1. The figure shows Beam Diagrams 23 in the CISC Handbook of Steel Construction. The left end is allowed to move freely in vertical direction, but rotation is prohibited (thus free but guided). (a) write the mathematic formulation (5 marks) (b) Find the deflection of the beam with a detailed derivation (5 marks). 23. BEAM FIXED AT ONE END, FREE BUT GUIDED AT OTHER AT GUIDED END M M "max P Shear Moment 7 S N= 2 max Equivalent Tabular Load R=V.... M max. (at both ends) My A max. (at deflected end) Ax - CONCENTRATED LOAD = 4P - P PI 2 P(1/2-x) P13 12 El P(1-x)² 12 El (/+2x)

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1. The figure shows Beam Diagrams 23 in the CISC Handbook of Steel Construction. The left end is allowed to move freely in vertical direction, but rotation is prohibited (thus free but guided). (a) write the mathematic formulation ( 5 marks) (b) Find the deflection of the beam with a detailed derivation ( 5 marks). 23. BEAM FIXED AT ONE END, FREE BUT GUIDED AT OTHER - CONCENTRATED LOAD AT GUIDED END Equivalent Tabular Load

? 4 P

A = V

= P

M

max. (at both ends)

= \frac{Pl}{2}

M_{x}

.

= P (\frac{1}{2} ? x)

? max

(at deflected end)

= \frac{P I ^{3}}{12 E I}

?

,

= \frac{P ( 1 ? x ) ^{2}}{12 E I} (1 + 2 x)

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