What is the defining characteristic of a multiforce member in a frame or machine?
Explanation
Unlike truss members which are idealized as two-force members (experiencing only axial tension or compression), members in frames and machines are often multiforce members. This means they are subjected to three or more forces, or a combination of forces and moments, leading to more complex internal loadings like shear and bending.
Other questions
According to the assumptions for the design of a truss, what is the primary characteristic of the connections between members?
A truss member that is subjected to a pulling force, causing it to elongate, is said to be in what state?
In the method of joints, why is it advisable to always start the analysis at a joint having at most two unknown forces?
What is the primary characteristic of a 'simple truss'?
Under what condition can a member in a truss be identified as a zero-force member by inspection?
What is the primary advantage of using the method of sections over the method of joints?
What is the simplest form of a space truss?
Consider a simple truss with a pin at joint B connecting members BA and BC at a 45-degree angle to the horizontal. A 500 N vertical downward force is applied at joint B. What is the force in member BC?
In the analysis of frames and machines, what principle is applied to the forces at a pin connecting two members when drawing separate free-body diagrams for each member?
In the Fink roof truss shown in Example 6.4, with a 5-kN vertical load at joint C and 2-kN vertical loads at joints B and D, which member is identified as a zero-force member by inspection of joint G?
A crane boom is modeled as a frame. Member AB is a two-force member. Member BC has a 2000 N load applied horizontally at its midpoint. The pin at C connects to the frame. Member BC is 4 m long, and the pin A is positioned such that member AB makes a 60-degree angle with the horizontal. What is the magnitude of the force in member AB?
A compound beam ABC is made of two segments, AB and BC, connected by a pin at B. It is supported by a fixed support at A and a roller at C. An 8 kN vertical load is applied 1 m from B on segment BC, and a 4 kN/m distributed load acts on the first 2 m of segment AB from A. Segment BC is 2 m long. What is the vertical reaction at the roller support C?
What is the key difference in the analytical approach between a frame and a machine?
A system of pulleys is used to hoist a 500-kg elevator car. The car is supported by 3 cables with tension T1 and two cables with tension T2. Pulley C connects the T2 cable to two T1 cables. Assuming constant speed, what is the tension T1?
In a truss where a joint connects three members, and two of those members are collinear, with no external force applied at the joint, what can be concluded about the third member?
When using the method of sections, what is the maximum number of members with unknown forces that a section should generally pass through?
In a space truss analysis using the method of joints, how many scalar equilibrium equations are available at each joint?
A smooth piston and link mechanism is used to crush a can. A force of 800 N is applied to the handle at a 30-degree angle to the horizontal. The handle EBD is pinned at D. Member AB is a two-force member connected at a 75-degree angle to the horizontal handle. What component of force does the pin at D exert on the handle in the x-direction?
A compound beam ABC is composed of segments AB and BC, pinned at B. It is under a distributed load and an 8 kN concentrated load on segment BC. The beam is supported by a fixed support at A and a roller at C. After finding the roller reaction Cy = 4 kN, what is the vertical reaction By at the internal pin B?
A two-plank system is connected by a cable BC and a smooth spacer DE. Plank AD rests on support A, while plank CF rests on support F. A 100 lb load is on plank AD and a 200 lb load is on plank CF. If the force in the spacer DE is found to be 140 lb, what is the tension in cable BC?
In the truss from Example 6.2, a 400 N vertical force is applied at joint C. The analysis of joint C shows the compressive force in member CD is 400 N. At joint D, member AD is at a 45-degree angle to the horizontal and member BD is at a 30-degree angle from AD. What is the force in member AD?
For the truss in Example 6.3, a free-body diagram of the entire truss is used to find the support reactions. The truss has a pin at A and a roller at C, separated by 6m. A 400N horizontal force acts at joint B (3m high) and a 600N horizontal force acts at joint D (on the bottom chord, 4m from A). What is the vertical support reaction at A, Ay?
If a free-body diagram of a joint in a truss is drawn and the numerical solution for a member force yields a positive scalar, what does this indicate according to the common analysis procedure?
When using the method of sections on a truss, summing moments about which point would provide a direct solution for a specific member's force?
A truss is analyzed using the method of sections by cutting through members GE, GC, and BC. The sectioned FBD has a 1000 N vertical downward force at joint A and an upward vertical support reaction of 300 N at A. The horizontal distance from A to G is 4 m. What is the force in member BC?
What is the key assumption regarding the joints of a space truss that allows its members to be treated as two-force members?
A space truss has a joint at A with a downward vertical force P = { -4j } kN. Members AB, AC, and AE connect at A. Member AB is along the y-axis, AC is along the x-axis, and AE connects to a point requiring it to have components in the x, y, and z directions. From equilibrium, F_AE = 0. What is the force in member AB?
When drawing a free-body diagram of an entire frame, what happens to the forces at the pins connecting its members?
A frame consists of a vertical member and a horizontal member joined by a pin at B. The vertical member has a pin support at A. The horizontal member has a roller support at C and is subjected to a 400N vertical downward load. The distance from A to B is 2m, and from B to C is 2m. Using the method of sections on the horizontal member from C, what is the force in member AB?
What is the primary difference between a 'frame' and a 'machine' as defined in structural analysis?
In the analysis of the pulley system in Example 6.10, the weight of the suspended block is W. The tensions in the conveyor belt are T. What is the relationship between the pin reaction components at B (Bx and By) and the belt tension T?
In the mechanism from Example 6.11, when the free-body diagram of the frame without the pulleys and cords is drawn, why must the forces from the cords and pulleys be shown?
In the backhoe from Example 6.12, members AB, BC, BE, and HI are all identified as what type of members?
A frame holds a smooth disk of weight 20 lb, pinned at D. Member AB is supported by a pin at A and connects to member BCD at B. Member BCD is pinned to the disk at D and rests on a support N_D at its end. If the horizontal distance from A to the center of the disk is 6 ft, and the horizontal reaction at A is 17.1 lb, what is the vertical reaction at B (By) on member AB?
A frictionless pulley system is used to support a 600 N force. It consists of three pulleys A, B, and C. A continuous cable with tension P passes around the pulleys. A link with tension T connects pulleys B and C. What is the tension T in the link connecting pulleys B and C?
A frame supporting a 50-kg cylinder consists of a bent member ABD and a two-force member BC. The cylinder hangs from a pulley at D. ABD is pinned at A. The horizontal distance from A to the vertical line through D is 1.2 m, and the vertical distance is 0.6 m. The force in member BC is found to be 245.25 N. What is the horizontal component of the reaction at pin A (Ax)?
In a truss analysis, if a joint has two known forces and three unknown forces, can it be solved using the method of joints at that point?
If you are analyzing a large truss and only need the force in a single member near the middle of the truss, which method is generally more efficient?
What are the two fundamental assumptions for design that allow the members of a planar truss to be treated as two-force members?
A man attempts to lift a 40-kg beam by pulling on a rope that goes over a pulley at E and attaches to the beam at C. The man has a mass of 75 kg and stands on the beam. The beam is supported by a pin at A. If the man is about to lift the beam off a roller at B, and the tension in the rope segment attached at C (T1) is 256 N, what is the normal force the man exerts on the beam (Nm)?
In a space truss, if you use the method of sections and make a cut, how many independent equilibrium equations are available for analyzing the resulting segment?
What is a gusset plate?
When analyzing a frame or machine, if a member is identified as a two-force member, how does this simplify its free-body diagram?
For the truss in Example 6.7, a section cut 'aa' is made through members ED, EB, FB, and AB. Summing moments about which point would allow for a direct solution for the force in member ED (F_ED)?
What is the primary reason that compression members in a truss often need to be made thicker than tension members?
A frame is composed of member AB and member BC, connected by a pin at B. There is a pin support at A and a roller support at C. The members form a triangle with the ground. A downward vertical force P is applied at the pin B. How many two-force members are in this frame?
A Warren truss is shown with metal gusset plates used in its construction. What is the analytical purpose of assuming these connections act as smooth pins?
A frame consists of a vertical boom and a bucket, as in a backhoe. If the free-body diagram of the entire assembly (boom plus bucket) is drawn, what kind of forces are the forces at the pin connecting the boom and the bucket?
In the truss from Example 6.3, after finding the reactions Ay = 600 N and Ax = 0, and analyzing joint A to find F_AD = 450 N (Tension) and F_AB = 750 N (Compression), what is the force in member DB?