Maximum spanning capacity of a catenary arch under self-weight against buckling

Figures & data

Figure 1. Catenary arch under its own weight and coordinates system.

Figure 2. HBM for buckling analysis of catenary arch (a) original undeformed state and (b) buckled state.

Figure 3. Rotational angle ϕ_i of i-th segment in buckled state.

Figure 4. Variation of critical buckling load parameters ${\lambda }_{\mathit{cr}}=q_{\mathit{cr}}{L}^3/\left(\mathit{EI}\right)$ with respect to number of arch segments for a pinned supported and fixed supported arch with h/L = 0.3.

Figure 5. Variations of ${\lambda }_{\mathit{cr}}$ with respect to $\mathit{h}/\mathit{L}$ for fixed supports, elastic rotationally retrained supports and pinned supports.

Figure 6. Optimal shapes of catenary arches for maximum self-buckling load and their buckled mode shapes for (a) fixed supports, (b) pinned supports.

Figure 7. Variations of ${\lambda }_{\mathit{cr}}$ with respect to $\mathit{h}/\mathit{L}$ for elastic rotationally retrained supports with various $\bar{K}$ and crown hinge.

Figure 8. Optimal shapes of catenary arches with a crown hinge for maximum self-buckling load and their buckled mode shapes for (a) fixed supports, (b) pinned supports.

Table 1. $\mathrm{Optimal}\mathrm{values}\mathrm{of}{\lambda }_{\mathit{max}}=\frac{{\mathit{q}}_{\mathit{max}}{L}^3}{\mathit{EI}}$, $\frac{{\mathit{h}}_{\mathit{opt}}}{\mathit{L}},$ $\frac{{\mathit{l}}_{\mathit{opt}}}{\mathit{L}}\mathrm{and}{L}_{\mathit{max}}\sqrt[3]{\frac{\mathit{q}}{\mathit{EI}}}$ for catenary arches with various support and crown conditions.

	${\lambda }_{\mathit{max}}=\frac{{\mathit{q}}_{\mathit{max}}{L}^3}{\mathit{EI}}$	$\frac{{\mathit{h}}_{\mathit{opt}}}{\mathit{L}}$	$\frac{{\mathit{l}}_{\mathit{opt}}}{\mathit{L}}$	$\mathrm{Maximum}\mathrm{span}$ $\mathrm{length}{\hat{L}}_{\mathit{max}}$
$\bar{K}=\mathrm{\infty }$ (i.e. fixed supports)	107.478	0.285	1.191	4.755
$\bar{K}=100$	103.591	0.288	1.195	4.697
$\bar{K}=10$	79.803	0.282	1.188	4.305
$\bar{K}=0$ (i.e. pinned supports)	44.840	0.243	1.144	3.553
$\bar{K}=\mathrm{\infty }$	71.974	0.367	1.297	4.160
$\bar{K}=100$	69.908	0.372	1.305	4.120
$\bar{K}=10$	58.874	0.367	1.298	3.890
$\bar{K}=0$	43.427	0.292	1.200	3.515