A composite beam is constructed by bolting four plates to four 60 ×60 ×12 -mm angles as shown. T

step 1 Here the force exerted on the bolt at B, you can see on the figure. Now, for the first moments a

A composite beam is constructed by bolting four plates to...

A composite beam is constructed by bolting four plates to four $60 \times$ $60 \times 12$ -mm angles as shown. The bolts are equally spaced along the beam, and the beam supports a vertical load. As proved in mechanics of materials, the shearing forces exerted on the bolts at $A$and $B$ are proportional to the first moments with respect to the centroidal $x$ axis of the red shaded areas shown, respectively, in parts $a$ and $b$ of the figure. Knowing that the force exerted on the bolt at $A$ is $280 \mathrm{N}$, determine the force exerted on the bolt at $B .$

A composite beam is constructed by bolting four plates to four $60 \times$
$60 \times 12$ -mm angles as shown. The bolts are equally spaced along
the beam, and the beam supports a vertical load. As proved in
mechanics of materials, the shearing forces exerted on the bolts at $A$and $B$ are proportional to the first moments with respect to the centroidal $x$ axis of the red shaded areas shown, respectively, in parts $a$
and $b$ of the figure. Knowing that the force exerted on the bolt at $A$
is $280 \mathrm{N}$, determine the force exerted on the bolt at $B .$

Key Concepts

Composite Beam

A composite beam is a structural element made up of two or more materials or component parts that work together to resist load. The analysis of composite beams involves transforming the materials, sections, or connecting arrangements into an equivalent section to predict stress distributions and deformations accurately.

Bolted Connections

Bolted connections are used to join different components of a structural system, ensuring that the load is transferred effectively between them. In composite structures, bolts play a crucial role by resisting shearing forces and providing continuous performance under load by maintaining the integrity of the composite action.

Shear Force Distribution

Shear force distribution refers to the way in which applied loads are shared among different points or connectors in a structure. In composite beams, the shearing forces at bolts or welds are often determined by geometric properties of the connected areas, ensuring that each connector carries an appropriate portion of the load.

First Moment of Area

The first moment of area is a geometric property calculated as the product of an area and its distance from a reference axis, typically used in shear flow and bending analysis. It is critical in predicting how shearing forces are distributed in a structure, as the force carried by connectors like bolts is proportional to the first moment of the area of the adjacent material segments relative to the centroidal axis.

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