Question

The member A-F is fixed to a wall at A. Determine the

(a) reaction at the wall; and
(b) total change in length (E = 200 GPa).

Answer 1

Main Answer:

(a) To determine the reaction at the wall (support A), a static equilibrium analysis is required. Summing the forces and moments acting on the member allows for the calculation of the reaction at the fixed support.

(b) To find the total change in length of the member, the axial deformation formula
`\( \delta = (PL)/(AE) \)` can be used, where
`\( \delta \)` is the deformation,
`\( P \)` is the force applied,
`\( L \)` is the original length of the member,
`\( A \)` is the cross-sectional area, and
`\( E \)` is the modulus of elasticity.

Step-by-step explanation:

(a) Reaction at the Wall (A):

Apply the equations of equilibrium to the member. Summing the forces and moments should be done in a way that considers the fixed support at A. The reaction at the wall can be determined by enforcing static equilibrium.

(b) Total Change in Length:

Use the axial deformation formula
`\( \delta = (PL)/(AE) \)` to find the total change in length. Identify the force
`\( P \)` acting on the member, the original length
`\( L \)`, cross-sectional area
`\( A \)`, and the modulus of elasticity
`\( E \)`.

It's important to note that without specific values for the applied force, original length, cross-sectional area, and other relevant parameters, the calculations for the reaction at the wall and the total change in length cannot be carried out. To obtain accurate results, numerical values for these parameters would be needed.