# Flexure Formula

**Flexure Formula**

Stresses caused by the bending moment are known as flexural or bending stresses. Consider a beam to be loaded as shown.

**Flexure Formula**

Stresses caused by the bending moment are known as flexural or bending stresses. Consider a beam to be loaded as shown.

**Stresses in Beams**

Forces and couples acting on the beam cause bending (flexural stresses) and shearing stresses on any cross section of the beam and deflection perpendicular to the longitudinal axis of the beam. If couples are applied to the ends of the beam and no forces act on it, the bending is said to be pure bending. If forces produce the bending, the bending is called ordinary bending.

**Moving Loads**

From the previous section, we see that the maximum moment occurs at a point of zero shears. For beams loaded with concentrated loads, the point of zero shears usually occurs under a concentrated load and so the maximum moment.

Beams and girders such as in a bridge or an overhead crane are subject to moving concentrated loads, which are at fixed distance with each other. The problem here is to determine the moment under each load when each load is in a position to cause a maximum moment. The largest value of these moments governs the design of the beam.

**Problem 440**

A frame ABCD, with rigid corners at B and C, supports the concentrated load as shown in Fig. P-440. (Draw shear and moment diagrams for each of the three parts of the frame.)

**Problem 439**

A beam supported on three reactions as shown in Fig. P-439 consists of two segments joined by frictionless hinge at which the bending moment is zero.

**Problem 438**

The beam loaded as shown in Fig. P-438 consists of two segments joined by a frictionless hinge at which the bending moment is zero.

**Problem 437**

Cantilever beam loaded as shown in Fig. P-437.

**Problem 436**

A distributed load is supported by two distributed reactions as shown in Fig. P-436.

**Problem 435**

Beam loaded and supported as shown in Fig. P-435.

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