Category: Stress And Strain

Modulus of rigidity (G) is the ratio of shear stress (τ) and shear strain (γ). Let us consider an elemental cube ABCD be subjected to a simple shear stress τxy as shown in Figure 12.24 (a). An equivalent system with principal stresses τxy and –τxy are acting along the diagonals as shown in Figure 12.24 (b). The distorted condition of the cube is shown in Figure 12.24…

Suppose a block is subjected by three-dimensional forces P as shown in Figure 12.23. Figure 12.23 Fluid Pressure and Volumetric Strain of a Cube Bulk modulus is a ratio of fluid pressure and volumetric strain. It is denoted by K. Here –ve sign is used for reduction in volume. Let us consider a cube of unit length is subjected to…

Impact load is a load which is applied to a body with some velocity as shown in Figure 12.21. Suppose a load W released from a height h on a collar of a rod of length l and change in length due to impact loading is δl. Now, work done by impact load W is Figure 12.21 Impact Loading on a Rod Suppose the equivalent load for…

Suppose W is a load suddenly applied on the collar of a rod and extension due to the load application is δl as shown in Figure 12.20 (a). The original length of the rod is l. The work done by the load W is U = W × δl Now consider the equivalent weight for same work is P which is applied gradually. Work done by gradually applied load P [Figure 12.20…

If the temperature of a material is increased, there will be expansion in the material (except ice) and if the temperature is decreased, there will be contraction in the material. If these expansion and contraction occur freely there will be no stress in the material and if these expansion or contraction is prevented then stress…

Any tensile or compressive member which consists of two or more bars in series, usually of different materials, is called composite bars (Figure 12.18). In this case, load on both the rods will be same but strain produced will be different. Figure 12.18 Composite Bar where A1, E1 ∈1 are cross-section area, modulus of elasticity, and strain produced in material…

Figure 12.13 shows stress and strain produced in a compound rod. Figure 12.13 An Assembly of Tube and Bolt where r subscript is used for rod. Rod is subjected to tensile stress and tube is subjected to compressive stress. The reduction in length of tube and extension in rod may be different due to difference in materials…

Any tensile or compressive member which consists of two or more bars or tubes in parallel, usually of different materials, is called a compound bar. Figure 12.12 shows an example of compound bar; it consists of a tube and a rod of different materials. Since the initial length of tube and rod are same, it will remain…

Consider a bar of varying cross-section of uniform strength subjected by a longitudinal stress σ as shown in Figure 12.10. Now consider a small element of axial length δx at a distance of x from smaller end. Let area of cross-section at section x be A and at section x + δx be A + δA. For the element of length δx to be in equilibrium, the total downward force must be equal to the total…