# flexural stress

## Solution to Problem 583 | Design for Flexure and Shear

**Problem 583**

A rectangular beam 6 in. wide by 10 in. high supports a total distributed load of W and a concentrated load of 2W applied as shown in Fig. P-583. If f_{b} ≤ 1500 psi and f_{v} ≤ 120 psi, determine the maximum value of W.

## Solution to Problem 582 | Design for Flexure and Shear

**Problem 582**

Find the cross-sectional dimensions of the smallest square beam that can be loaded as shown in Fig. P-582 if f_{v} ≤ 1.0 MPa and f_{b} ≤ 8 MPa.

## Solution to Problem 581 | Design for Flexure and Shear

**Problem 581**

A laminated beam is composed of five planks, each 6 in. by 2 in., glued together to form a section 6 in. wide by 10 in. high. The allowable shear stress in the glue is 90 psi, the allowable shear stress in the wood is 120 psi, and the allowable flexural stress in the wood is 1200 psi. Determine the maximum uniformly distributed load that can be carried by the beam on a 6-ft simple span.

## Design for Flexure and Shear

To determine the load capacity or the size of beam section, it must satisfy the allowable stresses in both flexure (bending) and shear. Shearing stress usually governs in the design of short beams that are heavily loaded, while flexure is usually the governing stress for long beams. In material comparison, timber is low in shear strength than that of steel.

## Solution to Problem 561 | Built-up Beams

**Problem 561**

A T section has the dimensions given in Fig. P-561. Show that the neutral axis is 3 inches below the top and that I_{NA} = 166.7 in4. If the tensile stress at the bottom of the flange is 1000 psi, calculate (a) the total tensile force in the flange and (b) the total compressive force in the cross section. Also compute (c) the moment of the compressive force about the NA, and (d) the moment of the total tensile force about the NA. (e) How does the sum of (c) and (d) compare with the total applied bending moment as computed from the flexure formula?

## Solution to Problem 559 | Built-up Beams

**Problem 559**

A beam is composed of 6 planks, each 100 mm wide and 20 mm thick, piled loosely on each other to an overall dimension of 100 mm wide by 120 mm high. (a) Compare the strength of such a beam with that of a solid beam of equal overall dimensions. (b) What would be the ratio if the built-up beam consisted of a 12 planks each 100 mm wide by 10 mm thick?

## Solution to Problem 558 | Unsymmetrical Beams

### Problem 558

In Prob. 557, find the values of x and w_{o} so that w_{o} is a maximum.

## Solution to Problem 557 | Unsymmetrical Beams

**Problem 557**

A cast-iron beam 10 m long and supported as shown in Fig. P-557 carries a uniformly distributed load of intensity w_{o} (including its own weight). The allowable stresses are f_{bt} ≤ 20 MPa and f_{bc} ≤ 80 MPa. Determine the maximum safe value of w_{o} if x = 1.0 m.

## Solution to Problem 556 | Unsymmetrical Beams

**Problem 556**

A T beam supports the three concentrated loads shown in Fig. P-556. Prove that the NA is 3.5 in. above the bottom and that I_{NA} = 97.0 in^{4}. Then use these values to determine the maximum value of P so that f_{bt} ≤ 4 ksi and f_{bc} ≤ 10 ksi.

## Solution to Problem 555 | Unsymmetrical Beams

**Problem 555**

A beam carries a concentrated load W and a total uniformly distributed load of 4W as shown in Fig. P-555. What safe value of W can be applied if f_{bc} ≤ 100 MPa and f_{bt} ≤ 60 MPa? Can a greater load be applied if the section is inverted? Explain.