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the station being watched, x = 3 unit load, at its worst position 2.100 shaded: where a spread load must stand to make this quantity worst the horizontal axis is where the load is, not where the beam is cut
influence-line3 essays
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 moment ÷ plastic moment axial force ÷ squash load rectangle: 25.0% of Mp outside the line I-section: 6.0% of Mp outside the line the straight-line rule
interaction-nm1 essay
H V 29.4 -38.6 reaction 0.0 reaction 25.0 ΣH = 0 and ΣV = 0, and nothing else is needed
joint-cut9 essays
0 20000 40000 60000 80000 100000 120000 140000 160000 0 0.2 0.4 0.6 0.8 1 joint rotational stiffness, kN·m/rad end moment ÷ wL²/12 6.04% 30% 62.16% rigid boundary semi-rigid fixed ended
joint-effect3 essays
worst secondary bending: 24.3% of the axial stress, in the member marked axial force there 16.7 kN · end moment 0.20 kNm · slenderness of the member 18 the same members, the same loads, the same solver — only the releases differ
joint-rigidity1 essay
flexibility contributed by each component they add, so the softest dominates — Sj = 25227.71 kN·m/rad what doubling it buys column web in shear 21.89% ×1.12 column web in compression 11.55% ×1.06 column flange in bending 39.62% ×1.25 end plate in bending 18.09% ×1.1 bolts in tension 8.85% ×1.05
joint-springs6 essays
resultant 24.0 at x = 5.33, the centroid of the area moment spread: 24.6 replaced: 42.7 reactions agree exactly (8.00 and 8.00); the peak moment does not
load-resultant1 essay
2000 4000 6000 8000 10000 12000 0 200 400 600 800 1000 distance between lateral restraints they cross at 3803 the plastic capacity of the section elastic critical moment St Venant torsion alone — what is left at long lengths warping dominates here
ltb-curve2 essays
pivot the same force of 20, moved along the lever moment about the pivot 1 20 × 1 = 20 2 20 × 2 = 40 3 20 × 3 = 60 4 20 × 4 = 80 5 20 × 5 = 100
moment-arm2 essays
0 2 4 6 8 10 12 0 0.5 1 1.5 curvature ÷ curvature at first yield moment ÷ moment at first yield rectangle: 1.50× the yield moment, at 4.3× the yield curvature I-section: 1.09× the yield moment, at 1.2× the yield curvature
moment-curvature5 essays
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0 50 100 150 200 rotation, radians moment, kN·m rigid above pinned below web cleats — pinned flush end plate — semi-rigid extended end plate — semi-rigid
moment-rotation4 essays
s = 50 g = 60 net width 166.42 mm of 200 the critical path crosses two holes, with s²/4g = 10.42 mm added back
net-section5 essays
0 0.2 0.4 0.6 0.8 0 2 4 6 8 10 applied load ÷ buckling load 1.3× 1.7× 2.5× 5.0× 10.0× first-order analysis says the answer is always 1× one over one minus the ratio
p-delta5 essays
100 150 200 250 300 0M 10M 20M 30M 40M 50M 60M overall depth 1.0× 2.6× 4.9× 7.9× 13.8× 21.3× same steel, moved apart
parallel-axis5 essays
span ÷ depth = 8 plane sections hold span ÷ depth = 4 plane sections hold span ÷ depth = 2 off by 19% span ÷ depth = 1 off by 31% the assumption is the theory — everything else is arithmetic on top of it
plane-sections2 essays
sagging hinge at 4.69 hinge at the fixed end lowest upper bound: 7.29 every hinge position gives an upper bound on the collapse load assumed position of the sagging hinge coefficient 11.66 Mp ÷ L²
plastic-mechanism2 essays
100 200 300 400 500 600 700 0 200 400 600 plate width (mm) slender beyond 370 mm yield critical stress — inverse square in the width what the plate actually delivers, over its full width
plate-buckling2 essays
20 H 10.0 M 22.2 H 10.0 M 22.2 the two base shears add to the applied 20 — the split came from stiffness, not statics the sway is exaggerated; a real frame at this load moves a fraction of a millimetre
portal-sway3 essays
0 5 10 15 20 25 30 1 1.2 1.4 1.6 flange thickness, mm bolt force ÷ applied force no prying above 26.97 mm flange is a mechanism
prying-curve2 essays
100 kN applied bolt 150.63 kN prying 50.63 kN m = 45 n = 40 flange 20 mm · one-hinge bolt force is 1.51 times the applied load
prying-tee4 essays
20 at 2 δ at B = 93.333 20 at 6 δ at A = 93.334 the shapes have nothing in common and the two readings agree to 1e-14 which is why an influence line can be measured by pushing the structure where it is easy to push
reciprocity2 essays
simply supported statics alone sag 32.0 propped at one end needs stiffness sag 18.0 hog 32.0 built in at both ends needs stiffness sag 10.7 hog 21.3 the load never changes; only what is holding the ends the built-in case peaks at two-thirds of the simple span's moment
redundant-beam9 essays
neutral axis contribution of each strip total I = 79.86 × 10⁶ the outer strips do almost all of the work
second-moment8 essays
flange outstand k = 0.43 18.6 at 235 15.2 at 355 13.3 at 460 quoted: 14ε 1.33× the quoted limit, at every grade web, in bending k = 4 56.8 at 235 46.2 at 355 40.6 at 460 quoted: 42ε 1.35× the quoted limit, at every grade 0 10 20 30 40 50 60 width ÷ thickness
section-class1 essay
the same, laid flat I = 0.06 × 10⁶ 1.0× the first square I = 0.75 × 10⁶ 13.3× the first tall rectangle I = 10.00 × 10⁶ 177.8× the first I-section I = 24.29 × 10⁶ 431.8× the first every section here has an area of 3000 — only the shape differs the bar is the second moment of area, to scale
section-compare13 essays
25.0 the cut — three members, three unknowns 47.06 -52.94 7.72 moments about here kill two of the three solved without touching any of the other 18 members
section-cut1 essay
web centreline shear centre e = 31.7 no twist twists the flange flows are equal, opposite, and separated — which is a couple and nothing about the section's 20.19 × 10⁶ second moment predicts it
shear-centre2 essays