How to calculate force and moment for trapezoidal load

1.

The uniform load can be regarded as a concentrated force. The size of the concentrated force is the area of the uniform load (Q · L), which acts on the midpoint (L / 2) of the distribution area

using the formula of uniformly distributed load to calculate bending moment, it can be simply considered that M = (Q * x ^ 2) / 2, X is the length of uniformly distributed load. Its origin is: Q * x is the resultant force F acting on the structure, the unit is n, the action point of resultant force is located at the midpoint of load action, so the arm of force of F is x / 2m, so the bending moment M = (Q * x ^ 2) / 2

In physics, torque refers to the tendency that the force makes the object rotate around the axis of rotation or fulcrum. The unit of moment is Newton meter. The Greek letter is tau

The concept of

moment originated from Archimedes' research on lever. Rotational torque is also called torque or torque. Torque can change the rotational motion of an object. Pushing or pulling involves forces, while torsion involves moments. The moment is equal to the cross proct of the radial vector and the applied force

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Properties of moment:

1. The moment of force F to point O is not only determined by the force, but also related to the position of moment center. The moment varies with the position of the moment center

When the force is zero or the arm of force is zero, the moment is zero

When the force moves along its action line, because the magnitude, direction and arm of the force do not change, the moment does not change

The algebraic sum of the moments of two mutually balanced forces at the same point is equal to zero

2.

Bending moment = (F + L) * 2 / M

where 4T should be understood as the total weight, then the uniformly distributed load q = 40 / L. users need to understand whether the two ends of the beam are simply supported on the column or fixed on the concrete column

If 4T is the total weight and the two ends of the beam are simply supported on the column, the maximum bending moment is at the midspan section. The calculation formula of bending moment M on this section is as follows: M = 1 / 8 · QL & # 178; Where l is the calculation span = 1.05 × The clear span is 3.5 = 3.675 (m), so q = 40 / 3.675 = 10.88kn/m

∴M＝1/8·qL² ＝ zero point one two five × ten point eight eight × 3.675²＝ 18.37KN·m

if the beam is embedded in the column, calculate the fixed support, and the maximum bending moment is at the support; if the beam is only built on the column, then it should be simply supported, and the maximum bending moment is in the middle of the span. Check the structural static calculation manual

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precautions:

1. The bending moment at the fixed end is different from that mentioned above. If the two ends of a beam are fixed and subjected to uniform load, the bending moment at the middle of the span is smaller than that at the fixed end. Generally, the fixed end bending moment is larger, but it also depends on the situation

The bending moment at the fixed end is the bending moment at the fixed end, but the bending moment is different from that mentioned above. If the two ends of a beam are fixed and subjected to uniform load, the bending moment at the middle of the span is smaller than that at the fixed end

Generally, the fixed end bending moment is larger, but it also depends on the situation. The resultant moment of the normal distribution of internal force component on the cross section is called bending moment

4. The bending moment at the bottom of the beam is positive, and the bending moment at the top of the beam or the beam surface is negative. The positive sign of the bending moment of the column section is determined by the direction around the centroid, which is positive clockwise and negative anticlockwise. Fixed end bending moment belongs to bending moment, which is because it is constrained by one or more fixed joints

3. q=(1-25 α^ 2+ α^ 3)q! a= α L A is 1 / 2 of the length of the lower side of the trapezoid longer than the upper side, l is the length of the lower side!

4. M=1/10qL2< 2 is superscript & gt;, According to the horizontal projection length of the inclined plate, the plate reinforcement should be configured according to the structural requirements.

5. Two equilibrium equations can be solved:
force equilibrium equation: that is, the vertical force satisfies the equilibrium, and the sum of the concentrated forces above is equal to the sum of the distributed forces below
moment balance equation: that is, the balance equation for the moment of the b-end train, of course, the balance equation for the moment of the a-end train can also be used. The same effect, solve two equations, you can get two unknowns

6. In order to convert the total load into the uniform distribution load, the equivalent conversion must be done, and the difference between the equivalent conversion of parts and the total load conversion of parts and the equivalent uniform distribution load must be made clear, which is mainly related to the type of total load and the point of action. The internal force value (main bending moment) at a certain point of the total load is equal to the same internal force value at the same point of the uniform distribution load

7.

1. First, calculate the total load of trapezoidal load (trapezoidal area * load concentration: actually two triangles + 1 rectangle) acting on the middle point of the beam to calculate the support reaction

2. Section method: take the moment of the middle point (support reaction force * beam length / 2-moment of the half trapezoidal load on the upper plate of the beam to the middle point) to get the weight of M

According to the limit equilibrium theory, the shear capacity of reinforced concrete beams without web reinforcement is composed of the shear resistance of concrete in shear compression zone, shear friction between inclined cracks, aggregate bite force and pin bolt action of longitudinal reinforcement

for the reinforced concrete beams with stirrups, the shear capacity of the beams without stirrups is improved e to the confinement of stirrups on the core concrete and the width of diagonal cracks. The stress of stirrups intersecting with diagonal cracks can basically reach its yield strength, and the shear resistance of stirrups is the proct of their tensile strength and the cross-sectional area of stirrups intersecting with diagonal cracks

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more knowledge points involved in trapezoidal distributed load:

when limit state design of bearing capacity or limit state design of serviceability is based on standard combination, standard value or combination value should be used as representative value for variable load according to combination regulations

variable load combination value should be the standard value of variable load multiplied by load combination value coefficient. When the serviceability limit state is designed according to the frequency combination, the frequency value and quasi permanent value should be used as the representative value of variable load; In the design of quasi permanent combination, the quasi permanent value should be used as the representative value of variable load

the variable load frequency value should take the variable load standard value multiplied by the load frequency value coefficient. The quasi permanent value of variable load shall be the standard value of variable load multiplied by the coefficient of quasi permanent value of load

8. The concrete structure and calculation method are different, such as simply supported beam
the span is l, the left fulcrum is RA, the right fulcrum is Rb, and the uniform load strength is Q
fulcrum reaction: RA = RB = QL / 2
if the fulcrum RA is the origin of the coordinate and the right is the positive direction of the X axis, then the bending moment equation is:
MX = ra * x-qx

9.

the above derivation process is only to help understand, and the conclusion need not be remembered. Because in the actual calculation, the more common method is to decompose the trapezoidal distributed load into uniform distributed load and triangular distributed load. So just break it down and remember the last two

10.

The method of calculating the moment of uniformly distributed load Q to the point:

the formula used:

1, M = f * D (the moment is equal to the resultant force multiplied by the arm of force)

d is the distance from the point of action to the straight line along the direction of force passing through the center of gravity of the triangle

D is not the distance between two points, but the distance between a point and a straight line

2, f = 1 / 2aq (a is the length of the bottom edge, q is the maximum line load)

resultant force F is the area of the load distribution, which is generally a right triangle

In this case, the uniformly distributed load can be regarded as a concentrated force acting in the middle × eighteen × 9 is to regard the uniformly distributed load as a concentrated force acting on point C, and then calculate the moment at point D. the formula you said is 1 / 2 * QL & # 178;, In this question, l = 18

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the difference of moment between uniformly distributed load and concentrated load:

1. The load is different in the picture, and the bending moment diagram of concentrated load will appear sharp point

When the load is continuous and equal in size, it is called uniform load. The uniformly distributed load per unit area is called the uniformly distributed surface load, which is usually expressed by the letter Q, and its unit is n / M & # 178 Newton / square meter) or kn / M & # 178 Kn / m2)

3. The uniform load per unit length is called uniform load, which is usually expressed by the letter Q, and the unit is n / M (n / M) or kn / M (KN / M)

4. Concentrated load refers to the load of reaction force acting on a point, which is called concentrated load, and its unit is kilonewton. The simple point is that the load acting on a point is called concentrated load. For example, if the structural column is arranged on the beam, then the load at this point is called concentrated load