Recently, George Beck introduced two partition statistics $NT(r,m,n)$ and $M_{\omega}(r,m,n)$, which count the total number of parts in partitions of $n$ with rank congruent to $r$ modulo $m$ and the total number of ones in partitions of $n$ with crank congruent to $r$ modulo $m$, respectively. Very recently,Chern discovered a number of Andrews-Beck type congruences on $NT(r,m,n)$ and $M_{\omega}(r,m,n)$ and some of them were conjectured by Chan, Mao and Osburn. Inspired by Chern's work, we use some congruences given by Atkin and Garvan to prove many new Andrews-Beck type congruences modulo 23,41 and 43