Question

To use Allowable Stress Design to calculate required dimensions using a specified factor of safety. A structural element that carries a load must be designed so that it can support the load safely. There are several reasons why an element may fail at loads that are less than the theoretical limit. For example, material properties may not exactly equal the reference values used in the design. The actual loading may differ from the design loading. The exact dimensions of the member may be different from the nominal values. These scenarios, and others, make it important to design structural members so that the expected load is less than the expected load that would make the member fail. One method of doing this uses a factor of safety. The allowed load Fallow can be related to the load that causes failure, Ffail, using a constant called the factor of safety, F.S.=FfailFallow, which should be larger than 1. For preliminary analysis, the stresses that are developed are assumed to be constant, so that the load and the stress are related by N=σA or V=τA, where A is the area subjected to the load.

An anchor rod with a circular head supports a load Fallow = 11 kN by bearing on the surface of a plate and passing through a hole with diameter h = 2.6 cm. One way the anchor could break is by the rod failing in tension.
What is the minimum required diameter of the rod if the factor of safety for tension failure is F.S. = 1.6, given that the material fails in tension at σfail = 60 MPa? Assume a uniform stress distribution.

Answer 1

Step-by-step explanation:

For preliminary analysis, the stresses that are developed are assumed to be constant, so that the load and the stress are related by N=σA or V=τA, where A is the area subjected to the load.

a.) An anchor rod with a circular head supports a load Pallow = 11 kN by bearing on the surface of a plate and passing through a hole with diameter h = 2.6 cm as shown (Figure 1). One way the anchor could break is by the rod failing in tension, as shown (Figure 2). What is the minimum required diameter of the rod if the factor of safety for tension failure is F.S. = 1.6, given that the material fails in tension at σfail = 60 MPa ? Assume a uniform stress distribution.

b.)The anchor from Part A can also fail in shear in the circular head, as shown (Figure 3). What is the minimum thickness t required for the head to support the allowed load Pallow = 11 kN if the material fails in shear at τfail = 30 MPa ? Use a factor of safety F.S. = 2.2.

c.)The anchor in Part A could also fail if the surface of the support plate is crushed by the bearing load (Figure 4). What is the required minimum head diameter using a factor of safety F.S. = 1.4? The maximum bearing stress is σ fail = 60 MPa .