Figure 5.52

A graph plots stress-concentration factor K for a notched beam of rectangular cross section in pure bending (h = height of beam; b = thickness of beam, perpendicular to the plane of the figure), where the dashed line is for semicircular notches (h = h₁ + 2R). Three curves and a dashed line are plotted on a coordinate plane with horizontal axis R/h₁ and vertical axis K. Each curve starts at the top of the viewing window with K = 3.0, curves down and to the right as the slope becomes more and more shallow, and exits the viewing window at or near K = 1.5. The first curve is labeled h/h₁ = 1.2, and passes through the approximate points:

(0.04, 3.0),

(0.05, 2.75),

(0.07, 2.5),

(0.10, 2.2),

(0.135, 2.0),

(0.15, 1.95),

(0.20, 1.8),

(0.25, 1.7), and

(0.30, 1.6).

The second curve is labeled h/h₁ = 1.1, and passes through the approximate points:

(0.03, 3.0),

(0.05, 2.55),

(0.055, 2.5),

(0.10, 2.05),

(0.11, 2.0),

(0.15, 1.8),

(0.20, 1.7),

(0.25, 1.6), and

(0.275, 1.5).

The third curve is labeled h/h₁ = 1.05, and passes through the approximate points:

(0.02, 3.0),

(0.035, 2.5),

(0.05, 2.25),

(0.07, 2.0),

(0.10, 1.8),

(0.15, 1.6), and

(0.19, 1.5).

The dashed line is labeled h = h₁ + 2R, and passes through the approximate points:

(0.005, 3.0) and

(0.05, 2.55)

before intersecting with the curve h/h₁ = 1.2 at approximately (0.08, 2.3). The rest of the line is not visible.

A diagram next to the graph shows a rectangular beam with vertical height h extending from left to right. Two curved arrows, one to the left of the beam and one to the right, are labeled M and curve up and away, then up and toward the beam. Two notches are bored through the beam and into the page.

One notch is U-shaped: the bottom of the notch is similar to the bottom of a U, and this bottom is below the top-front edge of the beam. The beam is bored above the bottom of the notch into the page, and the horizontal width of the top of the U-shaped notch is 2R.

The second notch is shaped like an inverted U: the top of the notch is similar to the top of an inverted U, and this top is above the bottom-front edge of the beam. The beam is bored below the top of the notch into the page, and the horizontal width of the bottom of the inverted U-shaped notch is 2R.

The bottommost point of the top notch and the topmost point of the bottom notch are separated by a vertical distance h₁. Three equations are also given below the diagram:

K = σ_max/σ_nom,

σ_nom = 6M/(b h₁²), and

b = thickness