# Truss Deflection Problem

Dear Readers, why doesnt the deflection formula depend on moment of inertia (I) or even the second momnet of area that are responsible for the cross-sectional shape of beam. Does that mean in the example below, for a round cross-sectional area vs a triangular cross-sectional are have the same amount of deflection? I feel so confused :)

• $\delta_{H,D}$ means horizontal deflection @ D? Commented Apr 22, 2022 at 12:45
• The answer to this is the same as in your previous question. because each member has axial tension only. If the elastic members do not undergo bending, then their section properties are not used. Possible duplicate of physics.stackexchange.com/q/704848/268448 Commented Apr 22, 2022 at 12:49
• Does this answer your question? Do inertia affect stiffness matrix of beam? Commented Apr 22, 2022 at 22:52

$$k = \frac{E A}{L}$$
You can clearly see this factor in the deflection formula. The shape of the cross section does not matter, as only the area $$A$$ and elastic modulus $$E$$ determine the elastic properties of the section.
In real life, the joints between members would not allow any rotation, thus needing to carry bending moments to enforce this constraint. Then each member would need to consider both the axial stiffness $$E A/L$$ as well as the bending stiffness $$3 E I/L^3$$.