. The strength of materials; a text-book for engineers and architects. iZ ID . ^. , WP I WP . •. Area actmg down x x = ^„ -^ v. = >./^ bi) 6 ZO „ WZ2 2 WZ M — V — = 20 Z 10,, WZ2 2 Wl M — - V = 30 Z 15 The resulting diagram then comes as shown shaded inFig. 201. The amount of shifting of the base line for shear will be wz wn w 7W ^TT. —, K -^ Z = ^^ SO that the shears at the ends are - ^ „_ 10 15 J SO 10 3 W and ^ respectively, the shear curve for the fixed beam then coming as shown. 2. Non-central Isolated Load.—The following construc-tiori can be used for this case : Let a b, Fig. 20
. The strength of materials; a text-book for engineers and architects. iZ ID . ^. , WP I WP . •. Area actmg down x x = ^„ -^ v. = >./^ bi) 6 ZO „ WZ2 2 WZ M — V — = 20 Z 10,, WZ2 2 Wl M — - V = 30 Z 15 The resulting diagram then comes as shown shaded inFig. 201. The amount of shifting of the base line for shear will be wz wn w 7W ^TT. —, K -^ Z = ^^ SO that the shears at the ends are - ^ „_ 10 15 J SO 10 3 W and ^ respectively, the shear curve for the fixed beam then coming as shown. 2. Non-central Isolated Load.—The following construc-tiori can be used for this case : Let a b, Fig. 202, representa fixed beam of span Z carrying an isolated load W at a pointp, the distances of which from a and b are a and b draw the free bending moment diagram adb, i. e. set up p D = —, —, and join d to a and B. Project d horizontally to meet the vertical through the support b atE and join e a. FIXED AND CONTINUOUS BEAMS 425 Then pf = Reverse or end bending moment at b = M^;and F D = reverse or end bending moment at A = M,.. Fig. 201.—Fixed Beam with Uniformly Increasing Load. Therefore set up b h = r p and a G^ = f d and join g^ h,the complete bending moment diagram then coming out asshown shaded. This may be done by projecting f horizontallyand drawing d g^ parallel to F a. 420 THE STRENGTH OF MATERIALS Proof.—To prove this construction ^\c must obtain valuesfor the reverse bending moments for this case. Referring toFig. 203, it will be remembered that in fixed beams the con- Jl ./J
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