mod_jk produces Error smh errno=13

The correct answer is online:

http://www.laliluna.de/articles/2008/09/14/apache_tomcat_mod_jk_selinux.html

The part you need is near the bottom, which I will copy and paste here in case that page goes away:

# mkdir /var/run/mod_jk
# semanage fcontext -a -t httpd_var_run_t "/var/run/mod_jk(/.*)?"

This apparently configures SELinux to allow mod_jk to work. It worked for me anyway.

Your OS might prevent access to the shared memory file. Try adding

# Set this to a location allowed to the 'Apache' user 
JkShmFile     /var/log/httpd/mod_jk.shm

in your mode-jk.conf (I am using the filename spelling from your post but it might be mod_jk.conf or similar)

Are you using selinux? If you are, you might want to check on it being an selinux context problem.