strut tie method pile caps

[SemiPE]

I am new to designing pile caps using Strut tie method (STM). Most books tackle examples for 2-pile group and 4 pile group for STM, but not 3-pile group. My reference has a quick formula to in getting the Tension force required for the tie, while I was able to derive the formula for 2-pile group and 4-pile group, my derivation for the pile group is different from what is shown in my reference. Most books shows the same formula for the 3-pile group as with my reference. Meaning my derivation for the is in correct. I searched the internet for the derivation but I got nothing.

Can anybody give me a hand and show me how did this formula for the tension force of a three pile group arrived? I attached my reference to serve as a guide.

another thing, if I design the 3 pile group using STM would my rebars be oriented in a triangular fashion (same as the directions of the tension tie)?

thanks a lot

 

[SemiPE]

I am new to designing pile caps using Strut tie method (STM). Most books tackle examples for 2-pile group and 4 pile group for STM, but not 3-pile group. My reference has a quick formula to in getting the Tension force required for the tie, while I was able to derive the formula for 2-pile group and 4-pile group, my derivation for the 3 pile group is different from what is shown in my reference. Most books shows the same formula for the 3-pile group as with my reference. Meaning my derivation for the is incorrect. I searched the internet for the derivation but I got nothing.

Can anybody give me a hand and show me how did this formula for the tension force of a three pile group arrived? I attached my reference to serve as a guide.

another thing, if I design the 3 pile group using STM would my rebars be oriented in a triangular fashion (same as the directions of the tension tie)?

thanks a lot

 

[asixth]

Solve by trigonometry. The reo layout is right, generally one of the sets is cranked so the bars fit.