SHEAR AND BENDING MOMENT DIAGRAMS BASICS AND TUTORIALS

SHEAR AND BENDING MOMENT DIAGRAMS BASIC INFORMATION
A Tutorials on Shear and Bending Moment Diagram? How To Make Shear and Bending Moment Diagram


In order to plot the shear force and bending moment diagrams it is necessary to adopt a sign convention for these responses. A shear force is considered to be positive if it produces a clockwise moment about a point in the free body on which it acts.

A negative shear force produces a counterclockwise moment about the point. The bending moment is taken as positive if it causes compression in the upper fibers of the beam and tension in the lower fiber. In other words, sagging moment is positive and hogging moment is negative.

The construction of these diagrams is explained with an example given in Figure 2.4.

The section at E of the beam is in equilibrium under the action of applied loads and internal forces acting at E as shown in Figure 2.5. There must be an internal vertical force and internal bending moment to maintain equilibrium at Section E.

The vertical force or the moment can be obtained as the algebraic sum of all forces or the algebraic sum of the moment of all forces that lie on either side of Section E.

The shear on a cross-section an infinitesimal distance to the right of pointAisC55 k and, therefore, the shear diagram rises abruptly from 0 to C55 at this point. In the portion AC, since there is no additional load, the shear remainsC55 on any cross-section throughout this interval, and the diagram is a horizontal as shown in Figure 2.4. 

An infinitesimal distance to the left of C the shear is C55, but an infinitesimal distance to the right of this point the 30 k load has caused the shear to be reduced to C25. 

Therefore, at point C there is an abrupt change in the shear force from C55 to C25. In the same manner, the shear force diagram for the portion CD of the beam remains a rectangle. In the portion DE, the shear on any cross-section a distance x from point D is 

               S = 55 − 30 − 4x D 25 − 4x

which indicates that the shear diagram in this portion is a straight line decreasing from an ordinate of C25 at D to C1 at E. 

The remainder of the shear force diagram can easily be verified in the same way. It should be noted that, in effect, a concentrated load is assumed to be applied at a point and, hence, at such a point the ordinate to the shear diagram changes abruptly by an amount equal to the load.

In the portion AC, the bending moment at a cross-section a distance x from point A isM D 55x. Therefore, the bending moment diagram starts at 0 at A and increases along a straight line to an ordinate of C165 k-ft at point C. 

In the portion CD, the bending moment at any point a distance x from C is M D 55.x C 3/ − 30x. Hence, the bending moment diagram in this portion is a straight line increasing from 165 at C to 265 at D. In the portion DE, the bending moment at any point a distance x from D is M D 55.x C 7/ − 30.X C 4/ − 4x2=2. 

Hence, the bending moment diagram in this portion is a curve with an ordinate of 265 at D and 343 at E. In an analogous manner, the remainder of the bending moment diagram can be easily constructed.

Bending moment and shear force diagrams for beamswith simple boundary conditions and subject to some simple loading are given in Figure 2.6.

FIVE TYPES OF PORTLAND CEMENT BASIC AND TUTORIALS

PORTLAND CEMENT TYPES BASIC INFORMATION
What Are The Five Types of Portland Cement?


Portland cement has become the most widely used cement in the world. Portland cement got its name because the cured concrete it produced was the same color as a gray stone quarried in nearby Portland, England.

There are five types of portland cement, each with different characteristics.

■ Type I is a general-purpose cement and is by far the most commonly used, especially in residential work. Type I portland cement is suitable whenever the special characteristics of other types are not required.

■ Type II cement has moderate resistance to sulfates, which are found in some soil and groundwater, and generates less heat during hydration than Type I. This reduced curing temperature can be particularly helpful in large structures such as piers and heavy retaining walls, especially when the concrete is placed in warm weather.

■ Type III is a “high early strength” cement. High early strength does not mean higher strength—only that strength develops at a faster rate. This can be an advantage during winter construction because it reduces the time during which fresh concrete must be protected from the cold. Early strength gain can also permit removal of forms and shoring more quickly.

■ Type IV cement produces less heat during hydration than Type I or Type II and is used only in massive civil engineering structures such as dams, large highway pilings, or heavy bridge abutments. Its strength development and curing rates, though, are much slower than Type I.

■ Type V cement is used in concrete exposed to soil or groundwater that has high sulfate concentrations. This type of cement is usually available only in areas where it is likely to be needed. In the United States, Type V cement is common only in the southwestern states.

Types I, II, and III portland cement can also be made with a foaming agent that produces millions of evenly distributed microscopic air bubbles in the concrete mix. When manufactured in this way, the cements are said to be air entrained, and are designated as Types IA, IIA, and IIIA. Air-entrained cements require mechanical mixing.

Finely ground cement increases the workability of harsh mixes, making them more cohesive and reducing tendencies toward segregation. Coarsely ground cement reduces stickiness. Cement packages that are marked ASTM A150 meet industry standards for both physical and chemical requirements.

Portland cement comes in three colors—grey, white, and buff. The white and buff are more expensive and typically used in commercial rather than residential projects to achieve special color effects.

 Liquid or powder pigments can be added to a concrete mix, and liquid stains can be used to color the surface of cured concrete, but both will add to the cost. For most applications, ordinary gray concrete made with gray cement is suitable. Colored concrete should be reserved for special areas like a front entrance, a patio, or a pool deck