# simple beam

## Solution to Problem 618 | Double Integration Method

**Problem 618**

A simply supported beam carries a couple M applied as shown in Fig. P-618. Determine the equation of the elastic curve and the deflection at the point of application of the couple. Then letting a = L and a = 0, compare your solution of the elastic curve with cases 11 and 12 in the Summary of Beam Loadings.

## Solution to Problem 613 | Double Integration Method

**Problem 613**

If E = 29 × 10^{6} psi, what value of I is required to limit the midspan deflection to 1/360 of the span for the beam in Fig. P-613?

## Solution to Problem 612 | Double Integration Method

**Problem 612**

Compute the midspan value of EI δ for the beam loaded as shown in Fig. P-612.

## 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 609 | Double Integration Method

**Problem 609**

As shown in Fig. P-609, a simply supported beam carries two symmetrically placed concentrated loads. Compute the maximum deflection δ.

## 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 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.

## Solution to Problem 524 | Flexure Formula

**Problem 524**

A beam with an S380 × 74 section carries a total uniformly distributed load of 3W and a concentrated load W, as shown in Fig. P-524. Determine W if the flexural stress is limited to 120 MPa.