the reaction force of the two supports is 1 2ql, and the body is cut off in the middle of the span, and the half-span uniform load is calculated.

The bending moment for this cross-section.

Total Uniform Load Distance from the center of gravity of the load to this section q l 2 l 4 1 8ql (clockwise.)

is negative).

The bending moment of the support reaction force for this cross-section is then calculated 1 2 2 l 1 2 l 1 4 ql (positive counterclockwise). The algebraic sum of all the moments on this section is 1 8ql 1 4ql 1 8ql.

1 2QLX1 2L: 1 2QL is the support reaction, and 1 2L is the distance between the support and the middle of the span.

1 2QLX1 4L: the load Q is evenly distributed on the beam, the load resultant force from the left side of the span is 1 2QL, the side length of the resultant force of the rectangular distributed load is half of the length of the side, and the distance between the action point of 1 2QL and the middle span is L 2 1 2=1 4L

Originally, I drew a picture, but Du Niang didn't let me upload it, sad urging.

It's not pictured. <>

The maximum bending moment of the simply supported beam under uniform load is 1 8pl, and the calculation principle pl=f; ②fl=m;pl =m, the maximum bending moment is l 2, and the maximum is (p l) l =m; i.e. 1 8pl

1 8ql is the bending moment value of the simply supported beam across the middle section under the action of uniform load q, and it is also the maximum bending moment value of all sections of the beam.

Using one of the static equilibrium equations y 0, the reaction force of the two supports is 1 2ql, and the body is cut off in the middle of the span, and the bending and dismantling moment of the half-span evenly distributed load on this section is calculated The total value of the uniform load The distance from the center of gravity of the load to this section q l 2 l 4 1 8ql (negative value clockwise); The bending moment of the support reaction force for this cross-section is calculated 1 2ql 1 2l 1 4ql (positive value counterclockwise). The algebraic sum of all the moments on this section is 1 8ql 1 4ql 1 8ql.

That's it.

The formula for calculating the bending moment of a simply supported beam is m = fl 4, where m represents the bending moment, f represents the force acting on the beam, and l represents the length of the beam. This formula is suitable for cases where only one concentrated force is acting on the beam. If there are other loads acting on the beam, they need to be split into several concentrated forces, and the bending moments generated by them are calculated separately, and finally they are added up to give the total bending moments.

In addition, if the cross-section of the beam changes or the material of the beam changes, the influence of the cross-section shape and material properties on the calculation results needs to be considered.

The bending moment calculation formula of simply supported beams is a basic knowledge in mechanics, and it can be used to solve various engineering problems. For example, in the fields of mechanics, structural analysis, architectural design, etc., this formula can be used to calculate the force of a beam, so as to evaluate whether the design of the beam is reasonable, or to determine other engineering parameters. In addition, in the fields of physics and mechanics, this formula can also be used to derive other related formulas, or to solve various practical problems.

It should be noted that the bending moment calculation formula of simply supported beams is only applicable to the specific structural late form of simply supported beams. If the beam is different in terms of support form, cross-sectional shape or material properties, it is necessary to use different calculation methods according to different situations. In addition, complex loads and structural forms may occur in actual engineering, and multiple factors need to be considered for calculation, so it is difficult for a single formula to cover all cases.

In practical application, it is necessary to comprehensively consider the specific situation and use systematic structural analysis methods to calculate. <>

Take simply supported beams as an example:

1. The distance between the centers of the support is 3m, and the width of the support is all, then the net span is. According to the net span + a support width = 3m, according to the net span =, the span is calculated at this time.

2. The distance between the centers of the support is 6m, and the width of the support is still the same, then the net span is. According to the net span + a support width = 6m, according to the net span =, the calculation span is 6m at this time.

Beams are a frequent component in building structures. In a frame structure, beams connect columns in all directions into a whole; In a wall structure, a connecting beam above the opening connects the two wall limbs so that they work together. As an important component of seismic design, it plays the role of the first line of defense.

In a frame-shear wall structure, the beam has both a role in the frame structure and a role in the shear wall structure.

Defined in material mechanics: a component with bending deformation as the main deformation is called a beam. The characteristics of the deformation of the beam under vertical load are shown.

Under the action of vertical load, the beam produces hidden bending deformation, and one side is tensile on one side. And the other side is compressed. At the same time, the shear force is transferred through the mutual dislocation between the cross-sections, and finally the vertical load acting on it is transferred to the supports on both sides.

The internal forces of a beam include shear forces and bending moments.

Functionally, there are structural beams, such as foundation ground beams, frame beams, etc.; Together with vertical components such as columns and load-bearing walls, it forms a spatial structural system, and there are structural beams, such as ring beams, lintel beams, connecting beams, etc., which play a structural role in crack resistance, earthquake resistance, and stability and fiber stabilization.

According to the structural engineering attributes, beams can be divided into: frame beams, frame beams supported by shear walls, inner frame beams, beams, masonry wall beams, masonry lintels, shear wall connecting beams, shear wall dark beams, and shear wall frame beams.

From the construction technology, there are cast-in-place beams, prefabricated beams, etc.

Oh, this one, I'll try to help you out:

The reaction force at the support of the simply supported beam is r, the uniform load on the beam is q, and the calculated span length of the beam is l.

From the principle of static equilibrium, it is obtained:

r=ql/2

The length of the calculated section of the intercepted beam is x, the detachment is taken, and the counterclockwise bending moment is positive, the moment is taken for the calculated point x-plane, and the combined bending moment is zero.

There is mx=rx-qx 2 2=(qlx 2)-(qx 2 2) to find the derivative of x, there is a derivative.

m’=ql/2-qx

There is a second derivative.

m’=-q＜0

Therefore, it can be determined that m has a maximum;

Let the first derivative be equal to zero, yes.

ql/2-qx=0

So, x=l 2

Bring it back to MX, there is.

mmax=m(x=l/2)=(ql^2/4)-(ql^2/8)=ql^2/8

That's it.

Oh, I'll help you with this question.

1. Beam weight: q1=;

2. Load quietly return to the load: q2=10*;

3. Total calculated load: q=q1+q2=;

4. Calculation span: l=;

5. Calculation of internal forces:

Maximum bending moment. It took place in the Jianzhi era to build a beam.

The mid-span cross-section: mmax=q*l2 8=

Maximum shear force for start-up.

Occurs in the support cross-section: q left max = q right max = q * l * calculated completed. So, okay?

Uh, I don't know if I want to design or standard.

m=(1 8)ql 2=4*36 8=9 tons of m; A=KM BH0 2=According to the concrete is C25, then A0=A 250=Check the table = The required reinforcement area is Fa= Bh0(RN The main cherry high reinforcement mining beam is 3 26, stirrups.

Use a side song to transport 6@200 one.