# Beam Deflection

## Solution to Problem 642 | Deflection of Cantilever Beams

**Problem 642**

Find the maximum deflection for the cantilever beam loaded as shown in Figure P-642 if the cross section is 50 mm wide by 150 mm high. Use E = 69 GPa.

## Solution to Problem 641 | Deflection of Cantilever Beams

**Problem 641**

For the cantilever beam shown in Fig. P-641, what will cause zero deflection at A?

## Solution to Problem 640 | Deflection of Cantilever Beams

**Problem 640**

Compute the value of δ at the concentrated load in Prob. 639. Is the deflection upward downward?

## Solution to Problem 639 | Deflection of Cantilever Beams

**Problem 639**

The downward distributed load and an upward concentrated force act on the cantilever beam in Fig. P-639. Find the amount the free end deflects upward or downward if E = 1.5 × 10^{6} psi and I = 60 in^{4}.

## Solution to Problem 638 | Deflection of Cantilever Beams

**Problem 638**

For the cantilever beam shown in Fig. P-638, determine the value of EIδ at the left end. Is this deflection upward or downward?

## Solution to Problem 637 | Deflection of Cantilever Beams

**Problem 637**

For the beam loaded as shown in Fig. P-637, determine the deflection 6 ft from the wall. Use E = 1.5 × 10^{6} psi and I = 40 in^{4}.

## Solution to Problem 636 | Deflection of Cantilever Beams

**Problem 636**

The cantilever beam shown in Fig. P-636 has a rectangular cross-section 50 mm wide by h mm high. Find the height h if the maximum deflection is not to exceed 10 mm. Use E = 10 GPa.

## Deflection of Cantilever Beams | Area-Moment Method

Generally, the tangential deviation t is not equal to the beam deflection. In cantilever beams, however, the tangent drawn to the elastic curve at the wall is horizontal and coincidence therefore with the neutral axis of the beam. The tangential deviation in this case is equal to the deflection of the beam as shown below.

## Area-Moment Method | Beam Deflections

Another method of determining the slopes and deflections in beams is the area-moment method, which involves the area of the moment diagram.