Painful triceps

Sore triceps is generally the sign of a fairly extreme positional short fall. 

You shouldn't need to strengthen your arms to sustain a position on a road bike.

The answer is a bike fit. 

Bike set up is to some degree a function of what you have the strength and flexibility to sustain.  If you have 'excess' load on your triceps you can go down the road of moving your weight backwards to increase the balance on the saddle rather than the bars or you can strengthen your core, lower back and triceps, to take the load. 

There will be limits to both - if you end up with a 70mm stem your steering will be off and if you're wrongly positioned over the BB you can end up with knee problems.  Interesting that its your arms and not your back that are complaining first. 

You can play around with these things yourself but a bike fit will probably get you there faster.  Strengthening your core never hurts though, well it does at the time but it wears off with practice!

I have a funny feeling the answer will be a shorter stem and moving the saddle back.

In my experience sore triceps are caused when the angle between the torso and upper arm is too great. I.e. you are too stretched. 

Having your saddle forward will only make this worse as you take more weight through your arms and have to stabilise your upper body. 

http://www.peterwhitecycles.com/fitting.htm

Excellent article which explains the "balance" principle that has been mentioned

Get a bike fit. Seriously.

A Retul bike fit will not only assess and resolve any incorrect positioning on the bike but will also identify any physical problems you have which will then be considered within your position.

I go to the gym and was aware that while squatting my left knee tracking was a little eratic. I thought this was a weak knee.

During the Retul bike fit we found that i have deepset scar tissue in my left ankle, likely from being studded during 12 years of football. This caused lack of mobility in my ankle and kicked my knee out to compensate.

I was then provided with some mobility exercises for my ankle and the issue is a long way down the road to resolution.

It is a bit of a wedge in terms of cash spending, but it is an investment in your comfort on the bike.

How much climbing are you doing in your rides? Only asking because I kept getting tricep pain because I was subconsciously wrenching on the bars when I hit anything that required some proper effort. I've managed to make myself check I'm not too tense and force myself to relax on the steeper stuff. It was a bit like when you're driving and realise you're gripping the wheel way more than you need to.

To add to the above, a good way of illustrating the point is that if you are set-up correctly, you should be able to sit in the saddle, feet in the pedals, but without pedalling and holding the drops, then let go of the bars and move your arms out to the sides without dropping forward. If you feel like you are going to just nose plant into the stem and cannot hold yourself up for a reasonable period of time, then you need to look at saddle/BB relationship. It also shows up any core strength deficienies which will also contribute to the arm pain.

Edit to add, do this on a turbo trainer that clamps the bike in, rather than attempting it on the open road!

I would suspect that your saddle is too far forward. It sounds counter-intuitive, but if you are too far forward of the bottom bracket (which is the point around which you are balancing), your tendency is for your body weight to be tipping forward. With your weight falling forward, you need to employ your arms, in particular your triceps, to resist that tendency.

It was quite common for me to find cyclists that were having lower back, hand or arm pain, that thought the best option was to shorten the cockpit in order to be more upright. This tended to have the opposite effect, and moving the saddle back to more correctly distribute their weight behind the BB tended to make a huge difference.

Remember to make any adjustments gradually, also your arms are probably fatigued already so it may take a good few rides to notice any real difference.

The plus-side is that moving the saddle back on its rails is free, assuming you have some adjustment left. If not, see if you can borrow a seat-post with greater layback to try.

Arms too straight.

Yeah, I'd check your reach but I'd guess at weakness - you take a lot of shock up your triceps. Does it feel like normal, beaten up muscle soreness or something more serious? Does your back or neck hurt?

If it's just conditioning you need, either plough through it via more regular rides of enough intensity to trigger the soreness, or schedule some time off the bike to focus on strengthening them. Google press-ups with differing hand positions - any are fine, but hands closer together under your chest will work your tris more. Dips are also good.

You want muscle endurance, so body weight exercises with high reps are fine and require no equipment.

Off the top of my head I'm struggling to think of anything more serious that would present itself in both sets of tris being sore but it should be obvious if it isnt just conditioning that you need.

Yeah can be reach, not always though. Maybe your saddle is pointed down a bit too much? If not then yeah, grab some cheap £5 stems on eBay to see if you can dial it in before the spring. Also worth doing a little strength work, basics like pushups and situps in the morning wouldn't hurt. Bike can be great for detecting weaknesses.