Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an anti-overturning reinforcing method for a single-column pier beam bridge. The method comprises the following steps:
(1) determining an anti-overturning side and an overturning side according to a preset load condition, and setting an overturning load target value;
(2) constructing a moment state equation of the overturning critical state according to the overturning load target value;
(3) and adjusting the size of the supports of the single-column pier beam bridge or the distance between the anti-torsion supports according to the moment state equation to reinforce the single-column pier beam bridge. The reinforcing method of the single-column pier beam bridge is simple and easy to realize, the reinforcement can be completed by changing the size of the support, and the anti-overturning capacity of the single-column pier beam bridge is improved.
The distance between the anti-torsion supports is adjusted, in particular to the distance between two anti-torsion supports in the same pair of anti-torsion supports.
In order to ensure that the single-column pier beam bridge does not overturn and improve the safety, the overturning load target value is larger than the load of the overturning side under the preset load condition, and is usually 1.3-2 times of the overturning side load under the preset load condition.
In the critical overturning state, the distance between the rotation axis of the box girder of the single-column pier girder bridge and the near edge (the edge on the nearest side) of the support is equal to the thickness of the support.
When the single-column pier beam bridge reaches the support-seat-free state, the rotating axis is located at 1/4R away from the support center for a round support seat, wherein R is the radius of the support seat, and the rotating axis for a rectangular support seat (the horizontal section is rectangular) is located at 1/6B away from the support seat center, and B is the width of the rectangle.
The automobile load produces vertical load and moment of torsion to the girder bridge under the unbalance loading effect:
in the stabilization stage, the counterforce of the pier is provided by the combination of the supports (anti-torsion supports) at the two side ends and the middle single-column pier; when the anti-overturning box girder is used, the rotating axis of the box girder gradually deviates from the geometric center of the support under the load action of two sides of the box girder, and when the deviation amount reaches a certain degree, the anti-overturning side anti-torque support is in a void phenomenon and enters a gradual change stage.
In the gradual change stage, because the support on the anti-overturning side (including the anti-overturning support on the side) is in a support-disengaging state before the critical state, the support on the side can not generate the anti-overturning moment;
in the overturning stage, the rotation axis reaches the limit position, the support on the anti-overturning side is already emptied at the moment, the overturning moment generated by the unbalanced load on the overturning side is equal to the sum of the self-gravity moment of the upper structure (namely the box girder), the moment of the anti-overturning side load and the counter-force moment of the anti-overturning side support, and the anti-overturning side support and the middle single-column pier support jointly resist the load in the vertical direction.
The single-column pier beam bridge adopts the overturning moment as the overturning critical state and adopts the overturning moment of the single-column pier beam bridge in the critical state as the anti-overturning bearing moment of the single-column pier beam bridge. When the method is actually applied, the overturning side is firstly determined, and then the other side is used as the anti-overturning side.
When the single-column pier beam bridge reaches the overturning stable critical state, the rotating axis of the single-column pier beam bridge is positioned at the position where the bottom edge of the support upwards spreads towards the inner side of the support by 45 degrees. When the shapes of the supports are different, the positions of the rotation axes in the critical state are also different.
When the support of the single-column pier beam bridge is circular in section, the distance from the rotation axis to the edge of the support (an intermediate support and a non-torsion support) is equal to the thickness of the support. When the cross section of the support of the single-column pier beam bridge is rectangular, the distance from the rotating axis to the edge of the support (an intermediate support and a non-torsion-resistant support) is equal to the thickness of the support.
The moment state equation of the overturning critical state is as follows:
LR=LO,
wherein L isRThe moment of resistance to overturning in the critical state of overturning:
LOthe target value of the overturning moment is calculated according to the target value of the overturning load.
The overturning moment L in the overturning critical stateRAccording to the formula:
<math>
<mrow>
<msub>
<mi>L</mi>
<mi>R</mi>
</msub>
<mo>=</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>P</mi>
<mi>A</mi>
<mi>i</mi>
</msubsup>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>A</mi>
<mi>i</mi>
</msubsup>
<mo>+</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msubsup>
<mi>P</mi>
<mi>B</mi>
<mi>j</mi>
</msubsup>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>B</mi>
<mi>j</mi>
</msubsup>
<mo>+</mo>
<msub>
<mi>q</mi>
<mi>G</mi>
</msub>
<mo>×</mo>
<msub>
<mi>l</mi>
<mn>0</mn>
</msub>
<mo>×</mo>
<msub>
<mi>l</mi>
<mi>q</mi>
</msub>
<mo>,</mo>
</mrow>
</math>
and calculating to obtain the result, wherein,to resist the ith load on the overturning side,the distance from the ith load center of the anti-overturning side to the rotation axis under the preset load condition is defined, and m is the number of loads on the anti-overturning side under the preset load condition;
for the counterforce of the jth torsion support on the overturning side under the preset load condition,the distance from the center of the jth anti-torsion support on the overturning side to the rotation axis under the preset load condition is defined, and n is the number of the anti-torsion supports on the overturning side under the preset load condition;
qGlinear weight of the box girder, /)0Is the span of the box girder, /)qThe distance between the center line of the box girder and the rotation axis in the horizontal direction.
The single-column pier beam bridge rotates under the action of unbalance loading, the bridge is not overturned and damaged at the moment, and the overturning axis (namely the rotating axis) of the single-column pier beam bridge is calculated according to the principle that the overturning moment is equal to the anti-overturning moment.
For a beam bridge, the load is typically an automobile,and the gravity of the ith automobile on the overturn resisting side is calculated according to the mass through a gravity formula.
When the linear single-column pier beam bridge is calculated, the counter force of each anti-torsion support in the overturning critical state can be calculated according to a continuous beam calculation method.
The values of m and n in the invention vary with the actual application.
The middle single-column pier generates vertical counter force and anti-sliding force along the bottom surface of the box girder to the box girder, the resultant force of the counter force and the anti-sliding force passes through the rotation axis, and the moment is zero. It follows that as the unbalance load increases, the axis of rotation gradually moves toward the side of the load application, and the overturning moment is provided by the reaction force of the end support, the self weight of the box girder and the load on the anti-overturning side.
In the actual use process, the loads on two sides of the single-column pier beam bridge change, and the load change of the anti-overturning side is fully considered, so that the bearing moment of the anti-overturning side can be accurately determined in real time.
Preferably, the target overturning moment value LOAccording to the formula:
<math>
<mrow>
<msub>
<mi>L</mi>
<mi>O</mi>
</msub>
<mo>=</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</munderover>
<msub>
<mi>P</mi>
<mi>O</mi>
</msub>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>o</mi>
<mi>t</mi>
</msubsup>
</mrow>
</math>
is calculated to obtain, wherein POIn order to obtain the target value of the overturning load,the distance between the center of the overturning load and the rotation axis in the horizontal direction is shown, and T is the number of the load on the overturning side.
In the invention, the step (3) of adjusting the size of the support of the single-column pier beam bridge comprises the steps of increasing the radius of the support and reducing the thickness of the support. When the single-column pier beam bridge is reinforced, the radius of the support is increased preferentially, then the thickness of the support is reduced, and finally the distance between the same antitorque supports is increased.
In practical application, the size adjusting range is 10-80% of the initial thickness of the support, and the radius adjusting range is R-RdWherein R isdIs the radius of the pier.
Without specific description, the two anti-torsion supports on the same pier are defined as the same anti-torsion support.
If three variables (including the thickness and the radius of the support and the distance between the anti-torque supports) are changed simultaneously, the overturning load can be improved more, namely the anti-overturning capability is improved, and a reinforcing scheme can be flexibly established according to specific use conditions.
Compared with the prior art, the reinforcing method of the single-column pier beam bridge is simple and easy to realize, the reinforcement is completed only by changing the size of the support, and the anti-overturning capacity of the single-column pier beam bridge is improved.
Detailed Description
The invention will be described in detail below with reference to the drawings and specific embodiments.
In the embodiment, the anti-overturning bearing moment of the single-column pier beam bridge is calculated by taking the Zhejiang Yu Chunhui ramp bridge as an example.
This bridge adopts one-way two lane (lane in every direction), and the cross-section is wide 8m, case roof beam cross-section concrete dimension: the diameter of each pier is 1.1m, the longitudinal gradient is 3.5%, a support with the diameter D of 600mm and the thickness h of 150mm is arranged on each pier, anti-torsion supports are arranged at the head end and the tail end of each pier, the distance l between the two anti-torsion supports in the same anti-torsion support is 2.1m, and the distance between the piers and the lower flange edge of the box girder is 0.4 m.
The reinforcing method of the single-column pier beam bridge comprises the following steps:
(1) determining an anti-overturning side and an overturning side according to a preset load condition, and setting an overturning load target value;
the preset load conditions in this embodiment are as follows:
the carrying capacity of 4 overloaded vehicles is 28.52t, 124.44t, 125.6t and 110.73t respectively, light vehicles are on the inner side, and three heavy vehicles pass by at a lower speed on the outer side.
In this embodiment, the side where the light vehicle is located is determined as the anti-overturning side, and the side where the three heavy vehicles are located is determined as the overturning side.
The distance between the load of 3 automobiles on the overturn side and the center of the box girder is 1.46m, and the distance between the load of 1 automobile on the overturn side and the center of the box girder is about 1.64 m. The vehicle load was applied according to (JTG D60-2004 common Specification for Highway bridge design). At this time, the load of each vehicle on the overturning side is 120 tons, and in order to ensure no overturning, the self weight target value of the vehicle set correspondingly is 165 tons, namely the overturning load target value PO=1617KN。
Setting the overturning critical state and the position of the rotation axis at the moment: and when the overturning critical state is set, the distance between the rotating axis of the box girder of the single-column pier girder bridge and the center of the support is equal to the thickness of the support.
Fig. 1 and 2 are schematic views of the single-column pier beam bridge in the overturning critical state in the embodiment, wherein a line a is a central line of the box girder in the overturning critical state, a line B is a rotation axis, and a large circle area is an enlarged view of a small circle area in fig. 2.
As shown in fig. 2, in the present embodiment, the distance a from the rotation axis of the box girder to the edge of the pedestal in the overturning critical state is determined as h, where h is the pedestal thickness (150 mm).
(2) Constructing a moment state equation of the overturning critical state according to the overturning load target value;
LR=LO,
wherein L isRThe moment of resistance to overturning in the critical state of overturning:
<math>
<mrow>
<msub>
<mi>L</mi>
<mi>R</mi>
</msub>
<mo>=</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>P</mi>
<mi>A</mi>
<mi>i</mi>
</msubsup>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>A</mi>
<mi>i</mi>
</msubsup>
<mo>+</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msubsup>
<mi>P</mi>
<mi>B</mi>
<mi>j</mi>
</msubsup>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>B</mi>
<mi>j</mi>
</msubsup>
<mo>+</mo>
<msub>
<mi>q</mi>
<mi>G</mi>
</msub>
<mo>×</mo>
<msub>
<mi>l</mi>
<mn>0</mn>
</msub>
<mo>×</mo>
<msub>
<mi>l</mi>
<mi>q</mi>
</msub>
<mo>,</mo>
</mrow>
</math>
and calculating to obtain the result, wherein,to resist the loading of the ith load on the capsizing side, as shown in figure 1,the distance from the ith load center of the anti-overturning side to the rotation axis under the preset load condition is defined, and n is the number of loads on the anti-overturning side under the preset load condition;
calculated according to the following formula:
wherein,the distance from the center of the box girder to the vehicle on the anti-overturning side is 1.64m in this embodiment.
For the reaction force of the jth torsion support on the overturning side under a preset load, as shown in figure 1,the distance from the center of the jth torsion-resistant support to the rotation axis of the overturning side under the preset load condition, and m is the preset loadThe number of the anti-torsion supports on the overturning side under the loading condition;
calculated according to the following formula:
wherein,the distance from the center of the torsion-resistant support on the overturning side to the center of the box girder is 1.05m in the embodiment.
qGLinear weight of the box girder, /)0The span of the box girder, as shown in FIG. 1qThe distance between the center line of the box girder and the rotation axis in the horizontal direction.
lqCalculated according to the following formula:
in the present embodiment, the number of anti-overturn side vehicles is 1, that is, n is 1, and the mass is 28.52 t.
In this embodiment m is 2, the reaction force of each torsion-resistant support is obtained by using a continuous beam calculation method, which is specifically as follows:
arranging vehicle loads according to the actual overturning load position of the spring roof bridge to obtain the overturning loads, and then calculating the counter force of each support (torsion-resistant support) under the action of the overturning loads by adopting a continuous beam calculation method.
LOThe target value of the overturning moment can be calculated by the following formula:
<math>
<mrow>
<msub>
<mi>L</mi>
<mi>O</mi>
</msub>
<mo>=</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</munderover>
<msub>
<mi>P</mi>
<mi>O</mi>
</msub>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>o</mi>
<mi>t</mi>
</msubsup>
</mrow>
</math>
is calculated to obtain, wherein POIn order to obtain the target value of the overturning load,t is the distance between the center of the overturning load and the rotation axis in the horizontal direction, and T is the number of the loads on the overturning side (T is 3 in this embodiment).
Calculated according to the following formula:
wherein,the distance from the center of the box girder to the vehicle on the overturn side is about 1.46m in this embodiment.
(3) And adjusting the size of the support saddle of the single-column pier beam bridge or the distance between the anti-torsion support saddles according to the moment state equation to reinforce the single-column pier beam bridge.
FIG. 3 is a graph showing the effect of increasing the diameter of the support on the anti-overturning load (the maximum overturning load that can be borne) of the bridge when the distance between the anti-torsion supports and the thickness of the support are fixed; FIG. 4 is a graph of the effect of reducing the thickness of the bearers on the load of the bridge resisting overturning while fixing the pitch of the anti-torque bearers and the diameter of the bearers; FIG. 5 is a graph of the effect of increasing the spacing (i.e., vertical displacement) of the end anti-torque bearers on the bridge anti-overturning load for a fixed bearer thickness and diameter. It can be seen that increasing the diameter of the abutments, or decreasing the thickness of the abutments, or increasing the spacing of the anti-torque abutments at the ends, increases the anti-overturning load carrying capacity of the bridge.
If the anti-torsion support interval l of the fixed end part (head and tail ends) changes, the support size is obtained by mechanical and geometric calculation:
<math>
<mrow>
<msubsup>
<mi>P</mi>
<mi>A</mi>
<mn>1</mn>
</msubsup>
<mo>=</mo>
<mn>28.52</mn>
<mo>×</mo>
<mn>9.8</mn>
<mi>kN</mi>
<mo>,</mo>
</mrow>
</math>
qG=130kN/m,
the ultimate anti-overturning moment (i.e. the anti-overturning moment in the overturning critical state) L of the bridge at this timeRComprises the following steps:
<math>
<mrow>
<msub>
<mi>L</mi>
<mi>R</mi>
</msub>
<mo>=</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>P</mi>
<mi>A</mi>
<mi>i</mi>
</msubsup>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>A</mi>
<mi>i</mi>
</msubsup>
<mo>+</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msubsup>
<mi>P</mi>
<mi>B</mi>
<mi>j</mi>
</msubsup>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>B</mi>
<mi>j</mi>
</msubsup>
<mo>+</mo>
<msub>
<mi>q</mi>
<mi>G</mi>
</msub>
<mo>×</mo>
<msub>
<mi>l</mi>
<mn>0</mn>
</msub>
<mo>×</mo>
<msub>
<mi>l</mi>
<mi>q</mi>
</msub>
<mo>=</mo>
<mn>2610.87</mn>
<mo>+</mo>
<mn>13829.50</mn>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mi>D</mi>
<mn>2</mn>
</mfrac>
<mo>-</mo>
<mi>h</mi>
<mo>)</mo>
</mrow>
<mi>kN</mi>
<mo>·</mo>
<mi>m</mi>
</mrow>
</math>
because three parking stalls of the side of toppling are on same lane, then all cars of the side of toppling are equal to the distance of axis of rotation, obtain through geometric computation in this embodiment:
the target value L of the overturning moment is calculatedO:
<math>
<mrow>
<msub>
<mi>L</mi>
<mi>O</mi>
</msub>
<mo>=</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</munderover>
<msub>
<mi>P</mi>
<mi>O</mi>
</msub>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>o</mi>
<mi>t</mi>
</msubsup>
<mo>=</mo>
<mo>[</mo>
<mn>7082.46</mn>
<mo>-</mo>
<mn>4851</mn>
<mrow>
<mo>(</mo>
<mfrac>
<mi>D</mi>
<mn>2</mn>
</mfrac>
<mo>-</mo>
<mi>h</mi>
<mo>)</mo>
</mrow>
<mo>]</mo>
<mi>kN</mi>
<mo>·</mo>
<mi>m</mi>
<mo>.</mo>
</mrow>
</math>
Substituting the moment state equation and solving to obtain:
<math>
<mrow>
<mfrac>
<mi>D</mi>
<mn>2</mn>
</mfrac>
<mo>-</mo>
<mi>h</mi>
<mo>≈</mo>
<mn>0.24</mn>
<mi>m</mi>
</mrow>
</math>
when the thickness h of the fixed support seat is 0.15m and the distance l between the anti-torsion support seats is 2.1m, the diameter D of the support seat is used as an unknown quantity, a moment state equation is substituted, the diameter D of the support seat is obtained by solving, namely the diameter D of the support seat is 0.78m, namely when the diameter of the support seat is increased to 0.78m, the anti-overturning bearing capacity of the bridge can be increased to 165 tons from the original 120 tons (the actual limit load is actually measured on a damage site, and the average load per vehicle is 120 tons).
When the diameter D of the fixed support is 0.6m and the distance l between the anti-torsion supports is 2.1m, the thickness h of the support is taken as an unknown quantity, a moment state equation is substituted, and the thickness h of the support is obtained by solving and is 0.06m, so that the anti-overturning bearing capacity of the bridge can be improved to 165 tons when the thickness of the support is reduced to 0.06 m.
If the size of the fixed support is changed, the anti-torsion support interval l of the end parts (head and tail ends) is changed, and then the anti-torsion support interval l is obtained through mechanical and geometric calculation:
<math>
<mrow>
<msubsup>
<mi>P</mi>
<mi>A</mi>
<mi>l</mi>
</msubsup>
<mo>=</mo>
<mn>28.52</mn>
<mo>×</mo>
<mn>9.8</mn>
<mi>kN</mi>
<mo>,</mo>
</mrow>
</math>
qG=130kN/m,
lq=0.15m,
the ultimate anti-overturning moment (i.e. the anti-overturning moment in the overturning critical state) L of the bridge at this timeRComprises the following steps:
<math>
<mrow>
<msub>
<mi>L</mi>
<mi>R</mi>
</msub>
<mo>=</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msubsup>
<mi>P</mi>
<mi>A</mi>
<mi>i</mi>
</msubsup>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>A</mi>
<mi>i</mi>
</msubsup>
<mo>+</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msubsup>
<mi>P</mi>
<mi>B</mi>
<mi>j</mi>
</msubsup>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>B</mi>
<mi>j</mi>
</msubsup>
<mo>+</mo>
<msub>
<mi>q</mi>
<mi>G</mi>
</msub>
<mo>×</mo>
<msub>
<mi>l</mi>
<mn>0</mn>
</msub>
<mo>×</mo>
<msub>
<mi>l</mi>
<mi>q</mi>
</msub>
<mo>=</mo>
<mn>500.30</mn>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mn>1038</mn>
<mo>+</mo>
<mn>1012</mn>
<mo>)</mo>
</mrow>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>B</mi>
<mi>j</mi>
</msubsup>
<mo>+</mo>
<mn>2340.00</mn>
<mi>kN</mi>
<mo>·</mo>
<mi>m</mi>
</mrow>
</math>
since the three cars on the overturning side are located on the same lane, the distances from all the cars on the overturning side to the rotation axis are equal, which is obtained by geometric calculation in the embodiment,the target value L of the overturning moment is calculatedO:
<math>
<mrow>
<msub>
<mi>L</mi>
<mi>O</mi>
</msub>
<mo>=</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</munderover>
<msub>
<mi>P</mi>
<mi>O</mi>
</msub>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>o</mi>
<mi>t</mi>
</msubsup>
<mo>=</mo>
<mn>6354.81</mn>
<mi>kN</mi>
<mo>·</mo>
<mi>m</mi>
<mo>.</mo>
</mrow>
</math>
Substituting the moment state equation to obtain:
<math>
<mrow>
<mn>2840.30</mn>
<mo>+</mo>
<mn>2050</mn>
<mo>×</mo>
<msubsup>
<mi>l</mi>
<mi>B</mi>
<mi>j</mi>
</msubsup>
<mo>=</mo>
<mn>6354.81</mn>
<mo>;</mo>
</mrow>
</math>
further solving results in:
<math>
<mrow>
<msubsup>
<mi>l</mi>
<mi>B</mi>
<mi>j</mi>
</msubsup>
<mo>≈</mo>
<mn>1.71</mn>
<mi>m</mi>
<mo>,</mo>
</mrow>
</math>
then <math>
<mrow>
<mi>l</mi>
<mo>=</mo>
<mn>2</mn>
<mo>×</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>l</mi>
<mi>B</mi>
<mi>j</mi>
</msubsup>
<mo>+</mo>
<mi>R</mi>
<mo>-</mo>
<mi>h</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>3.72</mn>
<mi>m</mi>
<mo>,</mo>
</mrow>
</math>
Namely, the distance between the anti-torsion supports at the two ends is increased to 3.72m, so that the overturning load of the single-column pier beam bridge can be increased to 165 tons.
The above-mentioned embodiments are intended to illustrate the technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only the most preferred embodiments of the present invention, and are not intended to limit the present invention, and any modifications, additions, equivalents, etc. made within the scope of the principles of the present invention should be included in the scope of the present invention.