MATH- IN- BRIDGE RAJKIYA PRATIBHA VIKAS VIDYALAYA, ROHINI, DELHI CONCEPTUALISED BY: Ms. SUSHMA SINGH HARSH BADHAN SHUBHAM KUMAR SPECIAL THANKS TO: NCERT AND Mr. RAL PAL SEHRAWAT PRINCIPAL RPVV ROHINI We are here to present our model Math-in-Bridge Any construction made in human history is a result of well planned structuring which uses MATHEMATICS, if we roll back into time we can see the use of mathematics in our ancient HARAPPA civilisation as well. Curious you all may be RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI Well, one example is that the roads were at right angle to each other. With evolution and advancement in technology, we have been able to master this art at a whole new level, BRIDGES are a remarkable example of this, truly can be said as LANDMARK IN MATHEMATICS RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI We all travel through the bridges, millions of vehicles pass through every day and bridges bear tonnes of load. Have you ever thought that what is the factor which makes them so strong so that they can bear this much load? RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI Why all over Delhi Metro rail is supported by cylindrical pillars? Is it concrete, cement or iron which makes the bridges so strong? RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI . NO Mathematics used behind them makes them so strong. RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI Can you imagine what mathematics is behind them? Let us solve these questions Our model is based on three mathematical concepts Strength of triangular shape. Role of circles in bridges Cylindrical shapes of pillars We can also take into account the proportionality as the fourth concept. RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI This model has combination of five types of bridges. Beam, arch, truss, suspension and cable stayed bridge Every type of bridge has at least one or two above mentioned mathematical concepts. RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI Beam Bridge Beam bridges are inexpensive to construct. In this type of bridge a beam is used to support bridge. In reality iron rods are used in Beam Bridge. The world longest beam bridge is Lake Panchartrain causeway. This is 24 miles long. One big drawback of Beam Bridge: it is not suitable for places where there is need for unobstructed clearance below the span as great numbers of (supports) are required. RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI Arch Bridge The oldest type of bridge is arch bridge. Now-a-days types of arch bridges are different because of modern technology. In ancient time arch bridges were made in those places where the span distance was less. Mathematical concept in arch bridge is role of circle. With the help of circular circumference, we are able to measure the arch of a bridge in degrees. The Natchez Trace Bridge in Franklin, Tennessee (America) is the first arch bridge of pre-casted concrete. RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI Truss Bridge Truss Bridge is strongest bridge. It contains different types of trusses. The Warren truss is one of the simplest yet strong designs. Warren truss is unique because it uses equilateral triangles. Each side of the triangles has same length. RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI Suspension Bridge Suspension Bridges are light, strong, and aesthetic, and their span distance is from 2000 to 7000 feet, and it can much longer than the other types of bridges. It is the most expensive type of bridges to construct. In earlier designs, the structures were suspended with bamboo cables; in 6 th century iron chains displaced the use of bamboo cables. RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI Cable-stayed Bridge Cable stayed bridges do look, almost much like the suspension bridges. They all have towers and roadways hanging from cables. The cables are secured to the towers that are responsible for bearing the load of the bridge. Cables are attached in radial pattern, in this cables extent from several points on the road to a single point at the top of the towers. It is considered a fairly new approach to bridge construction. For medium length span between 2,800 and 5000 feet, cable-stayed is fast becoming the bridge of choice. Compared to suspension, they require less cable and are faster to construct. Sunshine Skyway Bridge in Tampa, Florida is cable stayed bridge. RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI ACTIVITIES DONE TO EXPLAIN THE CONCEPTS To measure the arch of a bridge in degree. RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI ACTIVITIES DONE TO EXPLAIN THE CONCEPTS Triangular shape is the strongest RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI ACTIVITIES DONE TO EXPLAIN THE CONCEPTS To show cylinders with hole at the centre are strong RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI ACTIVITIES DONE TO EXPLAIN THE CONCEPTS Triangular fan fold is stronger than paper strip RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI ACTIVITIES DONE TO EXPLAIN THE CONCEPTS To construct a cable-stayed bridge. RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI ACTIVITIES DONE TO EXPLAIN THE CONCEPTS To apply the mathematics of proportion RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI HERE IS A VIDEO SHOWING THESE ACTIVITIES: ENJOY RAJKIYA PRATIBHA VIKAS VIDYALAYA SECTOR XI ROHINI DELHI