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What is the ILD (Influence Line Diagram) of a three hinged Arch of Span 'L' and rise 'h' due to horizontal thrust 'H'

What is the ILD (Influence Line Diagram) of a three hinged Arch of Span 'L' and rise 'h' due to horizontal thrust 'H' Correct Answer Triangle with its maximum ordinate at center equals to <span class="math-tex">\(\frac{L}{4h}\)</span>

Concept:

For a 3 hinged arch due to horizontal thrust 'H':

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ILD for beam moment in 3 hinged arch:

[ alt="F1 A.M Madhu 09.07.20 D14" src="//storage.googleapis.com/tb-img/production/20/07/F1_A.M_Madhu_09.07.20_D14.png" style="width: 192px; height: 175px;">

Bending moment in an arch is due to the combined action of beam moment & moment due to horizontal thrust. ILD for BM:

[ alt="F1 A.M Madhu 09.07.20 D15" src="//storage.googleapis.com/tb-img/production/20/07/F1_A.M_Madhu_09.07.20_D15.png" style="width: 335px; height: 299px;">

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