Ultimate tensile strength is the force required cause fracture under tensile loads.

Yield strength is the force required to cause plastic deformation.

Residual stress is the level of stress in the material as a result of forming, thermal cutting, welding, etc.

When you bend a piece of plate you have to exceed the yield strength of the material or the material will spring back into it's original shape. Even when you do exceed the yield strength of the material there is some spring back that has to be accounted for. The spring back is due to the deformation that occurs when the load is within the elastic range of the base metal.

To put it a different way. When you apply a small force on the plate being bent, it will spring back to its original position. The load is said to be within the elastic range for the material. Looking at a stress strain diagram for steel, the elastic range is the straight portion of the graph toward the left vertical axis. The slope of the straight line is what we refer to as the modulus of elasticity (E) which for steel is equal to 29 x 10 to the sixth power (29 million). E is a measure of stiffness for a material.

Once the applied load exceeds the yield strength of the material permanent deformation occurs. If you are bending a piece of plate, you have to exceed the yield strength of the material in order for the plate to stay bent. You usually have to bend beyond the required angle to account for the spring back (that portion of the load that is below the yield point and within the elastic range.

Once localized yielding occurs, the material is strain hardened if it is a ductile material (unhardened steel). The strain hardening (work hardening) strengthens the steel so that it can sustain additional load, but the rate of strain (stretching) increases. In other words the material stretches faster with increased loads.

Consider our ever faithful ASTM A36 carbon steel plate. It has a yield strength of 36 ksi and a tensile strength of 58 ksi. It begins to plastically  deform at 36 000 psi. Still it doesn't fracture. We can increase the stress up to 58 000 psi before the steel is in danger of fracturing.

Our designs usually limit the maximum stress to some fraction of the yield strength. For structures it is usually about 2/3's of the yield strength, well within the elastic range. We are talking about maximum stresses on the order of 21 to 27 ksi. There is plenty of reserve strength to accommodate the occasional overload and the uncertainty in our design calculations. That probably accounts for why building don't collapse when the erector or fabricator doesn't pay close attention to details and let some "quality" slip.

The residual stress act similar to pretensioned bolts in a bolted connection. The residual stress is greater than the applied stress. Plastic deformation has already occurred due to the residual stresses introduced by welding and the allowable stress is with in the elastic range. Limiting our discussion to CJP grooved joints, as long as the weld doesn't cause the connection to fail, there is little danger that a static tensile stress that is within the range permitted by design parameters is going to cause failure.

Additional complexity enters the picture due to the fact that the residual stresses are not uniformly distributed and they are both transverse to the weld and longitudinal to the axis of the weld. They act as vectors that can be added there by increasing the resultant. This is a real problem when you have two perpendicular intersecting welds or worse yet three intersecting welds (think of a web welded to a flange of a built-up girder with a stiffener welded continuously to the web and the flange, yikes!).

The problem of intersecting welds is more critical for the higher strength steels where the ratio of yield strength to tensile strength approach 1. Good old A36 has a YS/TS ratio of about 0.6. There is plenty of reserve strength and rarely do intersecting welds crack at the intersect. The material is ductile, as is the weld, so the resultant residual stress (by vector addition) is 51 ksi which is less than the UTS of 58 ksi.  The resultant simply exceeds YS so plastic deformation occurs and no crack is formed. The problem is a concern with steels like A992 which have higher YS (50 ksi) and TS (65 ksi). The ratio of YS/TS is 0.77. When two welds intersect the resultant vector force is 71 ksi which exceeds the TS. What happens when the applied force exceeds the UTS? That's right, you have a high probability of developing a crack at the point of intersection. When you have three intersecting welds in either A36 or A992, there is a   high probability of developing a crack at the point of intersection.

Interesting stuff.

Best regards - Al