# Problem 712 | Propped beam with initial clearance at the roller support

**Problem 712**

There is a small initial clearance D between the left end of the beam shown in Fig. P-712 and the roller support. Determine the reaction at the roller support after the uniformly distributed load is applied.

# Problem 711 | Cantilever beam with free end on top of a simple beam

**Problem 711**

A cantilever beam BD rests on a simple beam AC as shown in Fig. P-711. Both beams are of the same material and are 3 in wide by 8 in deep. If they jointly carry a load P = 1400 lb, compute the maximum flexural stress developed in the beams.

# Problem 710 | Two simple beams at 90 degree to each other

**Problem 710**

Two timber beams are mounted at right angles and in contact with each other at their midpoints. The upper beam A is 2 in wide by 4 in deep and simply supported on an 8-ft span; the lower beam B is 3 in wide by 8 in deep and simply supported on a 10-ft span. At their cross-over point, they jointly support a load P = 2000 lb. Determine the contact force between the beams.

# Problem 709 | Propped Beam with Spring Support

**Example 06**

The beam in Figure PB-006 is supported at the left by a spring that deflects 1 inch for each 300 lb. For the beam E = 1.5 × 10^{6} psi and I = 144 in^{4}. Compute the deflection of the spring.

# Problem 708 | Two Indentical Cantilever Beams

**Problem 708**

Two identical cantilever beams in contact at their ends support a distributed load over one of them as shown in Fig. P-708. Determine the restraining moment at each wall.

# Problem 707 | Propped Beam with Moment Load

**Problem 707**

A couple M is applied at the propped end of the beam shown in Fig. P-707. Compute R at the propped end and also the wall restraining moment.

# Problem 706 | Solution of Propped Beam with Decreasing Load

**Example 03**

The propped beam shown in Fig. P -706 is loaded by decreasing triangular load varying from w_{o} from the simple end to zero at the fixed end. Find the support reactions and sketch the shear and moment diagrams

# The Three-Moment Equation

The three-moment equation gives us the relation between the moments between any three points in a beam and their relative vertical distances or deviations. This method is widely used in finding the reactions in a continuous beam.

Consider three points on the beam loaded as shown.

# Chapter 08 - Continuous Beams

Continuous beams are those that rest over three or more supports, thereby having one or more redundant support reactions.

These section includes

1. Generalized form of three-moment equation

2. Factors for three-moment equation

3. Application of the three-moment equation

4. Reactions of continuous beams

5. Shear and moment diagrams of continuous beams

6. Continuous beams with fixed ends

7. Deflection determined by three-moment equation

8. Moment distribution method