Determine a recommended single size square box section for all members that will

Question

Determine a recommended single size square box section for all members that will most closely satisfy the stress requirements stated below. Use ANSYS APDL.

Assume that:

- The material is ASTM A500 Cold Formed with Grade B. The yield strength is 46 ksi and the Poisson’s ratio, , is 0.35.

- The truss members are pin-jointed and have a uniform cross-sectional area.-

- Assume a factor of safety of 3 based on both yielding in tension and buckling in compression.

- Base final recommendation on the most critical compression member unless allowable tensile stress based on yielding of the material occurs.

A) The deformed + undeformed shape plot for the truss.

B) Determine which node has the largest displacement and report its displacement value.

C) Determine the largest tensile stress in the truss and locate the truss member in which the largest tensile stress occur.

D) Determine the largest compressive stress in the truss and locate the truss member in which the largest compressive stress occur.

E) Determine a recommended single size square box section for all members.

Explanation / Answer

ei = [2 3]; ej = [4 7]; Ai=[0.5 1]; Aj=[1.5 3]; Pe = 7; Le=[4 2]; alpha = pi/3; beta = pi/4; node = [0, 0; Le(1)*cos(pi/2-alpha), Le(1)*sin(pi/2-alpha); Le(1)*cos(pi/2-alpha)+Le(2)*sin(beta),Le(1)*sin(pi/2-alpha)-Le(2)*cos(beta)]; fod=2*length(node); con=[1,2; 2,3]; lm = [1, 2, 3, 4; 3, 4, 5, 6]; elem=size(lm,1); Ke=zeros(fod); Re = zeros(fod,1); deb = [1, 2, 5, 6]; ebcVals = zeros(length(deb),1); %load vector Re = zeros(fod,1); Re(4) = Pe; % Assemble global stiffness matrix Ke=zeros(fod); for i=1:elem lme=lm(i,:); cone=con(i,:); k_local=(1/(6*Le(i)))*(2*ei(i)*Ai(i) + ei(i) * Aj(i) + ej(i) * Ai(i) + 2*ej(i) * Aj(i)) * [1 -1; -1 1] ke=NewPlaneTrussElement(ei(i), ej(i), Ai(i), Aj(i), node(cone,:)) Ke(lme, lme) = Ke(lme, lme) + ke; end Ke Re % Nodal solution and reactions [d, reactions] = NodalSoln(Ke, Re, deb, ebcVals) result=[]; for i=1:elems result = [result; NewPlaneTrussResults(ei(i), ej(i), Ai(i), Aj(i), ... nodes(con(i,:),:), d(lm(i,:)))]; end format short g result

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