Maximum Load Calculation for a Simply Supported Beam with Wooden Planks

What is the maximum load a simply supported beam can carry?

Given the dimensions of two wooden planks (300 mm x 20 mm and 200 mm x 20 mm) and permissible stresses of 8 MPa and 12 MPa, what is the maximum load the beam can handle?

Maximum Load Calculation for Simply Supported Beam

For the simply supported beam composed of two wooden planks (300 mm x 20 mm and 200 mm x 20 mm) subjected to a uniformly distributed load, and assuming permissible stresses of 8 MPa and 12 MPa, we can calculate the maximum load it can carry.

The maximum load is limited by the smallest of the values between the two wooden planks, which is 32 kN.

Explanation of Maximum Load Calculation

When analyzing the maximum load a simply supported beam can carry, we consider the dimensions of the wooden planks and the permissible stresses. In this case, the maximum load is determined by the weakest point in the beam structure.

Using the formula σ = P/A, where σ is stress, P is force (load), and A is area, we calculate the maximum loads for both wooden planks. For the 300 mm x 20 mm section, the area is 6000 mm², resulting in maximum loads of 48 kN under tension and 72 kN under compression. On the other hand, the 200 mm x 20 mm plank has an area of 4000 mm², leading to maximum loads of 32 kN under tension and 48 kN under compression.

Ultimately, the maximum load the beam can carry is 32 kN, as this represents the limiting value at the weakest point of the beam. Understanding these calculations is crucial in structural engineering and the mechanics of materials field.