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z_7?e=oL|JzDK0+s#4x7O3vWdHgJfu>h{GJcNqoKUpVhCPfOl|qDhHdk*(Bu$o_*qm z$2%w1?C9~Z20NGpk@;XM$2`oyTZJ6&KHn!W#=%8%uVCG(RORB~FM7ncGutpb6x6kI zQxv72QAy#)@kspO%I@$2MU)ll#*yhSa8$BzWhp72u2hP+XSquqMYexmD$7y!R=Dk6 zw`fZAZ$Vut_s*NkG<6Sy1Oi^dlOFp-Qp*u;0EMfhZG^^vbI3%2ox8_SOHs!w^t!h< zRyiZSv&&d*ir@D!G+boK*QG^pcB4#iyREgwEPRlka@WPCz2E_isA7t^tA=$2s};=~ erIR}NT|F?o-fX;^?^uF1Y1=KbTRG_8 Identify any two-force members and apply the two force member assumptions (see the Truss reference pages for more details) - Identify any multi force members and make free body diagrams for each multip force member. Remember that the same forces in two different free body diagrams will be equal and opposite! - + + Identify any multi force members and make free body diagrams for each multi force member. + When two connected members share a common force at their connection point, that force is equal in magnitude, but acts in the direction opposite of the direction it acts on the other member. + This comes from Newton's third law, as this force is internal to the overall system. + Use equations of equilibrium to solve for the unknown forces in the free body diagrams.

+ +

+ This example is adapted from Engineering Statics by Daniel Baker and William Haynes. +

+ Image from PxHere. CC0 +

+ A ladder is a common example of an A-frame. + An A-frame is a basic structure designed to bear loads in a lightweight economical manner. + The simplest form of an A-frame is formed by joining two similarly sized beams at an angle of 45 degrees or less and additionally connecting them with a third horizontal beam, so that the structure looks like that of an uppercase letter "A." +

+

+ Consider the simply supported A-frame shown below, which has a pin support at point a roller support at point and is supporting a horizontal load on the right beam. +

+ +

+ Free body diagrams for each member would like this. +

+ +

+ Take note that if a common force is shared between two free body diagrams, the force will be equal in magnitude, but act in the direction opposite of the direction it acts on the other member—this comes from Newton's third law. + Equilibrium equations can then be written for each member to solve for the unknowns. +

+

+ For this example, we are asked to find the internal force at point on member + Assume the height of the A-frame is and the width of the base is + Assume that point is at the midpoint of member and that point is at the midpoint of member + Assume that the structure is symmetrical. +

+
+

+ First, analyze the free body diagram of the entire system. Take the moment about pin and solve for the reaction force at roller +

+ +

+ Next, analyze the free body diagram for member Take the moment about point on member and solve for the internal force at point +

+ +

+ Since the magnitude of the force was found to be positive, the assumption that the force is in the direction shown on free body diagram of member is correct. +

+

+ Therefore, on member +

+ +

+ Next, Analyze the free body diagram for member Analyze the forces along the x-direction and solve for the internal force + Remember, on member the force acts in the direction opposite of the direction it acts on member +

+ +

+ On member the force acts in the direction opposite of the direction it acts on member +

+

+ Therefore, on member +

+ +
+