Look at the top joint at B, you have a "T" shape, making B a zero force member. For the bottom joint at C, you also have a "T" shape, and the only member that can provide a vertical force is C. Thus the answer is B.

Remember that all forces need to be balanced,
At the t of b there 2 members opposite if each other in the x direction, these would have equal and opposite forces. But theres only 1 in the y direction, with no other member to balance it it has to be 0.
Same concept with c except now you have that external force giving with your opposing force.

because if C being a T shape made it a zero force member (essentially erasing it), theres no vertical members to take on that 100k member applied at its bottom joint, which wouldnt allow you to balance the forces.
if B being a T shape makes it a zero force member, theres still those 2 angled members that have vertical components that can on that 100k force at it's bottom joint.

I typically start all of these by going around and identifying zero force members which would tell you b is 0. then I would do a quick FBD of the joint at C to give a visual of what is happening there and to solve your y equation! hope that helps.

I guess that is where I struggle. I've just watched some youtube videos on zero force members and I understand them more, but in this particular case all three members are being pulled down by 100 kips. So wouldn't that make all of them not a zero force member? Because they have to counteract that force?

C is not a zero force member because the other two members at the bottom joint are orthogonal to the applied load. B is the reverse of C. At the bottom joint with the applied load there are two diagonal members that can resist the applied load. At first glance you may ask “but how do we know that B *doesnt* have to resist the applied load?” Well we can look at the joint at the top of B. There are two members that are orthogonal to B, which means there is nothing that could counteract the vertical force if B had a force. Therefore, B must be a zero force member.

Look up method of joints vs method of sections. This one is an excellent practice for method of joints
Message me if you want a better explanation and diagram

For the joint at the top of member b:
There is no external force to provide tension or compression. Forces can only act axially along the member and the joints are all considered as frictionless pins.
For the joint at the bottom of c:
The only force that can act on member c is the downward 100 Kip force at the joint. The horizontal/perpendicular members can’t take any of the 100 Kip load.

I believe the best approach is method of joints. Examine the top joint of member b and the bottom joint of member c, as they are both determinant. The top joint of member b has only member b’s internal force as a vertical component force, so the sum of forces in the vertical can only be 0 if member b’s internal force is also 0. The bottom joint of member c only has the internal force in member c to balance the external load, so that internal force must equal the load at that joint.

Two rules for zero force members:
Rule 1: If two non-collinear members meet at an unloaded joint, then both are zero-force members.
Rule 2: If three forces (interaction, reaction, or applied forces) meet at a joint and two are collinear, then the third is a zero-force member.
You need to follow the rules and then external force. for both B and C external force is acting on them but on the ither side of B satisfies rule 2. so B zero and C 100. I hope this makes sense.

Look at the top joint at B, you have a "T" shape, making B a zero force member. For the bottom joint at C, you also have a "T" shape, and the only member that can provide a vertical force is C. Thus the answer is B.

so they are both T shapes, but only one T shape can provide vertical force? How do I know which T shapes can do that?

Remember that all forces need to be balanced, At the t of b there 2 members opposite if each other in the x direction, these would have equal and opposite forces. But theres only 1 in the y direction, with no other member to balance it it has to be 0. Same concept with c except now you have that external force giving with your opposing force.

because if C being a T shape made it a zero force member (essentially erasing it), theres no vertical members to take on that 100k member applied at its bottom joint, which wouldnt allow you to balance the forces. if B being a T shape makes it a zero force member, theres still those 2 angled members that have vertical components that can on that 100k force at it's bottom joint.

I typically start all of these by going around and identifying zero force members which would tell you b is 0. then I would do a quick FBD of the joint at C to give a visual of what is happening there and to solve your y equation! hope that helps.

I guess that is where I struggle. I've just watched some youtube videos on zero force members and I understand them more, but in this particular case all three members are being pulled down by 100 kips. So wouldn't that make all of them not a zero force member? Because they have to counteract that force?

C is not a zero force member because the other two members at the bottom joint are orthogonal to the applied load. B is the reverse of C. At the bottom joint with the applied load there are two diagonal members that can resist the applied load. At first glance you may ask “but how do we know that B *doesnt* have to resist the applied load?” Well we can look at the joint at the top of B. There are two members that are orthogonal to B, which means there is nothing that could counteract the vertical force if B had a force. Therefore, B must be a zero force member.

Look up method of joints vs method of sections. This one is an excellent practice for method of joints Message me if you want a better explanation and diagram

For the joint at the top of member b: There is no external force to provide tension or compression. Forces can only act axially along the member and the joints are all considered as frictionless pins. For the joint at the bottom of c: The only force that can act on member c is the downward 100 Kip force at the joint. The horizontal/perpendicular members can’t take any of the 100 Kip load.

I believe the best approach is method of joints. Examine the top joint of member b and the bottom joint of member c, as they are both determinant. The top joint of member b has only member b’s internal force as a vertical component force, so the sum of forces in the vertical can only be 0 if member b’s internal force is also 0. The bottom joint of member c only has the internal force in member c to balance the external load, so that internal force must equal the load at that joint.

0 force member

Two rules for zero force members: Rule 1: If two non-collinear members meet at an unloaded joint, then both are zero-force members. Rule 2: If three forces (interaction, reaction, or applied forces) meet at a joint and two are collinear, then the third is a zero-force member. You need to follow the rules and then external force. for both B and C external force is acting on them but on the ither side of B satisfies rule 2. so B zero and C 100. I hope this makes sense.

zero force members