A horizontal beam A B with cross-sectional dimensions (b=19 mm) ×(h=200 mm) is supported by an i

step 1 cross -section area of the beam is 0 .75 into 8 is 6 inch square then a lowered p is 27 12 kilo

A horizontal beam A B with cross-sectional dimensions (b=19...

A horizontal beam $A B$ with cross-sectional dimensions $(b=19 \mathrm{mm}) \times(h=200 \mathrm{mm})$ is supported by an inclined strut $C D$ and carries a load $P=12 \mathrm{kN}$ at joint $B$ (see figure part a). The strut, which consists of two bars each of thickness $5 b / 8,$ is connected to the beam by a bolt passing through the three bars meeting at joint $C$ (see figure part b). (a) If the allowable shear stress in the bolt is $90 \mathrm{MPa}$ what is the minimum required diameter $d_{\min }$ of the bolt at $C ?$ (b) If the allowable bearing stress in the bolt is $130 \mathrm{MPa},$ what is the minimum required diameter $d_{\min }$ of the bolt at $C ?$

A horizontal beam $A B$ with cross-sectional dimensions $(b=19 \mathrm{mm}) \times(h=200 \mathrm{mm})$ is supported by an inclined strut $C D$ and carries a load $P=12 \mathrm{kN}$ at joint $B$ (see figure part a). The strut, which consists of two bars each of thickness $5 b / 8,$ is connected to the beam by a bolt passing through the three bars meeting at joint $C$ (see figure part b). (a) If the allowable shear stress in the bolt is $90 \mathrm{MPa}$ what is the minimum required diameter $d_{\min }$ of the bolt at $C ?$
(b) If the allowable bearing stress in the bolt is $130 \mathrm{MPa},$ what is the minimum required diameter $d_{\min }$ of the bolt at $C ?$

Key Concepts

Cross-Sectional Geometry of Structural Elements

Understanding the relationship between the geometry of a structural element and the stresses within it is essential in designing any connection. For bolts, this means using the formula for the area of a circle to relate the load-bearing capacity to the bolt’s diameter. This concept also ties in with the analysis of how the load is distributed across the bolt's cross section in shear and the surrounding material in bearing, thus linking geometric properties to mechanical performance and safety.

Bolt Sizing Based on Allowable Stress

Bolt sizing is a critical aspect of structural design, where both shear and bearing stresses must be considered. The minimum required diameter of a bolt is determined by ensuring that the stresses (whether shear or bearing) do not exceed their respective allowable limits. This involves calculating the required cross-sectional area to resist the load and then relating that to the diameter of a circular bolt. The designer must account for factors such as load distribution and geometry of the connection in order to achieve a safe and effective design.

Shear Stress in Bolts

This concept involves understanding how forces are transmitted through a bolt in a direction parallel to its cross?section. When a bolt is subject to a load, the force results in a stress distributed over the bolt's cross-sectional area. The design must ensure that the induced shear stress does not exceed the material's allowable limit. Calculations typically involve computing the force applied, determining the bolt’s area (usually assuming a circular cross section), and then applying the shear stress formula to size the bolt appropriately.

Bearing Stress on Bolt Holes

Bearing stress refers to the stress developed on the surface of a bolt due to its contact with the material in the connected plates or bars. It is the stress that occurs on the interface where the bolt exerts pressure on the hole through which it passes. In connection design, checking against bearing stress is critical to ensure that the material being clamped by the bolt doesn’t deform or fail due to excessive local compressive stress. The design involves comparing the applied load divided by the projected contact area to the allowable bearing stress.

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