Final answer:
A statically determinate beam under symmetrically distributed loads would have symmetrical shear and moment diagrams. This is due to equal and opposite forces applied in a balanced manner across the beam's span when the beam, loading, and supports are symmetric.
Step-by-step explanation:
A type of beam that would have shear and moment diagram symmetrical is a statically determinate beam that is subject to perfectly distributed symmetrical loads. In such cases, the shear and moment diagrams exhibit symmetry about the center of the beam or the applied loads. This typically occurs in scenarios where the geometry of the beam, the loading, and the support conditions are symmetric with respect to the midpoint of the beam's span.
For instance, if you were to place equal weights at equal distances from the fulcrum in a torque balance scenario, the beam remains level and in static equilibrium, illustrating a symmetrical condition. Likewise, in the context of shear stress, if forces of equal magnitude and opposite direction are applied tangentially across the entirety of two opposite parallel surfaces of a beam, a symmetric shear deformation will result, assuming the material is homogeneous and the beam geometry is symmetric.
The shear modulus (S) is a measure of the material's response to shear stress and is involved in calculating the deformation under such conditions. It is defined by the equation Ax = (F/A)/S where Ax is the deformation, F is the force applied, A is the cross-sectional area, and S is the shear modulus. A symmetrical shear stress would result in a symmetrical deformation assuming the object has uniform properties.