Calculation of concentrated load by concentrated force
Publish: 2021-05-22 01:12:41
1. If the resultant force is in the third place, your linear load may be distributed in a triangle. The solution of the resultant force is the same as that of the area. In your question, the concentrated load F1 is 3 / 2 * QL. In addition, you can go through the definition of higher mathematics definite integral derivation, is also the meaning, hope to help you.
2. Concentrated load refers to the load of reaction force acting on a point, which is called concentrated load, and its unit is kilonewton
concentrated load: in any case, 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
uniformly distributed load: the load that continuously acts on a large area of the component surface can not be regarded as concentrated load, and any two loads with the same magnitude and direction are called uniformly distributed load. For example, the self weight of the wall. Its unit is kilonewton per meter
calculation method of concentrated line load
concentrated line load = permanent load (dead weight of reinforced concrete + dead weight of formwork timber) × Partial factor + Construction uniform live load × Partial coefficient
self weight of reinforced concrete = sectional area of beam (M2) × 26kn / m3 (26kn / m3 is the specific gravity of reinforced concrete, converted into kn / m3 as the unit, and the specific gravity of reinforced concrete is 26kn / m3 when calculating the concentrated line load.)
the self weight of formwork wood = perimeter of beam section formwork (m) × 0.5kn/m2 (the value is 0.5kn/m2 when calculating the concentrated line load)
construction uniform live load = beam width m × 3kn / m2
partial factor
the partial factor of permanent load is 1.2; The partial coefficient of live load is taken as 1.4 < br / < br / < br / < br / < br / < br / < br /
example: beam height 700 and beam width 700 < br / < br / < br /
example: beam height 700 and beam width 700 are as follows: beam height 700 and beam width 700 < br /
Case: beam height 700 and beam width 700 < br /
example: beam height 700 and beam width 700 < br /
Case: case: beam height 700: beam height 700, and beam width 700: case: as: beam height 700, and beam width 700 < br / < br /
example: beam height 700 and beam height and beam height 1000, beam height 1000 and beam width 500 are as height 1000 and beam height 1000 and beam height 1000, beam width 500 < br / < br / < br / < br /
Case: beam height 1000: beam height 1000 and beam height 1000: beam height 1000 and beam height 1000, beam width 500 < and beam width 500 < br] + 0.60x3x1.40 = 20.808 ＞ 20 needs to be demonstrated.
concentrated load: in any case, 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
uniformly distributed load: the load that continuously acts on a large area of the component surface can not be regarded as concentrated load, and any two loads with the same magnitude and direction are called uniformly distributed load. For example, the self weight of the wall. Its unit is kilonewton per meter
calculation method of concentrated line load
concentrated line load = permanent load (dead weight of reinforced concrete + dead weight of formwork timber) × Partial factor + Construction uniform live load × Partial coefficient
self weight of reinforced concrete = sectional area of beam (M2) × 26kn / m3 (26kn / m3 is the specific gravity of reinforced concrete, converted into kn / m3 as the unit, and the specific gravity of reinforced concrete is 26kn / m3 when calculating the concentrated line load.)
the self weight of formwork wood = perimeter of beam section formwork (m) × 0.5kn/m2 (the value is 0.5kn/m2 when calculating the concentrated line load)
construction uniform live load = beam width m × 3kn / m2
partial factor
the partial factor of permanent load is 1.2; The partial coefficient of live load is taken as 1.4 < br / < br / < br / < br / < br / < br / < br /
example: beam height 700 and beam width 700 < br / < br / < br /
example: beam height 700 and beam width 700 are as follows: beam height 700 and beam width 700 < br /
Case: beam height 700 and beam width 700 < br /
example: beam height 700 and beam width 700 < br /
Case: case: beam height 700: beam height 700, and beam width 700: case: as: beam height 700, and beam width 700 < br / < br /
example: beam height 700 and beam height and beam height 1000, beam height 1000 and beam width 500 are as height 1000 and beam height 1000 and beam height 1000, beam width 500 < br / < br / < br / < br /
Case: beam height 1000: beam height 1000 and beam height 1000: beam height 1000 and beam height 1000, beam width 500 < and beam width 500 < br] + 0.60x3x1.40 = 20.808 ＞ 20 needs to be demonstrated.
3. The length of load concentration x is the equivalent force (also known as equivalent concentrated force). At this time, the equivalent action point is at the middle point of the length, so the bending moment to one end is half of the length of the equivalent force * (that is, the distance from the equivalent action point to a section); This can only be used for uniform load concentration
load concentration: it refers to the concentration degree of load, including line load concentration degree and area load concentration degree. The former unit is kn / m; The latter is the external force of kn / m2
acting on the component. If the area of the acting surface is far less than the size of the component, it can be simplified as a concentrated force.
load concentration: it refers to the concentration degree of load, including line load concentration degree and area load concentration degree. The former unit is kn / m; The latter is the external force of kn / m2
acting on the component. If the area of the acting surface is far less than the size of the component, it can be simplified as a concentrated force.
4. The difference between uniform load and concentrated load is that the action point line or plane of uniform load, the action point of concentrated load is a point, and the action effect of uniform load can be converted into concentrated load< However, there are three basic principles:
1) when the load position is the same, the resultant point of uniform load is the action point of concentrated load
2) with the same total value, the total load value of uniform load is the load value of concentrated load
3) the error is the smallest, and the influence of the simplified model on different internal forces is different. Different simplified models can be selected according to different internal forces to minimize the error<
specific steps:
1) draw the figure of uniformly distributed load
2) find out the centroid of the figure of uniformly distributed load
3) uniformly distributed load can be transformed into a concentrated load whose size is the sum of uniformly distributed load, and the action point is the centroid of the figure of uniformly distributed load.
1) when the load position is the same, the resultant point of uniform load is the action point of concentrated load
2) with the same total value, the total load value of uniform load is the load value of concentrated load
3) the error is the smallest, and the influence of the simplified model on different internal forces is different. Different simplified models can be selected according to different internal forces to minimize the error<
specific steps:
1) draw the figure of uniformly distributed load
2) find out the centroid of the figure of uniformly distributed load
3) uniformly distributed load can be transformed into a concentrated load whose size is the sum of uniformly distributed load, and the action point is the centroid of the figure of uniformly distributed load.
5. According to the strength control: 35KN is 3500kg concentrated force. The premise is that both sides of I-beam should be fixed, not both ends. Just to keep it from swinging left and right. See calculation 1
if it is only an independent one, it can bear 1300kg concentrated force. See calculation 2
calculation 1:
1, section characteristic calculation
A = 5.5370e-003; Xc =6.1000e-002; Yc =1.4000e-001;< br /> Ix =7.1150e-005; Iy =3.4410e-006;< br /> ix =1.1340e-001; iy =2.4900e-002;< br /> W1x=5.0820e-004; W2x=5.0820e-004;< br /> W1y=5.6400e-005; W2y=5.6400e-005;
2. Calculation of self weight action of simply supported beam
calculation of self weight load action of beam:
self weight of simply supported beam (KN): g = 3.9119e + 000
the average line load (KN / M) P = 4.3465e-001 under the action of self weight
3. Dead load action on beam
Load No.
load type load value 1 load parameter 1 load parameter 2 load value 2
1 435.004.500.00 0.00
4. Bearing reaction (pressure is positive, unit: KN)
△ dead load standard value bearing reaction
left bearing reaction RD1 = 19.456, Right support reaction RD2 = 19.456
5 Calculation results of internal force of each section on beam
△ combination 1:1.2 constant + 1.4 live
section No.: 1 23 4 5 6 7
bending moment (kn. M): - 0.000 17.364 34.434 51.211 67.694 83.884 99.781
shear force (KN): 23.347 22.956 22.565 22.174 21.782 21.391 - 21.000
section No.: 8 9 10 11 12 13
bending moment (kn. M): 83.884 67.694 51.211 34.434 17.364 - 0.000
shear force (KN): - 21.391 - 21.782 - 22.174 - 22.565 - 22.956 - 23.347
△ combination 2: 1.35 constant + 0.7 * 1.4 live
section No.: 1 23 45 6 7
moment (kn. M): - 0.000 19.534 38.738 57.612 76.156 94.370 112.254
shear force (KN): 26.266 25.825 25.385 24.945 24.505 24.065 - 23.625
section No.: 8 9 10 11 12 13
moment (kn. M): 94.370 76.156 57.612 38.738 19.534 - 0.000
moment (kn. M): 94.370 76.156 57.612 38.738 19.534 - 0.000 Shear force (KN): - 24.065 - 24.505 - 24.945 - 25.385 - 25.825 - 26.266
6, local stability checking
flange width thickness ratio B / T = 3.50 & lt; Allowable width thickness ratio [B / T] = 15.0
calculated height thickness ratio of Web H0 / TW = 27.25 & lt; The allowable height thickness ratio [H0 / TW] = 80.0
7, the section strength checking calculation of simply supported beam
the maximum positive bending moment of simply supported beam (kn. M): 112.254 (combination: 2; Control position: 4.500m)
maximum stress of strength calculation (n / mm2): 210.367 & lt; F = 215.000
the checking calculation of bending strength of simply supported beam meets the requirements
the maximum shear force of simply supported beam (KN): 26.266 (combination: 2; Control position: 0.000m)
shear calculation stress of simply supported beam (n / mm2): 12.712 & lt; FV = 125.000
the shear bearing capacity of simply supported beam meets the requirements<
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calculation 2:
1, section characteristic calculation
A = 5.5370e-003; Xc =6.1000e-002; Yc =1.4000e-001;< br /> Ix =7.1150e-005; Iy =3.4410e-006;< br /> ix =1.1340e-001; iy =2.4900e-002;< br /> W1x=5.0820e-004; W2x=5.0820e-004;< br /> W1y=5.6400e-005; W2y=5.6400e-005;
2. Calculation of self weight action of simply supported beam
calculation of self weight load action of beam:
self weight of simply supported beam (KN): g = 3.9119e + 000
the average line load (KN / M) P = 4.3465e-001 under the action of self weight
3. Dead load action on beam
load number load type load value 1 load parameter 1 load parameter 2 load value 2
1 412.00 4.50 0.00 0.00
4. Bearing reaction (pressure is positive, unit: KN)
△ dead load standard value bearing reaction
left bearing reaction RD1 = 7.956, Right support reaction RD2 = 7.956
5 Calculation results of internal force of each section on beam
△ combination 1:1.2 constant + 1.4 live
section No.: 1 23 4 5 6 7
bending moment (kn. M): - 0.000 7.014 13.734 20.161 26.294 32.134 37.681
shear force (KN): 9.547 9.156 8.765 8.374 7.982 7.591 - 7.200
section No.: 8 9 10 11 12 13
bending moment (kn. M): 32.134 26.294 20.161 13.734 7.014 - 0.000
shear force (KN): - 7.591 - 7.982 - 8.374 - 8.765 - 9.156 - 9.547
△ combination 2: 1.35 constant + 0.7 * 1.4 live
section No.: 1 23 4 5 6 7
bending moment (kn. M): - 0.000 7.890 15.451 22.681 29.581 36.151 42.391
shear force (KN): 10.741 10.300 9.860 9.420 8.980 8.540 - 8.100
section No.: 8 9 10 11 12 13
bending moment (kn. M): 36.151 29.581 22.681 15.451 7.890 - 0.000
shear Force (KN): - 8.540 - 8.980 - 9.420 - 9.860 - 10.300 - 10.741
6, local stability checking
flange width thickness ratio B / T = 3.50 & lt; Allowable width thickness ratio [B / T] = 15.0
calculated height thickness ratio of Web H0 / TW = 27.25 & lt; The allowable height thickness ratio [H0 / TW] = 80.0
7, the section strength checking calculation of simply supported beam
the maximum positive bending moment of simply supported beam (kn. M): 42.391 (combination: 2; Control position: 4.500m)
maximum stress of strength calculation (n / mm2): 79.442 & lt; F = 215.000
the checking calculation of bending strength of simply supported beam meets the requirements
the maximum shear force of simply supported beam (KN): 10.741 (combination: 2; Control position: 0.000m)
shear calculation stress of simply supported beam (n / mm2): 5.198 & lt; FV = 125.000
the shear bearing capacity of simply supported beam meets the requirements
8. Checking calculation of overall stability of simply supported beam
slenderness ratio outside the plane λ y: 361.446
overall stability coefficient of beam φ b: 400
the maximum positive bending moment of simply supported beam (kn. M): 42.391 (combination: 2; Control position: 4.500m)
maximum stress for overall stability calculation of simply supported beam (n / mm2): 208.536 & lt; F = 215.000
the overall stability of the simply supported beam meets the requirements< br />9、 Deflection checking calculation of simply supported beam
△ standard combination: 1.0 constant + 1.0 live
section No.: 1 23 4 5 6 7
bending moment (kn. M): - 0.000 5.845 11.445 16.801 21.912 26.779 31.401
shear force (KN): 7.956 7.630 7.304 6.978 6.652 6.326 - 6.000
section No.: 8 9 10 11 12 13
bending moment (kn. M): 26.779 21.912 16.801 11.445 5.845 - 0.000
shear force (KN): - 6.326 - 6.652 - 6.978 - 7.304 - 7.630 - 7.956
deflection calculation result of simply supported beam:
section No.: 1 23 4 56 7
deflection value (mm): 0.000 3.742 7.261 10.343 12.782 14.381 14.954
section No.: 8 9 10 11 12 13
deflection value (mm): 14.381 12.782 10.343 7.261 3.742 0.000
position of maximum deflection: 4.500m
calculated maximum deflection: 14.954 (mm) < Allowable deflection: 50.000 (mm)
the deflection of simply supported beam meets the requirements.
if it is only an independent one, it can bear 1300kg concentrated force. See calculation 2
calculation 1:
1, section characteristic calculation
A = 5.5370e-003; Xc =6.1000e-002; Yc =1.4000e-001;< br /> Ix =7.1150e-005; Iy =3.4410e-006;< br /> ix =1.1340e-001; iy =2.4900e-002;< br /> W1x=5.0820e-004; W2x=5.0820e-004;< br /> W1y=5.6400e-005; W2y=5.6400e-005;
2. Calculation of self weight action of simply supported beam
calculation of self weight load action of beam:
self weight of simply supported beam (KN): g = 3.9119e + 000
the average line load (KN / M) P = 4.3465e-001 under the action of self weight
3. Dead load action on beam
Load No.
load type load value 1 load parameter 1 load parameter 2 load value 2
1 435.004.500.00 0.00
4. Bearing reaction (pressure is positive, unit: KN)
△ dead load standard value bearing reaction
left bearing reaction RD1 = 19.456, Right support reaction RD2 = 19.456
5 Calculation results of internal force of each section on beam
△ combination 1:1.2 constant + 1.4 live
section No.: 1 23 4 5 6 7
bending moment (kn. M): - 0.000 17.364 34.434 51.211 67.694 83.884 99.781
shear force (KN): 23.347 22.956 22.565 22.174 21.782 21.391 - 21.000
section No.: 8 9 10 11 12 13
bending moment (kn. M): 83.884 67.694 51.211 34.434 17.364 - 0.000
shear force (KN): - 21.391 - 21.782 - 22.174 - 22.565 - 22.956 - 23.347
△ combination 2: 1.35 constant + 0.7 * 1.4 live
section No.: 1 23 45 6 7
moment (kn. M): - 0.000 19.534 38.738 57.612 76.156 94.370 112.254
shear force (KN): 26.266 25.825 25.385 24.945 24.505 24.065 - 23.625
section No.: 8 9 10 11 12 13
moment (kn. M): 94.370 76.156 57.612 38.738 19.534 - 0.000
moment (kn. M): 94.370 76.156 57.612 38.738 19.534 - 0.000 Shear force (KN): - 24.065 - 24.505 - 24.945 - 25.385 - 25.825 - 26.266
6, local stability checking
flange width thickness ratio B / T = 3.50 & lt; Allowable width thickness ratio [B / T] = 15.0
calculated height thickness ratio of Web H0 / TW = 27.25 & lt; The allowable height thickness ratio [H0 / TW] = 80.0
7, the section strength checking calculation of simply supported beam
the maximum positive bending moment of simply supported beam (kn. M): 112.254 (combination: 2; Control position: 4.500m)
maximum stress of strength calculation (n / mm2): 210.367 & lt; F = 215.000
the checking calculation of bending strength of simply supported beam meets the requirements
the maximum shear force of simply supported beam (KN): 26.266 (combination: 2; Control position: 0.000m)
shear calculation stress of simply supported beam (n / mm2): 12.712 & lt; FV = 125.000
the shear bearing capacity of simply supported beam meets the requirements<
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
calculation 2:
1, section characteristic calculation
A = 5.5370e-003; Xc =6.1000e-002; Yc =1.4000e-001;< br /> Ix =7.1150e-005; Iy =3.4410e-006;< br /> ix =1.1340e-001; iy =2.4900e-002;< br /> W1x=5.0820e-004; W2x=5.0820e-004;< br /> W1y=5.6400e-005; W2y=5.6400e-005;
2. Calculation of self weight action of simply supported beam
calculation of self weight load action of beam:
self weight of simply supported beam (KN): g = 3.9119e + 000
the average line load (KN / M) P = 4.3465e-001 under the action of self weight
3. Dead load action on beam
load number load type load value 1 load parameter 1 load parameter 2 load value 2
1 412.00 4.50 0.00 0.00
4. Bearing reaction (pressure is positive, unit: KN)
△ dead load standard value bearing reaction
left bearing reaction RD1 = 7.956, Right support reaction RD2 = 7.956
5 Calculation results of internal force of each section on beam
△ combination 1:1.2 constant + 1.4 live
section No.: 1 23 4 5 6 7
bending moment (kn. M): - 0.000 7.014 13.734 20.161 26.294 32.134 37.681
shear force (KN): 9.547 9.156 8.765 8.374 7.982 7.591 - 7.200
section No.: 8 9 10 11 12 13
bending moment (kn. M): 32.134 26.294 20.161 13.734 7.014 - 0.000
shear force (KN): - 7.591 - 7.982 - 8.374 - 8.765 - 9.156 - 9.547
△ combination 2: 1.35 constant + 0.7 * 1.4 live
section No.: 1 23 4 5 6 7
bending moment (kn. M): - 0.000 7.890 15.451 22.681 29.581 36.151 42.391
shear force (KN): 10.741 10.300 9.860 9.420 8.980 8.540 - 8.100
section No.: 8 9 10 11 12 13
bending moment (kn. M): 36.151 29.581 22.681 15.451 7.890 - 0.000
shear Force (KN): - 8.540 - 8.980 - 9.420 - 9.860 - 10.300 - 10.741
6, local stability checking
flange width thickness ratio B / T = 3.50 & lt; Allowable width thickness ratio [B / T] = 15.0
calculated height thickness ratio of Web H0 / TW = 27.25 & lt; The allowable height thickness ratio [H0 / TW] = 80.0
7, the section strength checking calculation of simply supported beam
the maximum positive bending moment of simply supported beam (kn. M): 42.391 (combination: 2; Control position: 4.500m)
maximum stress of strength calculation (n / mm2): 79.442 & lt; F = 215.000
the checking calculation of bending strength of simply supported beam meets the requirements
the maximum shear force of simply supported beam (KN): 10.741 (combination: 2; Control position: 0.000m)
shear calculation stress of simply supported beam (n / mm2): 5.198 & lt; FV = 125.000
the shear bearing capacity of simply supported beam meets the requirements
8. Checking calculation of overall stability of simply supported beam
slenderness ratio outside the plane λ y: 361.446
overall stability coefficient of beam φ b: 400
the maximum positive bending moment of simply supported beam (kn. M): 42.391 (combination: 2; Control position: 4.500m)
maximum stress for overall stability calculation of simply supported beam (n / mm2): 208.536 & lt; F = 215.000
the overall stability of the simply supported beam meets the requirements< br />9、 Deflection checking calculation of simply supported beam
△ standard combination: 1.0 constant + 1.0 live
section No.: 1 23 4 5 6 7
bending moment (kn. M): - 0.000 5.845 11.445 16.801 21.912 26.779 31.401
shear force (KN): 7.956 7.630 7.304 6.978 6.652 6.326 - 6.000
section No.: 8 9 10 11 12 13
bending moment (kn. M): 26.779 21.912 16.801 11.445 5.845 - 0.000
shear force (KN): - 6.326 - 6.652 - 6.978 - 7.304 - 7.630 - 7.956
deflection calculation result of simply supported beam:
section No.: 1 23 4 56 7
deflection value (mm): 0.000 3.742 7.261 10.343 12.782 14.381 14.954
section No.: 8 9 10 11 12 13
deflection value (mm): 14.381 12.782 10.343 7.261 3.742 0.000
position of maximum deflection: 4.500m
calculated maximum deflection: 14.954 (mm) < Allowable deflection: 50.000 (mm)
the deflection of simply supported beam meets the requirements.
6. Very simple from the literal meaning can understand. Concentrated load, for example, for a bridge, a car with a load of tens of tons stops on the bridge, then the big car is the concentrated load of the bridge, and the scattered load of the bridge, that is, the distributed load, is its own weight, including the bridge and the concrete pavement above the bridge.
7. In order to transform uniform load into concentrated load, e to different structural characteristics and boundary conditions, it is impossible to have a unified calculation formula, but there are three basic principles:
when the load position is the same, the resultant point of uniform load is the action point of concentrated load
with the same total value, the total load value of uniform load is the load value of concentrated load
the error is the smallest, and the influence of the simplified model on different internal forces is different. Different simplified models can be selected according to different internal forces to minimize the error. The specific steps are as follows: 1) draw the figure of uniform load
2) find out the centroid of the figure of uniform load
3) uniform load can be transformed into a concentrated load whose size is the sum of uniform load, and the action point is the centroid of the figure of uniform load.
when the load position is the same, the resultant point of uniform load is the action point of concentrated load
with the same total value, the total load value of uniform load is the load value of concentrated load
the error is the smallest, and the influence of the simplified model on different internal forces is different. Different simplified models can be selected according to different internal forces to minimize the error. The specific steps are as follows: 1) draw the figure of uniform load
2) find out the centroid of the figure of uniform load
3) uniform load can be transformed into a concentrated load whose size is the sum of uniform load, and the action point is the centroid of the figure of uniform load.
8. Divide this concentrated force by the area of action, and it becomes a surface load!
9.
There will be sharp points in the bending moment diagram of concentrated load
the following is the basic load diagram, please refer to the textbook
10. In short, if I use acupuncture, you are the concentrated load, if I use brick to pat you, you are the evenly distributed load. There is a saying about this thing. For example, when people stand on the board, it is a concentrated load. When snow falls on the board, it is a uniformly distributed load
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