How SSR Works?

Totally unsuitable for DC side because SCR's or Triacs are used as switching devices on almost all AC Solid State Relays and will NOT switch off untill driven current gets close enough to zero cross. And some SSR types will not even start because their gate driving cirquit waits for a voltage zero cross. S.M.

Quite right. There are alternatives though. Here's one.

the input voltage is 4 to 32 VDC, so the ssr would only activate if input voltage is between 4-32VDC right? if below 4 volts it would de-activate am i right? or the input voltage should be @ zero volts?

the load is rated @ ac voltage, does it mean that dc voltage has no effect on it?

If you feed it with less than 4V input will not turn 'on'. If already 'on' (meaning it was fed with more than 4V before) and activating voltage gets lower than 4V it will go to 'off' state as soon as the momentary output (driven) current goes under a predefined level depending on SSR specifics. It's safe to assume this level is very low (near zero), so driving DC current it never will. Pretty straightforward. Also notice the potential activating problem in previous post. S.M.

i tested the ssr, 5 vdc input and connected the output side to a 24vdc beacon light, the problem is, whenever i closed the circuit the output side [24vdc for beacon light] and i input 5vdc to the input side of the ssr, the beacon doesn't turn on, unless i disconnect its power and power it again [still there is a 5vdc input in the input side], and when i remover the 5vdc input, the beacon is latched [always on] unless i disconnect the power again of the beacon. and after that if i input again 5vdc it will not work, and im back to the beginning, so im wondering if there is a solution to this circuit, so that i could work my ssr as an ordinary relay [mechanical type] that will not latch on and the output depends on my input...