Final answer:
In this case, at the mid-span of the bridge, the maximum shear force is 2450 N and the maximum bending moment is 16625 Nm.
Step-by-step explanation:
To calculate the maximum shear force and maximum bending moment at the mid-span of the simply supported beam bridge, we need to consider the uniform load and the weight of the car.
Step 1: Calculate the total weight of the car:
The weight of the car is given as 1000 kg. We need to convert it to Newtons by multiplying it with the acceleration due to gravity, which is approximately 9.8 m/s²:
Weight of the car = 1000 kg * 9.8 m/s² = 9800 N
Step 2: Calculate the weight per lane:
Since the car is evenly distributed across two lanes, we need to divide the total weight by 2:
Weight per lane = 9800 N / 2 = 4900 N
Step 3: Calculate the maximum shear force:
The maximum shear force occurs when the car is at the mid-span of the bridge. For a simply supported beam, the maximum shear force is equal to half the total weight of the car:
Maximum shear force = 4900 N / 2 = 2450 N
Step 4: Calculate the maximum bending moment:
The maximum bending moment occurs when the car is at the mid-span of the bridge. For a simply supported beam with a uniform load, the maximum bending moment is given by the equation:
Maximum bending moment = (total load * span) / 4
Here, the total load consists of the weight per lane (4900 N) and the uniform load (500 N/m) multiplied by the lane width (3.5 m):
Total load = (4900 N + 500 N/m * 3.5 m) = 4900 N + 1750 N = 6650 N
Now, we can calculate the maximum bending moment:
Maximum bending moment = (6650 N * 10 m) / 4 = 16625 Nm
So, at the mid-span of the bridge, the maximum shear force is 2450 N and the maximum bending moment is 16625 Nm.