# Uniformly Distributed Load

## Solution to Problem 611 | Double Integration Method

**Problem 611**

Compute the value of EI δ at midspan for the beam loaded as shown in Fig. P-611. If E = 10 GPa, what value of I is required to limit the midspan deflection to 1/360 of the span?

## Solution to Problem 610 | Double Integration Method

**Problem 610**

The simply supported beam shown in Fig. P-610 carries a uniform load of intensity w_{o} symmetrically distributed over part of its length. Determine the maximum deflection δ and check your result by letting a = 0 and comparing with the answer to Problem 606.

## Solution to Problem 590 | Design for Flexure and Shear

**Problem 590**

A box beam carries a distributed load of 200 lb/ft and a concentrated load P as shown in Fig. P-590. Determine the maximum value of P if f_{b} ≤ 1200 psi and f_{v} ≤ 150 psi.

## Solution to Problem 589 | Design for Flexure and Shear

**Problem 589**

A channel section carries a concentrated loads W and a total distributed load of 4W as shown in Fig. P-589. Verify that the NA is 2.17 in. above the bottom and that I_{NA} = 62 in^{4}. Use these values to determine the maximum value of W that will not exceed allowable stresses in tension of 6,000 psi, in compression of 10,000 psi, or in shear of 8,000 psi.

## Solution to Problem 588 | Design for Flexure and Shear

**Problem 588**

The distributed load shown in Fig. P-588 is supported by a wide-flange section of the given dimensions. Determine the maximum value of w_{o} that will not exceed a flexural stress of 10 MPa or a shearing stress of 1.0 MPa.

## Solution to Problem 586 | Design for Flexure and Shear

**Problem 586**

The distributed load shown in Fig. P-586 is supported by a box beam having the same cross-section as that in Prob. 585. Determine the maximum value of w_{o} that will not exceed a flexural stress of 10 MPa or a shearing stress of 1.0 MPa.

## Solution to Problem 585 | Design for Flexure and Shear

**Problem 585**

A simply supported beam of length L carries a uniformly distributed load of 6000 N/m and has the cross section shown in Fig. P-585. Find L to cause a maximum flexural stress of 16 MPa. What maximum shearing stress is then developed?

## 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 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.