A Timber Beam 150 mm x 250 mm Reinforced with Steel Plate

Calculating the Safe Concentrated Load

A timber beam with dimensions of 150 mm x 250 mm is reinforced at the bottom only by a steel plate. If the number of steel plates, n, is equal to 20, we need to determine the following:

a. The concentrated load that can be applied at the center of the simply supported span 6 m long without exceeding the stress of wood of 8 MPa

b. The concentrated load that can be applied at the center of the simply supported span 6 m long without exceeding the stress of steel of 120 MPa

c. The safe concentrated load after solving (a) and (b)

Answer:

a. Calculating Load without Exceeding Wood Stress

To determine the load without exceeding the stress, use the formula σ = P / (A * n).

- For (a), P = 6,000,000 N.

b. Calculating Load without Exceeding Steel Stress

To determine the load without exceeding the stress of the steel, use the formula P = σ * (A + A₁) * n.

- For (b), P = 120 MPa * (37500 mm² + 150 mm * t) * 20.

c. Calculating Safe Concentrated Load

The safe concentrated load is the smaller value of (a) and (b).

Explanation:

To determine the concentrated load that can be applied at the center of the simply supported span without exceeding the stress of the wood or steel, we can use the formula σ = P / (A * n), where σ is the stress, P is the load, A is the cross-sectional area, and n is the number of reinforcing steel plates.

a. To calculate the load without exceeding the stress of the wood (8 MPa),

- P = σ * A * n = 8 MPa * 37500 mm² * 20 = 6,000,000 N.

b. To calculate the load without exceeding the stress of the steel (120 MPa),

- P = σ * (A + A₁) * n = 120 MPa * (37500 mm² + 150 mm * t) * 20.

c. The safe concentrated load can be calculated by substituting the values of P from (a) and (b) into the formula and choosing the smaller value.