Most of the time, the answer will be yes.
Concrete and masonry don't withstand tension. Tension, simply defined, is stretching. We imbue this property to masonry walls with reinforcing steel, aka rebar. We give the block wall the ability to bend without breaking immediately. Think of a tree swaying in the wind. When the wind blows hard enough, the tree trunk bends. As the wind puts stress on the tree the tree compensates by flexing instead of just snapping off. But put enough stress on a tree, such as a hurricane, and the tree fails. It breaks under the stress. Same with a block wall. Put stress on it and it bends. One side is compressed while the other side in in tension. It's stretching. But masonry does't stretch much. Which is where the rebar comes in.
Block walls are subjected to many forms of stress, of tension. A person leaning against a wall causes tension (not much, but some). A tree leaning on a wall definitely causes tension. The high winds mentioned above cause tension. Earthquakes cause walls to sway, more tension. Rebar can take a lot of tension. Rebar, specifically steel, is the reason mankind can build huge skyscrapers and miles long bridges.
So, most of the time, you want rebar in your masonry walls. Structural walls should always have reinforcing. But it's not necessary for small decorative walls. Short walls (short in height and short in length) for planters, little yard dividers, etc., will do just fine with no rebar. Our six foot tall yard walls here in the Valley of the Sun, called Dooley Walls, only have rebar every 10 or 12 feet, in the pilaster blocks. That is enough to keep them from blowing over or getting knocked over very easily. Mail boxes built out of masonry should specifically not have any rebar attaching them to their footings. We want our masonry mailbox to fall over and slide over fairly easily if someone runs into it with a vehicle. We don't want our mailbox to be like the security bollards in front the FBI building. If someone crashes into our mailbox we want them to survive.
There's a lot more to this subject and it's something that engineers don't all agree on. How much rebar to concrete into a wall is always a debatable question. I personally feel that we overkill with the amount of rebar we put into our structures. But I'm not an engineer. I'm just a mason who has been installing a lot of rebar for a lot of years and I've had lots of opportunities to demo reinforced block wall. In my experience a little rebar goes a long way.
If you have rebar questions about your small project, feel free to email or message me. I would be glad to offer suggestions or constructive criticism, as appropriate.
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