Tensile strength of a braided steel wire vs. a solid steel bar? I am wondering which one is the strongest between a steel rope and a steel bar with same diameter and made of the same steel?
EDIT : The test could be: attach rope/bar to ceiling and suspend a mass until it break
EDIT2 : Can I have also some order of magnitude? For example, is the rope 2 times stronger than the bar?
 A: I assume the total cross section of the wires in the rope is equal to the cross section of the steel bar. Since there is some space between the fibers, the rope will have a larger diameter.
If the fibers in the rope were all straight and you were careful to pull equally on each fiber, the bar and rope should be equally strong. But they typically won't be. 
Suppose one fiber is a little weaker than the others, and breaks first. Now the rest have a heavier load. 

In practice, you can buy copper wire in single strand or multiple strand forms. 
The advantage of multiple strands is flexibility. You use them in cables you plug in often. Flexing them too much can break individual fibers, and eventually break the wire. 
The advantage of single strand is durability. Wires inside walls are single strand because they are inconvenient to replace. They are seldom handled, so stiffness isn't a problem. 
A: I can only speak for steel and aluminum which I have had engineering experience with. The answer is that a solid rod is going to be stronger than a stranded one of the same area. There are a few effects to consider, and most of them work against the stranded cables.


*

*Geometry Effects. Strands are not straight and so pulling on them causes contact pressure between the layers of strands which add to the normal stress. Also the helix angle $\alpha$ causes the internal tensile force to be equal to the external force divided by $\cos \alpha$. The internal normal stress is then $\sigma_N = \frac{F}{A \cos \alpha} > \frac{F}{A } $. For this reason ASTM B221 standard provides for a derating of cables based on the number of layers. Typical values are at about $88\% \ldots 92\%$ for outer layers, and $94\% \ldots 98\%$ for core strands.

*Skin Effects. Stranded cables almost always use heat treated materials, which cause the skin of the strand to be stronger than the core. So overall the smaller the diameter of a strand the higher the ultimate stress. The exception would be soft materials like Aluminum 1350-O or similar. This skin effect is specified as a function of strand diameter $d$ in inches: 

*

*Aluminum,  $d<0.14$ : $sf=1.213-2.185d$

*Aluminum,  $d \ge 0.14$ : $sf=0.972-0.402d$

*Steel, $d={\rm all}$ : $sf = 1.1277-1.096d$

*Alumoweld, $d={\rm all}$ : $sf = 1.377-2.936d$


*Fatigue. The strands are flexible (which is why they are used) but the internal contacts might cause fretting failures due to small repeating motions between the strands. This is why the fatigue life of a stranded cable is much harder to predict than a solid rod, and typically much less in value.


There is more to this, but I cannot come up with anything right now. Please use comments to add to this list.
A: My career was as a metallurgist.  The high strength of steel wire is primarily due to cold work, not heat treatment.  Cold drawing of wire, like cold rolling of sheet, plate or rod, basically compresses the material at and near the surface, significantly increasing its strength, especially in the direction of drawing. 
read about the atomic level details here: https://en.wikipedia.org/wiki/Work_hardening
Because of all the work hardened surfaces, I believe a steel cable is stronger than a rod of similar size.
