Question

Determine the reactions in the bearing A and B and determine the laws for the internal statics quantities of the beam ( transfer forces, attack moments and axial forces).

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Answer 1

The reactions at supports A and B are:
`A_y` = F * (L - a) / L and
`B_y` = F * a / L. The laws for the internal statics quantities of the beam are: Transfer force = Shear force; Attack moment = Bending moment and Axial force = Normal force

Determining Reactions at Supports:

To determine the reactions at supports, we can use two equilibrium equations:

∑
`F_y` = 0

∑
`M_A` = 0

where:

∑
`F_y` is the sum of all forces in the y-direction

∑
`M_A` is the sum of all moments about point A

Since the beam is in static equilibrium, the sum of all forces and moments must be equal to zero.

Determining Reaction at A

To determine the reaction at A, we can take the sum of moments about point B. This gives us:

∑
`M_B` = 0

F(L - a) -
`A_y` * L = 0

`A_y` = F * (L - a) / L

Determining Reaction at B

To determine the reaction at B, we can take the sum of forces in the y-direction. This gives us:

∑
`F_y`= 0

`A_y + B_y - F = 0`

`B_y` = F -
`A_y`

`B_y` = F * a / L

Laws for Internal Statics Quantities

The three internal statics quantities of a beam are:

Transfer force - The force that is transferred from the beam to the support.

Attack moment - The moment that is applied to the beam by the support.

Axial force - The force that acts along the axis of the beam.

The laws for the internal statics quantities of a beam can be summarized as follows:

Transfer force - The transfer force at a point is equal to the shear force at that point.

Attack moment - The attack moment at a point is equal to the bending moment at that point.

Axial force - The axial force at a point is equal to the normal force at that point.