Understanding Support Reactions in Frames

When analyzing frames or any structure, it is crucial to understand the types of reactions that different supports provide. These reactions are the forces exerted by the supports on the structure to maintain equilibrium under applied loads. The type of support dictates the number and direction of the reaction forces.

We are looking for a type of frame support where both reactions are always vertical and can be determined using the principle of moments (which is based on the equations of static equilibrium, typically $\sum F_x = 0$, $\sum F_y = 0$, and $\sum M = 0$).

Frames with Simply Supported Ends

Consider a frame or beam that is simply supported at both ends. A classic example is a beam resting on two simple supports. A simple support typically allows rotation but prevents vertical movement. For the entire structure to have only vertical reactions at the external supports under general loading conditions (especially considering external forces), the supports must be configured in a way that provides no horizontal restraint. This is most commonly achieved by having one end as a hinge (allowing rotation) and the other as a roller (allowing horizontal movement and rotation, but preventing vertical movement). In such a setup, the hinge provides vertical and horizontal reactions, but the roller provides only a vertical reaction (assuming the roller is on a horizontal surface). However, the question states "both reactions are always vertical". This condition is met if both supports effectively act as rollers or if the frame configuration and loading ensure that the horizontal reaction at a hinge support is zero. In the context of basic structural analysis and MCQs, "frames with simply supported ends" often implies a scenario where the structure is supported in a way that results in only vertical external reactions, similar to a simply supported beam where one end is often implicitly considered a roller to ensure static determinacy and only vertical reactions from vertical loads.

For a structure with only vertical reactions $R_A$ and $R_B$ at supports A and B, subjected to vertical loads, the equations of equilibrium become:

• $\sum F_x = 0$ (This is satisfied as there are no horizontal reactions or external horizontal loads mentioned that would prevent this).
• $\sum F_y = 0 \implies R_A + R_B = \text{Sum of all vertical loads}$
• $\sum M_A = 0 \implies$ Sum of moments of all forces about A = 0. This equation directly involves $R_B$ and the applied loads, allowing $R_B$ to be calculated.
• $\sum M_B = 0 \implies$ Sum of moments of all forces about B = 0. This equation directly involves $R_A$ and the applied loads, allowing $R_A$ to be calculated.

Thus, when only vertical reactions are present, the principle of moments ($\sum M = 0$) can be effectively used to find the magnitude of these vertical reactions.

Analyzing Other Support Types

• Frames with both end hinged: A hinged support provides both vertical and horizontal reactions. Therefore, the reactions are not always purely vertical. You would need $\sum F_x = 0$, $\sum F_y = 0$, and $\sum M = 0$ to solve for the two vertical and two horizontal reactions (four unknowns in total, which is statically indeterminate for a simple frame, but even if determinate, there would be horizontal reactions).
• Frames with both the ends fixed: A fixed support provides vertical reaction, horizontal reaction, and a moment reaction. With two fixed ends, there are six unknown reactions (three at each support), making it highly statically indeterminate. Reactions are definitely not just vertical.
• Frames with one end hinged and other supported freely on rollers: A hinged end provides vertical and horizontal reactions. A roller support provides only a vertical reaction (if on a horizontal surface). Thus, one support has a horizontal reaction, meaning both reactions are not always vertical.

Comparing the options, the case where both reactions are always vertical and solvable by moments aligns best with the interpretation of "frames with simply supported ends" where the support conditions (like hinge + roller) are configured to eliminate horizontal reactions under typical loading, leaving only vertical ones at the external supports.